Scientific Output

Over 10.000 scientific papers have been published by members of the Materials Chain since the foundation of the University Alliance Ruhr in 2010. This tremendous output is proof of the excellent environment the Ruhr Area provides for research in the field of materials science and technology.

Below, you can either scroll through the complete list of our annually published material, or search for a specific author or term via the free text search to get to know our research strengths. You can also review the publication record of every Materials Chain member via his or her personal member’s page.

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• 2024 • 408	A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods Balzani, Daniel and Heinlein, Alexander and Klawonn, Axel and Knepper, Jascha and Nurani Ramesh, Sharan and Rheinbach, Oliver and Saßmannshausen, Lea and Uhlmann, Klemens GAMM Mitteilungen (2024) A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed. © 2024 The Authors. GAMM - Mitteilungen published by Wiley-VCH GmbH.
  	view abstract	doi: 10.1002/gamm.202370002

• 2023 • 407	Elucidation of alkaline electrolyte-surface interaction in SECCM using a pH-independent redox probe Varhade, Swapnil and Meloni, Gabriel and Tetteh, Emmanuel Batsa and Kim, Monjoo and Schumacher, Simon and Quast, Thomas and Andronescu, Corina and Unwin, Patrick and Schuhmann, Wolfgang Electrochimica Acta 460 (2023) Scanning electrochemical cell microscopy (SECCM) has been used to elucidate the interaction between aqueous alkaline electrolyte and a glassy carbon electrode surface using a free-diffusing Os complex, Os(2,2’-bipyridine)2(N,N’-dimethyl-2,2 ́-biimidazole), as a pH-independent redox probe (Os3+/Os2+). The voltammetric response of the complex showed a significant component of surface-confined behavior, rather than the expected purely sigmoidal nanoelectrode voltammogram. To elucidate and understand the response, we complemented the SECCM experiments with numerical simulations to investigate the impact of the droplet geometry and size on the voltammetric signature. Comparison of experimental and simulated voltammograms reveals a surprisingly large wetted area over the glassy carbon substrate, as confirmed by scanning electron microscopy of droplet residues. By investigating different tip sizes, tip approach rates and pH values, we elucidated the key factors controlling the wetting behavior. Simulations further indicated that the analysis of the peak to limiting current and charge passed provides a route to elucidating the extent of wetting in-situ, although quantitative analysis requires further understanding of evaporation and convective flow. In general, knowledge about droplet geometry and size through this study provides an improved understanding of droplet-surface interactions which is essential for a quantitative interpretation of SECCM measurements. © 2023
  	view abstract	doi: 10.1016/j.electacta.2023.142548

• 2023 • 406	Numerical simulation of materials-oriented ultra-precision diamond cutting: review and outlook Zhao, Liang and Zhang, Junjie and Zhang, Jianguo and Dai, Houfu and Hartmaier, Alexander and Sun, Tao International Journal of Extreme Manufacturing 5 (2023) Ultra-precision diamond cutting is a promising machining technique for realizing ultra-smooth surface of different kinds of materials. While fundamental understanding of the impact of workpiece material properties on cutting mechanisms is crucial for promoting the capability of the machining technique, numerical simulation methods at different length and time scales act as important supplements to experimental investigations. In this work, we present a compact review on recent advancements in the numerical simulations of material-oriented diamond cutting, in which representative machining phenomena are systematically summarized and discussed by multiscale simulations such as molecular dynamics simulation and finite element simulation: the anisotropy cutting behavior of polycrystalline material, the thermo-mechanical coupling tool-chip friction states, the synergetic cutting responses of individual phase in composite materials, and the impact of various external energetic fields on cutting processes. In particular, the novel physics-based numerical models, which involve the high precision constitutive law associated with heterogeneous deformation behavior, the thermo-mechanical coupling algorithm associated with tool-chip friction, the configurations of individual phases in line with real microstructural characteristics of composite materials, and the integration of external energetic fields into cutting models, are highlighted. Finally, insights into the future development of advanced numerical simulation techniques for diamond cutting of advanced structured materials are also provided. The aspects reported in this review present guidelines for the numerical simulations of ultra-precision mechanical machining responses for a variety of materials. © 2023 The Author(s). Published by IOP Publishing Ltd on behalf of the IMMT.
  	view abstract	doi: 10.1088/2631-7990/acbb42

• 2023 • 405	Simulation of local metastable microstructural states in large tools: construction and validation of the model Schuppener, Jannik and Berger, Aaron and Benito, Santiago and Weber, Sebastian International Journal of Advanced Manufacturing Technology 128 4235 – 4252 (2023) This study presents the development and experimental verification of a simulation model for estimating the local microstructure of a tool geometry after heat treatment. The experiment involved subjecting a metallic block of dimensions 40 × 50 × 50 mm, made of the ledeburitic cold work steel DIN EN 1.2379 (X153CrMoV12; AISI D2), to a heat treatment in a laboratory furnace at 1000 °C for 20 min. Thermocouples were strategically placed to record time-temperature profiles at different locations within the block. Following the heat treatment, the local microstructure was determined through quantitative image analysis, and the local hardness was measured as a function of the distance from the block’s edge to its core. These measurements were then correlated with the corresponding time-temperature curves obtained from the thermocouples. To replicate the local time-temperature profiles, the thermophysical properties of the steel were experimentally determined and incorporated into a finite element analysis heat transfer simulation using Abaqus FEA® software. This simulation approach, combined with the MatCalc software, facilitated the calculation of various local microstructural characteristics such as carbide content, carbide type, carbide distribution, and chemical composition of the matrix. Furthermore, the content fractions of the microconstituents of the matrix, including martensite and retained austenite, were determined based on the simulated martensite start temperature, employing an optimized function fitted to experimental data. The developed simulation model offers potential applications in two important areas. Firstly, it can be used to adapt heat treatment processes for tools of different sizes in production, optimizing their mechanical properties. Secondly, it enables efficient optimization of heat treatment routes by considering changing initial states, leading to high process quality in terms of mechanical properties. Overall, this study provides valuable insights into the estimation and control of local microstructure in tool geometries through the use of a validated simulation model. © 2023, The Author(s).
  	view abstract	doi: 10.1007/s00170-023-12195-2

• 2023 • 404	Surrogate modeling for interactive tunnel track design using the cut finite element method Bui, Hoang-Giang and Cao, Ba-Trung and Freitag, Steffen and Hackl, Klaus and Meschke, Günther Engineering with Computers 39 4025 – 4043 (2023) The Cut Finite Element Method (CutFEM) is recently shown to be a versatile approach for tunnel construction modeling and settlement analysis. The CutFEM can significantly simplify the computational workflow by facilitating the discretization and coupling of different components in structural analysis, while maintaining the same accuracy as the standard boundary-fitted method. In this work, three surrogate models based on the Proper Orthogonal Decomposition and Radial Basis Functions (POD-RBF), Artificial Neural Networks (ANN) and Gradient Boosting (GBoost) are proposed and compared for tunnel alignment design. The flexibility of generating multiple designs quickly and conveniently using CutFEM, to provide snapshot data for surrogate model construction, is exploited. As an illustration of the concept, the surrogate model resulting from the linear analysis, involving linear elastic material with compatible parameters, is presented. This approach can be extended to the analysis including a city model, which leads to efficient damage assessment analysis on the existing infrastructure. The resulting surrogate model is used for tunnel track design, where the settlement field can be determined quickly in seconds , which allows real-time applications. The surrogate model is integrated into an interactive platform, named as TunAID, that can be used for real-time design of the tunnel alignment in urban area. © 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
  	view abstract	doi: 10.1007/s00366-023-01867-y

• 2022 • 403	3D modeling of generalized Newtonian fluid flow with data assimilation using the least-squares finite element method Averweg, S. and Schwarz, A. and Schwarz, C. and Schröder, J. Computer Methods in Applied Mechanics and Engineering 392 (2022) In this contribution we present a least-squares finite element formulation to model steady-state flow of incompressible, non-Newtonian fluids in three dimensions including data assimilation. The approach is based on the incompressible Navier–Stokes equations and the nonlinear viscosity is considered by means of the Carreau–Yasuda viscosity model, which can account for shear-thickening and shear-thinning behavior of generalized Newtonian fluids. We outline the procedure how to integrate given data into the numerical solution of flow problems without additional computational cost using the least-squares FEM. Assimilation of experimental data provides the opportunity to reduce model errors resulting in a solution which more closely approximates reality. Furthermore, the preprocessing of the available data using Kriging interpolation is also described briefly. The presented formulation is first validated by investigating the flow in a cube with an exact solution without data assimilation. Convergence is evaluated based on the error in velocities and pressure compared to the exact solution. Then the effect of data assimilation is shown by modeling blood flow through a carotid bifurcation model and integrating data either along lines or over entire cross-sectional areas. The improvement of the numerical solution by means of data assimilation is revealed by comparing the calculated velocity profiles with experimental and numerical reference values. © 2022
  	view abstract	doi: 10.1016/j.cma.2022.114668

• 2022 • 402	A CutFEM based framework for numerical simulations of machine driven tunnels with arbitrary alignments Bui, H.-G. and Schillinger, D. and Zendaki, Y. and Meschke, G. Computers and Geotechnics 144 (2022) We describe a novel computational framework based on the cut finite element method (CutFEM) for process-oriented simulation in mechanized tunneling. The framework incorporates all relevant components required for the simulation of the tunnel advance process, namely the ground, the staged installation of the lining support, the tail void grouting and the tunnel boring machine. We demonstrate that CutFEM concepts can significantly facilitate the modeling, discretization and coupling of the different components, while maintaining the same accuracy as the standard boundary-fitted finite element method. The proposed CutFEM technology, which is being applied and investigated in the context of advancement simulations in mechanized tunneling for the first time, enables the seamless analysis of an arbitrary number of different tunnel alignment variants on the same structured background mesh without the need to set up a new model for each variant. This is a shift of paradigm in simulation-supported tunnel design, as the CutFEM based framework considerably facilitates a direct integration of geometric, building information and simulation models in early stages of a tunnel project. The simulation model allows for the damage assessment of the buildings during tunnel advancement with regards to different excavation scenarios, as shown in the numerical examples in this paper. © 2022 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compgeo.2022.104637

• 2022 • 401	A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method Biswas, A. and Kalidindi, S.R. and Hartmaier, A. Modelling and Simulation in Materials Science and Engineering 30 (2022) Direct experimental evaluation of the anisotropic yield locus (YL) of a given material, representing the zeros of the material's yield function in the stress space, is arduous. It is much more practical to determine the YL by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted YL estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal YL for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire YL and also experiments. In the second step, the point cloud data of stress tensors on the YL predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced YL from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis. © 2022 The Author(s). Published by IOP Publishing Ltd.
  	view abstract	doi: 10.1088/1361-651X/ac4a24

• 2022 • 400	A methodology to integrate process-induced subsurface characteristics into a digital twin-based framework for the evaluation of machining processes Bergmann, J.A. and Wöste, F. and Wiederkehr, P. Procedia CIRP 107 125-130 (2022) The consideration of process-induced subsurface characteristics as an essential quality parameter of manufactured components is of primary relevance. An established means for the prediction of these characteristics such as residual stress, hardness or phase transformations is the use of finite element analysis, which can be used to model changes in the material for defined process configurations and engagement scenarios. However, due to high simulation times and in many cases limited model sizes, only selected scenarios can be evaluated. Process simulation systems which model the cutting process using empirical models and geometric representations of the tool and workpiece to predict the process forces and, e. g., deflections, offer the possibility to simulate entire machining processes efficiently. In this contribution, a methodology is presented to integrate process-induced alterations of the subsurface during milling into the workpiece model of a process simulation system. For the evaluation of these alterations, finite element analyses can be used for representative engagement and process scenarios, which have to be selected a priori based on each process. By extending the digital-twin of the workpiece with this information, the influence of complex machining operations with time-variant engagement conditions can be evaluated continuously. As a result, the presented framework thus provides a basis for predicting the resulting quality of the manufactured component with respect to subsurface characteristics. © 2022 The Authors. Published by Elsevier B.V.
  	view abstract	doi: 10.1016/j.procir.2022.04.021

• 2022 • 399	A restricted additive Vanka smoother for geometric multigrid Saberi, S. and Meschke, G. and Vogel, A. Journal of Computational Physics 459 (2022) The solution of saddle-point problems, such as the Stokes equations, is a challenging task, especially in large-scale problems. Multigrid methods are one of the most efficient solvers for such systems of equations and can achieve convergence rates independent of the problem size. The smoother is a crucial component of multigrid methods and significantly affects its overall efficiency. We propose a Vanka-type smoother that we refer to as Restricted Additive Vanka and investigate its convergence in the context of adaptive geometric multigrid methods for the Stokes equations. The proposed smoother has the advantage of being an additive method and provides favorable properties in terms of algorithmic complexity, scalability and applicability to high-performance computing. We compare the performance of the smoother with two variants of the classical Vanka smoother using numerical benchmarks for the Stokes problem. We find that the restricted additive smoother achieves comparable convergence rates to the classical multiplicative Vanka smoother while being computationally less expensive per iteration, which results in faster solution runtimes. © 2022 Elsevier Inc.
  	view abstract	doi: 10.1016/j.jcp.2022.111123

• 2022 • 398	An Assessment of Solvers for Algebraically Stabilized Discretizations of Convection-Diffusion-Reaction Equations Jha, A. and Pártl, O. and Ahmed, N. and Kuzmin, D. Journal of Numerical Mathematics (2022) We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include flux-corrected transport schemes and monolithic limiters. We discretize in space using a continuous Galerkin method and P1 or Q1 finite elements. Time integration is performed using the Crank-Nicolson method or an explicit strong stability preserving Runge-Kutta method. Nonlinear systems are solved using a fixed-point iteration method, which requires solution of large linear systems at each iteration or time step. The great variety of options in the choice of discretization methods and solver components calls for a dedicated comparative study of existing approaches. To perform such a study, we define new 3D test problems for time dependent and stationary convection-diffusion-reaction equations. The results of our numerical experiments illustrate how the limiting technique, time discretization and solver impact on the overall performance. © 2022 Walter de Gruyter GmbH, Berlin/Boston 2022.
  	view abstract	doi: 10.1515/jnma-2021-0123

• 2022 • 397	Extrusion process simulation and layer shape prediction during 3D-concrete-printing using the Particle Finite Element Method Reinold, J. and Nerella, V.N. and Mechtcherine, V. and Meschke, G. Automation in Construction 136 (2022) Product quality and processing of additively manufactured concrete components strongly depend on the flow processes during material extrusion. To control layer deformations and enable purposeful design, numerical analyses with varying process and material parameters were performed to obtain a deeper understanding of flow processes and forces developing in the vicinity of the nozzle using the Lagrangian-based Particle Finite Element Method in association with a Bingham constitutive model. This model was validated by comparing the simulated layer geometries with those obtained from laboratory 3D-printing experiments. Within the investigated parameter range, the forces generated under the extrusion nozzle can be 6 times higher than those induced by self-weight and may cause deformations in substrate layers. Since the distribution of extrusion forces may change substantially under the nozzle for varying parameters, a novel indicator based on the yielding material is introduced to find optimal 3D-printing parameters to prevent plastic deformations in substrate layers. © 2022 Elsevier B.V.
  	view abstract	doi: 10.1016/j.autcon.2022.104173

• 2022 • 396	Hybrid Mixed Finite Element Formulations Based on a Least-Squares Approach Igelbüscher, M. and Schröder, J. Lecture Notes in Applied and Computational Mechanics 98 169-189 (2022) In this contribution we focus on the relaxation of continuity conditions and the enforcement of these continuity constraints for the considered fields via Lagrange multipliers. Therefore, a stress-displacement least-squares formulation F(σ, u) is considered, which is defined by the squared L2(B) -norm applied to the first-order system of differential equations, given by the balance of momentum and the constitutive equation as well as an additional (mathematically redundant) residual for the enforcement of the moment of momentum. In general the continuity conditions are enforced by the conforming discretization of the individual fields. The conforming discretization, which demands continuity of the displacements and normal continuity of the stresses, is given by polynomial functions of Lagrange type for the displacements, i.e. uh∈ H1(B), and a stress approximation e.g. with Raviart–Thomas functions, i.e. σh∈ H(div, B). A non-conforming discretization of the stresses and displacements considering discontinuous Raviart–Thomas and discontinuous Lagrange approximation functions with σh∈ d RTm and uh∈ d Pk yield a relaxation of the continuity conditions. However the fulfillment of these relaxed constraints is enforced by the introduction of Lagrange multipliers. Additionally, a continuous as well as a discontinuous stress approximation with σh∈ H1(B) and σh∈ L2(B) is considered. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
  	view abstract	doi: 10.1007/978-3-030-92672-4_7

• 2022 • 395	Lagrange and H(curl , B) based finite element formulations for the relaxed micromorphic model Schröder, J. and Sarhil, M. and Scheunemann, L. and Neff, P. Computational Mechanics 70 1309-1333 (2022) Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model has shown many advantages in this field. In this contribution, we present significant aspects related to the relaxed micromorphic model realization with the finite element method (FEM). The variational problem is derived and different FEM-formulations for the two-dimensional case are presented. These are a nodal standard formulation H1(B) × H1(B) and a nodal-edge formulation H1(B) × H(curl , B) , where the latter employs the Nédélec space. In this framework, the implementation of higher-order Nédélec elements is not trivial and requires some technicalities which are demonstrated. We discuss the computational convergence behavior of Lagrange-type and tangential-conforming finite element discretizations. Moreover, we analyze the characteristic length effect on the different components of the model and reveal how the size-effect property is captured via this characteristic length parameter. © 2022, The Author(s).
  	view abstract	doi: 10.1007/s00466-022-02198-3

• 2022 • 394	Least-Squares Finite Element Formulation for Finite Strain Elasto-Plasticity Igelbüscher, M. and Schröder, J. and Schwarz, A. and Starke, G. Lecture Notes in Applied and Computational Mechanics 98 149-167 (2022) This work presents a mixed least-squares finite element formulation for rate-independent elasto-plasticity at finite strains. In this context, the stress-displacement formulation is defined by the L2(B) -norm minimization of a first-order system of differential equations written in residual form. The utilization of the least-squares method (LSM) provides some well-known advantages. For the proposed rate-independent elasto-plastic material law a straight forward application of the LSM leads to discontinuities within the first variation of the formulation, based on the non-smoothness of the constitutive relation. Therefore, a modification by means of a modified first variation is necessary to guarantee a continuous weak form, which is done in terms of the considered test spaces. In addition to that an antisymmetric displacement gradient in the test space is added to the formulation due to a not a priori fulfillment of the stress symmetry condition, which results from the stress approximation with Raviart-Thomas functions. The resulting formulation is validated by a numerical test and compared to a standard displacement finite element formulation. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
  	view abstract	doi: 10.1007/978-3-030-92672-4_6

• 2022 • 393	Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems Kuzmin, D. and Hajduk, H. and Rupp, A. Computer Methods in Applied Mechanics and Engineering 389 (2022) The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. The desired properties are enforced by applying a limiter to antidiffusive fluxes that represent the difference between the high-order baseline scheme and a property-preserving approximation of Lax–Friedrichs type. In the first step of the limiting procedure, the given target fluxes are adjusted in a way that guarantees preservation of local and/or global bounds. In the second step, additional limiting is performed, if necessary, to ensure the validity of fully discrete and/or semi-discrete entropy inequalities. The limiter-based entropy fixes considered in this work are applicable to finite element discretizations of scalar hyperbolic equations and systems alike. The underlying inequality constraints are formulated using Tadmor's entropy stability theory. The proposed limiters impose entropy-conservative or entropy-dissipative bounds on the rate of entropy production by antidiffusive fluxes and Runge–Kutta (RK) time discretizations. Two versions of the fully discrete entropy fix are developed for this purpose. The first one incorporates temporal entropy production into the flux constraints, which makes them more restrictive and dependent on the time step. The second algorithm interprets the final stage of a high-order AFC-RK method as a constrained antidiffusive correction of an implicit low-order scheme (algebraic Lax–Friedrichs in space + backward Euler in time). In this case, iterative flux correction is required, but the inequality constraints are less restrictive and limiting can be performed using algorithms developed for the semi-discrete problem. To motivate the use of limiter-based entropy fixes, we prove a finite element version of the Lax–Wendroff theorem and perform numerical studies for standard test problems. In our numerical experiments, entropy-dissipative schemes converge to correct weak solutions of scalar conservation laws, of the Euler equations, and of the shallow water equations. © 2021 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2021.114428

• 2022 • 392	Numerical Approaches for Investigating Quasiconvexity in the Context of Morrey’s Conjecture Voss, J. and Martin, R.J. and Sander, O. and Kumar, S. and Kochmann, D.M. and Neff, P. Journal of Nonlinear Science 32 (2022) Deciding whether a given function is quasiconvex is generally a difficult task. Here, we discuss a number of numerical approaches that can be used in the search for a counterexample to the quasiconvexity of a given function W. We will demonstrate these methods using the planar isotropic rank-one convex function Wmagic+(F)=λmaxλmin-logλmaxλmin+logdetF=λmaxλmin+2logλmin,where λmax≥ λmin are the singular values of F, as our main example. In a previous contribution, we have shown that quasiconvexity of this function would imply quasiconvexity for all rank-one convex isotropic planar energies W: GL +(2) → R with an additive volumetric-isochoric split of the form W(F)=Wiso(F)+Wvol(detF)=W~iso(FdetF)+Wvol(detF)with a concave volumetric part. This example is therefore of particular interest with regard to Morrey’s open question whether or not rank-one convexity implies quasiconvexity in the planar case. © 2022, The Author(s).
  	view abstract	doi: 10.1007/s00332-022-09820-x

• 2022 • 391	Optimization of high performance aerogel concrete [Hochleistungsaerogelbeton – Optimierung, Tragverhalten, Festigkeit] Fickler, S. and Heidrich, T. and Welsch, T. and Schnellenbach-Held, M. Beton- und Stahlbetonbau 117 498-509 (2022) Optimization of High Performance Aerogel Concrete. The development of a new type of high-performance lightweight concrete based on silica aerogels, the so-called high-performance aerogel concrete (HPAC), was reported in [1]. In addition to excellent fire and acoustic protection properties, HPAC shows a very favorable relationship between compressive strength and thermal conductivity and is therefore suitable to produce monolithic exterior walls without additional thermal insulation. In order to expand the possible applications of the new material in construction practice, it has been continuously developed at the Institute for Structural Concrete at the University of Duisburg-Essen since its presentation in 2016. This affects, on the one hand, the optimization of the material with regard to its shrinkage behavior and, on the other hand, the investigation of the load bearing behaviour and the statistical evaluation of the compressive strength. While the first aspect is particularly relevant for the production of reinforced HPAC components, the statistical investigations provide the basis for Finite Element Simulations and the determination of the characteristic strengths. The results of these investigations are reported subsequently. © 2022, Ernst und Sohn. All rights reserved.
  	view abstract	doi: 10.1002/best.202200037

• 2022 • 390	Primal and mixed finite element formulations for the relaxed micromorphic model Sky, A. and Neunteufel, M. and Muench, I. and Schöberl, J. and Neff, P. Computer Methods in Applied Mechanics and Engineering 399 (2022) The classical Cauchy continuum theory is suitable to model highly homogeneous materials. However, many materials, such as porous media or metamaterials, exhibit a pronounced microstructure. As a result, the classical continuum theory cannot capture their mechanical behaviour without fully resolving the underlying microstructure. In terms of finite element computations, this can be done by modelling the entire body, including every interior cell. The relaxed micromorphic continuum offers an alternative method by instead enriching the kinematics of the mathematical model. The theory introduces a microdistortion field, encompassing nine extra degrees of freedom for each material point. The corresponding elastic energy functional contains the gradient of the displacement field, the microdistortion field and its Curl (the micro-dislocation). Therefore, the natural spaces of the fields are [H1]3 for the displacement and [H(curl)]3 for the microdistortion, leading to unusual finite element formulations. In this work we describe the construction of appropriate finite elements using Nédélec and Raviart–Thomas subspaces, encompassing solutions to the orientation problem and the discrete consistent coupling condition. Further, we explore the numerical behaviour of the relaxed micromorphic model for both a primal and a mixed formulation. The focus of our benchmarks lies in the influence of the characteristic length Lc and the correlation to the classical Cauchy continuum theory. © 2022 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2022.115298

• 2022 • 389	Thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method Iqbal, M.D. and Birk, C. and Ooi, E.T. and Pramod, A.L.N. and Natarajan, S. and Gravenkamp, H. and Song, C. Engineering Fracture Mechanics 264 (2022) The scaled boundary finite element method is extended to model fracture in functionally graded materials (FGM) under coupled thermo-mechanical loads. The governing equations of coupled thermo-mechanical equilibrium are discretized using scaled boundary shape functions enriched with the thermal load terms. The material gradient is modeled as a series of power functions, and the stiffness matrix is calculated semi-analytically. Stress intensity factors and T−stress are directly calculated from their definition without any need for additional post-processing techniques. Arbitrary-sided polygon elements are employed for flexible mesh generation. Several numerical examples for isotropic and orthotropic FGMs are presented to validate the proposed technique. © 2022 Elsevier Ltd
  	view abstract	doi: 10.1016/j.engfracmech.2022.108305

• 2022 • 388	Very fast finite element Poisson solvers on lower precision accelerator hardware: A proof of concept study for Nvidia Tesla V100 Ruda, D. and Turek, S. and Ribbrock, D. and Zajac, P. International Journal of High Performance Computing Applications 36 459-474 (2022) Recently, accelerator hardware in the form of graphics cards including Tensor Cores, specialized for AI, has significantly gained importance in the domain of high-performance computing. For example, NVIDIA’s Tesla V100 promises a computing power of up to 125 TFLOP/s achieved by Tensor Cores, but only if half precision floating point format is used. We describe the difficulties and discrepancy between theoretical and actual computing power if one seeks to use such hardware for numerical simulations, that is, solving partial differential equations with a matrix-based finite element method, with numerical examples. If certain requirements, namely low condition numbers and many dense matrix operations, are met, the indicated high performance can be reached without an excessive loss of accuracy. A new method to solve linear systems arising from Poisson’s equation in 2D that meets these requirements, based on “prehandling” by means of hier-archical finite elements and an additional Schur complement approach, is presented and analyzed. We provide numerical results illustrating the computational performance of this method and compare it to a commonly used (geometric) multigrid solver on standard hardware. It turns out that we can exploit nearly the full computational power of Tensor Cores and achieve a significant speed-up compared to the standard methodology without losing accuracy. © The Author(s) 2022.
  	view abstract	doi: 10.1177/10943420221084657

• 2021 • 387	A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness Witt, C. and Kaiser, T. and Menzel, A. Journal of Engineering Mathematics 128 (2021) It is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material. © 2021, The Author(s).
  	view abstract	doi: 10.1007/s10665-021-10117-3

• 2021 • 386	A finite element implementation of the stress gradient theory Kaiser, T. and Forest, S. and Menzel, A. Meccanica 56 1109-1128 (2021) In this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions. © 2021, The Author(s).
  	view abstract	doi: 10.1007/s11012-020-01266-3

• 2021 • 385	A hysteresis model for the unfrozen liquid content in freezing porous media Saberi, P.S. and Meschke, G. Computers and Geotechnics 134 (2021) The description of the freezing characteristics of porous media is one of the most conspicuous ingredients in flow and heat transport models that involve freezing and thawing processes. Unfrozen liquid content (ULC) shows strong hysteresis during freezing and thawing cycles in different types of soils and other porous media. We discuss the possible mechanisms of hysteresis in porous media and develop a numerical model for the unfrozen liquid content that is capable of describing the hysteresis phenomenon in freezing and thawing cycles. We present a coupled finite element model as the framework for the numerical simulation of fluid flow and heat transport in partially frozen porous media. The implementation aspects of the ULC model as well as its integration into numerical codes are discussed in detail. We investigate the potential impact of the hysteresis phenomenon on the numerical simulation of transport processes in porous media through benchmark examples and validate the behavior of the model against available laboratory measurement data. © 2021
  	view abstract	doi: 10.1016/j.compgeo.2021.104048

• 2021 • 384	A mixed u–p edge-based smoothed particle finite element formulation for viscous flow simulations Reinold, J. and Meschke, G. Computational Mechanics (2021) A mixed u–p edge-based smoothed particle finite element formulation is proposed for computational simulations of viscous flow. In order to improve the accuracy of the standard particle finite element method, edge-based and face-based smoothing operations on the displacement gradient are proposed for 2D and 3D analyses, respectively. Consequently, spatial integration involving the smoothing operator is performed on smoothing domains. The constitutive model is based on an elasto-viscoplastic formulation allowing for simulations of viscous fluid or fluid-like solid materials. The viscous response is modeled using an overstress function. The performance of the proposed edge-based smoothed particle finite element method (ES-PFEM) is demonstrated by several numerical benchmark studies, showing an excellent agreement with analytical and reference solutions and an improved accuracy and computational efficiency in comparison with results from the standard PFEM model. Finally, a numerical application of the ES-PFEM to the computational simulation of the extrusion process during 3D-concrete-printing is discussed. © 2021, The Author(s).
  	view abstract	doi: 10.1007/s00466-021-02119-w

• 2021 • 383	A numerical investigation on the effects of porosity on the plastic anisotropy of additive manufactured stainless steel with various crystallographic textures Wu, J. and Liu, W. and Vajragupta, N. and Hartmaier, A. and Lian, J. ESAFORM 2021 - 24th International Conference on Material Forming (2021) For additive manufacturing materials, different process parameters might cause non-negligible microstructural defects. Due to the deficient or surplus energy input during the process, porosity would result in significantly different mechanical responses. In addition, the heterogeneity of the microstructure of additive manufactured material could increase the anisotropic behavior in both deformation and failure stages. The aim of this study is to perform a numerical investigation of the anisotropic plasticity affected by the microstructural features, in particular, texture and porosity. The coupling of the synthetic microstructure model and the crystal plasticity method is employed to consider the microstructural features and to predict the mechanical response at the macroscopic level, including both flow curve and r-value evolution. The additive manufactured 316L stainless steel is chosen as the reference steel in this study. Porosity decreases the stress of material, however, it reduces the anisotropy of material with both two types of textures. Regardless of porosity, grains with <111>//BD fiber of reference material is preferable for high strength requirement while the random orientations are favorable for homogeneous deformation in applications. © ESAFORM 2021 - 24th Inter. Conf. on Mat. Forming. All rights reserved.
  	view abstract	doi: 10.25518/esaform21.4308

• 2021 • 382	A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind Meyer, C. and Weymuth, M. Numerical Functional Analysis and Optimization (2021) We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a quadratic growth condition we derive nearly optimal a priori error estimates. Moreover, we establish second order sufficient optimality conditions that ensure a quadratic growth condition. These conditions are rather restrictive, but allow us to construct a one-dimensional locally optimal solution with reduced regularity, which serves as an exact solution for numerical experiments. © 2021 Taylor & Francis Group, LLC.
  	view abstract	doi: 10.1080/01630563.2021.2001750

• 2021 • 381	Analysis on the mechanical response of composite pressure vessels during internal pressure loading: FE modeling and experimental correlation Nebe, M. and Soriano, A. and Braun, C. and Middendorf, P. and Walther, F. Composites Part B: Engineering 212 (2021) Commercial development of gaseous hydrogen storage in fuel cell electric vehicles is inevitably subjected to reliable and cost-effective design of composite pressure vessels. In this context, certainty in the design process is sought, which is determined by how well the vessel's mechanical response is understood, but more importantly to which accuracy the final collapse can be predicted. As such, a symbiosis of numerical and experimental work appears as a leading path towards robust design methodologies, where both analyses complement and scrutinize each others validity. This research presents the analysis on the mechanical response of composite pressure vessels during internal pressure loading through the correlation of numerical and experimental results on various degrees of complexity. Based on an extensive experimental dataset, a three-dimensional FE model is implemented on a realistic vessel geometry, evaluating its constitutively elastic behavior, and its response under failure and damage progression. Likewise, an established experimental framework is used to derive data by means of contour scans, outer surface strains, airborne acoustic emissions and final burst pressure. The precise recreation of the vessel geometry, together with the detailed analysis approach, permits to show a reasonable agreement between the predicted and the measured structural responses, the sequence of damage onset, and the final collapse occurring in the cylindrical region (<1%). Discrepancies still exist because of the remaining uncertainty concerning the individual layer geometry and the characterization of damage in the helical plies. Altogether, through the alignment of experimental and numerical analyses, this work provides the base for further optimization frameworks, in which an adequate representation of the vessel's meridional thickness profile and material properties stands out as necessary feat to accurately reproduce the mechanical response and final strength in a time- and cost-effective design process. © 2020 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compositesb.2020.108550

• 2021 • 380	Boundary and interface conditions in the relaxed micromorphic model: Exploring finite-size metastructures for elastic wave control Rizzi, G. and d’Agostino, M.V. and Neff, P. and Madeo, A. Mathematics and Mechanics of Solids (2021) In this paper, we establish well-posed boundary and interface conditions for the relaxed micromorphic model that are able to unveil the scattering response of fully finite-size metamaterial samples. The resulting relaxed micromorphic boundary value problem is implemented in finite-element simulations describing the scattering of a square metamaterial sample whose side counts nine unit cells. The results are validated against a direct finite-element simulation encoding all the details of the underlying metamaterial’s microstructure. The relaxed micromorphic model can recover the scattering metamaterial’s behavior for a wide range of frequencies and for all possible angles of incidence, thus showing that it is suitable to describe dynamic anisotropy. Finally, thanks to the model’s computational performances, we can design a metastructure combining metamaterials and classical materials in such a way that it acts as a protection device while providing energy focusing in specific collection points. These results open important perspectives for the short-term design of sustainable structures that can control elastic waves and recover energy. © The Author(s) 2021.
  	view abstract	doi: 10.1177/10812865211048923

• 2021 • 379	Depth-sensing ductile and brittle deformation in 3C-SiC under Berkovich nanoindentation Zhao, L. and Zhang, J. and Pfetzing, J. and Alam, M. and Hartmaier, A. Materials and Design 197 (2021) The interplay between ductile and brittle deformation modes in hard brittle materials exhibits a strong size effect. In the present work, indentation depth-dependent deformation mechanisms of single-crystal 3C-SiC under Berkovich nanoindentation are elucidated by finite element simulations and corresponding experiments. A novel finite element framework, that combines a crystal plasticity constitutive model for describing dislocation slip-based ductile deformation and a cohesive zone model for capturing crack initiation and propagation-induced brittle fracture, is established. The utilized parameters in the crystal plasticity model of 3C-SiC are calibrated according to the load-displacement curves obtained from corresponding Berkovich nanoindentation experiments. Subsequent finite element simulations and experiments of nanoindentation jointly reveal co-existing microscopic plastic deformation and brittle fracture of 3C-SiC at different indentation depths, which significantly affect the observed macroscopic mechanical response and surface pile-up topography. In particular, the predicted morphology of surface cracks at an indentation depth of 500 nm agrees well with experimental observation, and the correlation of crack initiation and propagation with surface pile-up topography is theoretically analyzed. © 2020 The Authors
  	view abstract	doi: 10.1016/j.matdes.2020.109223

• 2021 • 378	Development of the scaled boundary finite element method for crack propagation modeling of elastic solids subjected to coupled thermo-mechanical loads Iqbal, M.D. and Birk, C. and Ooi, E.T. and Gravenkamp, H. Computer Methods in Applied Mechanics and Engineering 387 (2021) This study presents the development of the scaled boundary finite element method to model discrete crack propagation induced by thermal loads. The SBFEM excels in modeling stress singularities at sharp crack tips with high accuracy. Polygon meshes are used so that a robust local re-meshing algorithm can be utilized to propagate the crack. The scaled boundary finite element formulation for steady-state thermal stress analysis is presented. Following a scaled boundary finite element analysis of a given thermal problem, the effect of initial strains due to temperature is taken into account semi-analytically in a subsequent stress analysis. Several numerical examples are presented to validate the technique and illustrate its salient features. © 2021
  	view abstract	doi: 10.1016/j.cma.2021.114106

• 2021 • 377	Fully-coupled micro–macro finite element simulations of the Nakajima test using parallel computational homogenization Klawonn, A. and Lanser, M. and Rheinbach, O. and Uran, M. Computational Mechanics 68 1153-1178 (2021) The Nakajima test is a well-known material test from the steel and metal industry to determine the forming limit of sheet metal. It is demonstrated how FE2TI, our highly parallel scalable implementation of the computational homogenization method FE2, can be used for the simulation of the Nakajima test. In this test, a sample sheet geometry is clamped between a blank holder and a die. Then, a hemispherical punch is driven into the specimen until material failure occurs. For the simulation of the Nakajima test, our software package FE2TI has been enhanced with a frictionless contact formulation on the macroscopic level using the penalty method. The appropriate choice of suitable boundary conditions as well as the influence of symmetry assumptions regarding the symmetric test setup are discussed. In order to be able to solve larger macroscopic problems more efficiently, the balancing domain decomposition by constraints (BDDC) approach has been implemented on the macroscopic level as an alternative to a sparse direct solver. To improve the computational efficiency of FE2TI even further, additionally, an adaptive load step approach has been implemented and different extrapolation strategies are compared. Both strategies yield a significant reduction of the overall computing time. Furthermore, a strategy to dynamically increase the penalty parameter is presented which allows to resolve the contact conditions more accurately without increasing the overall computing time too much. Numerically computed forming limit diagrams based on virtual Nakajima tests are presented. © 2021, The Author(s).
  	view abstract	doi: 10.1007/s00466-021-02063-9

• 2021 • 376	Modelling of the friction in the chip formation zone depending on the rake face topography Saelzer, J. and Berger, S. and Iovkov, I. and Zabel, A. and Biermann, D. Wear 477 (2021) In the machining process, both the tool wear and the surface integrity of the machined workpiece are significantly influenced by the friction. For this reason, the reliable prediction of friction behavior is of great importance for simulation-based tool and process design. It is known from previous investigations that the relative speed is a significant factor influencing the friction behavior between metallic materials and cemented carbide. The exact relationship, particularly in relation to the topography of the tool surfaces, is mainly unexplored. In the context of this publication, results from a friction characterization under machining-similar conditions for AISI 1045 and differently prepared cemented carbide surfaces are presented. The focus of the paper is to develop models for the friction coefficient, based on these results, which take the relative speed and the surface topography into account. Within a Finite-Element chip formation simulation, these models are compared to conventional models that assume the friction coefficient to be constant. For the validation of the simulations, results are used, which were determined from orthogonal cutting tests with differently prepared rake faces. Within the scope of these cutting tests, knowledge was gained about the influence of the rake face topography and the cutting parameters on the friction in the secondary shear zone. © 2021 Elsevier B.V.
  	view abstract	doi: 10.1016/j.wear.2021.203802

• 2021 • 375	On the simultaneous use of simple geometrically exact shear-rigid rod and shell finite elements Costa e Silva, C. and Maassen, S.F. and Pimenta, P.M. and Schröder, J. Computational Mechanics (2021) This work addresses simultaneous use of geometrically exact shear-rigid rod and shell finite elements and describes both models within the same framework. Parameterization of the rotation field is performed by Rodrigues rotation vector, which makes the incremental updating of the rotational variables remarkably simple. For the rod element, cubic Hermitian interpolation for the displacements together with quadratic Lagrange interpolation for the incremental torsion angle were employed, while, for the triangular shell element, a complete quadratic Lagrange interpolation was used. The internal incremental torsion angle resulting from the displacement field within the shell element is then made compatible with the boundary incremental torsion angle of the shell element by an internal Lagrange multiplier. The compatibility between contiguous shell elements as well rod elements is mastered in the standard way by simply connecting nodes. This technique is an important contribution of the work, whose performance is illustrated by several numerical examples. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
  	view abstract	doi: 10.1007/s00466-020-01967-2

• 2021 • 374	Rot-free mixed finite elements for gradient elasticity at finite strains Riesselmann, J. and Ketteler, J.W. and Schedensack, M. and Balzani, D. International Journal for Numerical Methods in Engineering 122 1602-1628 (2021) Through enrichment of the elastic potential by the second-order gradient of deformation, gradient elasticity formulations are capable of taking nonlocal effects into account. Moreover, geometry-induced singularities, which may appear when using classical elasticity formulations, disappear due to the higher regularity of the solution. In this contribution, a mixed finite element discretization for finite strain gradient elasticity is investigated, in which instead of the displacements, the first-order gradient of the displacements is the solution variable. Thus, the C1 continuity condition of displacement-based finite elements for gradient elasticity is relaxed to C0. Contrary to existing mixed approaches, the proposed approach incorporates a rot-free constraint, through which the displacements are decoupled from the problem. This has the advantage of a reduction of the number of solution variables. Furthermore, the fulfillment of mathematical stability conditions is shown for the corresponding small strain setting. Numerical examples verify convergence in two and three dimensions and reveal a reduced computing cost compared to competitive formulations. Additionally, the gradient elasticity features of avoiding singularities and modeling size effects are demonstrated. © 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.6592

• 2020 • 373	A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification Sprave, L. and Menzel, A. Acta Mechanica 231 5159-5192 (2020) A gradient-enhanced ductile damage model at finite strains is presented, and its parameters are identified so as to match the behaviour of DP800. Within the micromorphic framework, a multi-surface model coupling isotropic Lemaitre-type damage to von Mises plasticity with nonlinear isotropic hardening is developed. In analogy to the effective stress entering the yield criterion, an effective damage driving force—increasing with increasing plastic strains—entering the damage dissipation potential is proposed. After an outline of the basic model properties, the setup of the (micro)tensile experiment is discussed and the importance of including unloading for a parameter identification with a material model including damage is emphasised. Optimal parameters, based on an objective function including measured forces and the displacement field obtained from digital image correlation, are identified. The response of the proposed model is compared to a tensile experiment of a specimen with a different geometry as a first approach to validate the identified parameters. © 2020, The Author(s).
  	view abstract	doi: 10.1007/s00707-020-02786-5

• 2020 • 372	A numerical method for the generation of hierarchical Poisson Voronoi microstructures applied in micromechanical finite element simulations—part I: method Schneider, Y. and Weber, U. and Wasserbäch, W. and Zielke, R. and Schmauder, S. and Tillmann, W. Computational Mechanics 66 651-667 (2020) Poisson Voronoi (PV) tessellations as artificial microstructures are widely used in investigations of material deformation behaviors. However, a PV structure usually describes a relative homogeneous field. This work presents a simple numerical method for generating 2D/3D artificial microstructures based on hierarchical PV tessellations. If grains/particles of a phase cover a large size span, the concept of “artificial phases” can be used to create a more realistic size distribution. From case to case, detailed microstructural features cannot be directly achieved by commercial or free softwares, but they are necessary for a deep or thorough study of the material deformation behavior. PV tessellations created in our process can fulfill individual requirements from material designs. Another reason to use PV tessellations is due to the limited experimental data. Concerning the application of PV microstructures, four examples are given. The FE models and results will be presented in consecutive works, i.e. “part II: applications”. © 2020, The Author(s).
  	view abstract	doi: 10.1007/s00466-020-01869-3

• 2020 • 371	Adaptive Concurrent Topology Optimization of Coated Structures with Nonperiodic Infill for Additive Manufacturing Hoang, V.-N. and Tran, P. and Nguyen, N.-L. and Hackl, K. and Nguyen-Xuan, H. CAD Computer Aided Design 129 (2020) The present research develops a direct multiscale topology optimization method for additive manufacturing (AM) of coated structures with nonperiodic infill by employing an adaptive mapping technique of adaptive geometric components (AGCs). The AGCs consist of a framework of macro-sandwich bars that represent the macrostructure with the solid coating and a network of micro-solid bars that represent the nonperiodic infill at the microstructural scale. The macrostructure including the coating skin and the internal architecture of the microstructures of cellular structures is simultaneously optimized by straightforwardly searching optimal geometries of the AGCs. Compared with most existing methods, the proposed method does not require material homogenization technique at the microscale; the continuity of microstructures and structural porosities are ensured without additional constraints; Finite element analysis (FEA) and geometric parameter updates are required only once for each optimization iteration. AGCs allow us to model coated structures with porosity infill on a coarse finite element mesh. The adaptive mapping technique may reduce mapping time by up to 50%. Besides, it is easy to control the length scales of the coating and infill as desired to make it possible with AM. This investigation also explores the ability to realize concurrent designs of coated structures with nonperiodic infill patterns using 3D printing techniques. © 2020 Elsevier Ltd
  	view abstract	doi: 10.1016/j.cad.2020.102918

• 2020 • 370	Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws Kuzmin, D. and Quezada de Luna, M. Computer Methods in Applied Mechanics and Engineering 372 (2020) In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization and constrain antidiffusive corrections of a property-preserving low-order scheme. The addition of a second-order entropy dissipative component to the antidiffusive part of a nearly entropy conservative numerical flux is generally insufficient to prevent violations of local bounds in shock regions. Our monolithic convex limiting technique adjusts a given target flux in a manner which guarantees preservation of invariant domains, validity of local maximum principles, and entropy stability. The new methodology combines the advantages of modern entropy stable/entropy conservative schemes and their local extremum diminishing counterparts. The process of algebraic flux correction is based on inequality constraints which provably provide the desired properties. No free parameters are involved. The proposed algebraic fixes are readily applicable to unstructured meshes, finite element methods, general time discretizations, and steady-state residuals. Numerical studies of explicit entropy-constrained schemes are performed for linear and nonlinear test problems. © 2020 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2020.113370

• 2020 • 369	Bathymetry Reconstruction Using Inverse ShallowWater Models: Finite Element Discretization and Regularization Hajduk, H. and Kuzmin, D. and Aizinger, V. Lecture Notes in Computational Science and Engineering 132 223-230 (2020) In the present paper, we use modified shallow water equations (SWE) to reconstruct the bottom topography (also called bathymetry) of a flow domain without resorting to traditional inverse modeling techniques such as adjoint methods. The discretization in space is performed using a piecewise linear discontinuous Galerkin (DG) approximation of the free surface elevation and (linear) continuous finite elements for the bathymetry. Our approach guarantees compatibility of the discrete forward and inverse problems: for a given DG solution of the forward SWE problem, the underlying continuous bathymetry can be recovered exactly. To ensure well-posedness of the modified SWE and reduce sensitivity of the results to noisy data, a regularization term is added to the equation for the water height. A numerical study is performed to demonstrate the ability of the proposed method to recover bathymetry in a robust and accurate manner. © Springer Nature Switzerland AG 2020.
  	view abstract	doi: 10.1007/978-3-030-30705-9_20

• 2020 • 368	Crystal anisotropy-dependent shear angle variation in orthogonal cutting of single crystalline copper Wang, Z. and Zhang, J. and Xu, Z. and Zhang, J. and Li, G. and Zhang, H. and Li, Z. and Hassan, H.U. and Fang, F. and Hartmaier, A. and Yan, Y. and Sun, T. Precision Engineering 63 41-48 (2020) Shear deformation that dominates elementary chip formation in metal cutting greatly relies on crystal anisotropy. In the present work we investigate the influence of crystallographic orientation on shear angle in ultra-precision orthogonal diamond cutting of single crystalline copper by joint crystal plasticity finite element simulations and in-situ experiments integrated in scanning electron microscope. In particular, the experimental cutting conditions including a straight cutting edge are the same with that used in the 2D finite element simulations. Both simulations and experiments demonstrate a well agreement in chip profile and shear angle, as well as their dependence on crystallography. A series of finite element simulations of orthogonal cutting along different cutting directions for a specific crystallographic orientation are further performed, and predicated values of shear angle are used to calibrate an extended analytical model of shear angle based on the Ernst–Merchant relationship. © 2020 Elsevier Inc.
  	view abstract	doi: 10.1016/j.precisioneng.2020.01.006

• 2020 • 367	Gradient-Based Limiting and Stabilization of Continuous Galerkin Methods Kuzmin, D. Lecture Notes in Computational Science and Engineering 132 331-339 (2020) In this paper, we stabilize and limit continuous Galerkin discretizations of a linear transport equation using an algebraic approach to derivation of artificial diffusion operators. Building on recent advances in the analysis and design of edge-based algebraic flux correction schemes for singularly perturbed convection-diffusion problems, we derive algebraic stabilization operators that generate nonlinear high-order stabilization in smooth regions and enforce discrete maximum principles everywhere. The correction factors for antidiffusive element or edge contributions are defined in terms of nodal gradients that vanish at local extrema. The proposed limiting strategy is linearity-preserving and provides Lipschitz continuity of constrained terms. Numerical examples are presented for two-dimensional test problems. © Springer Nature Switzerland AG 2020.
  	view abstract	doi: 10.1007/978-3-030-30705-9_29

• 2020 • 366	Influence of anisotropic damage evolution on cold forging Langenfeld, K. and Schowtjak, A. and Schulte, R. and Hering, O. and Möhring, K. and Clausmeyer, T. and Ostwald, R. and Walther, F. and Tekkaya, A.E. and Mosler, J. Production Engineering 14 115-121 (2020) This contribution deals with the influence of anisotropic material degradation (damage) within numerical simulations of cold forging. For that purpose, two constitutive frameworks for modeling ductile damage are presented: an isotropic and an anisotropic model. In a first step, both models are calibrated based on a uniaxial tensile test. Then, the forward rod extrusion process is simulated with the isotropic model. The deformation of a characteristic element is transferred to the anisotropic model and the local response is investigated. Both models are compared to one another in terms of the process induced ductile damage. It will be shown, that the magnitude of the induced damage agrees reasonably well, but that the orientation of ductile damage is of major importance. © 2020, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-019-00942-y

• 2020 • 365	Influence of muck properties and chamber design on pressure distribution in EPB pressure chambers – Insights from computational flow simulations Dang, T.S. and Meschke, G. Tunnelling and Underground Space Technology 99 (2020) Earth Pressure Balance (EPB) shield machines are widely used in mechanized tunneling operations in soft grounds. In contrast to slurry shield machines, the pressure distribution in EPB excavation chambers is not well undersood, as it is influenced by the muck properties and the chamber design. A computational model specifically developed in Dang and Meschke (2018) for the numerical simulation of material transport in EPB pressure chambers is employed to investigate the pressure distribution in two different types of EPB chambers, characterized by a different design of the mixing components, the rotators and the screw conveyor. The numerical model allows for the description of all rotating and fixed components of the EPB chambers including the screw conveyor and considers adequately the compressibility and the consistency of the soil paste. The spatio-temporal pressure distribution is investigated with respect to the influence of chamber design and the properties of the soil paste. Essential characteristics of the pressure distribution, such as the pressure unbalance between the left and right side and pressure fluctuations observed in in situ measurements are captured by the numerical analyses. The key factors influencing the pressure unbalance and pressure fluctuations are identified by parametric studies for two different EPB chamber designs. © 2020 Elsevier Ltd
  	view abstract	doi: 10.1016/j.tust.2020.103333

• 2020 • 364	Integrated BIM-to-FEM approach in mechanised tunnelling Alsahly, A. and Hegemann, F. and König, M. and Meschke, G. Geomechanik und Tunnelbau 13 212-220 (2020) In current tunnelling practice, Finite Element (FE) simulations form an integral element in the planning and the design phase of mechanised tunnelling projects. The generation of adequate computational models is often time consuming and requires data from many different sources, in particular, when manually generated using 2D-CAD drawings. Incorporating Building Information Modelling (BIM) concepts offers opportunities to simplify this process by using geometrical BIM sub-models as a basis for structural analyses. This paper presents a Tunnel Information Model (TIM) as a BIM specifically tailored to fit the needs of mechanised tunnelling projects and a ”BIM-to-FEM“ technology, that automatically extracts relevant information (geology, alignment, lining, material and process parameters) needed for FE simulations from BIM sub-models and subsequently performs FE analysis of the tunnel drive. The results of the analysis are stored centrally on a data server to which the user has continuous access. A case study from the Wehrhahn-Metro line project in Düsseldorf, Germany, is presented and discussed to demonstrate the efficiency and the applicability of the proposed BIM-to-FEM workflow. © 2020, Ernst und Sohn. All rights reserved.
  	view abstract	doi: 10.1002/geot.202000002

• 2020 • 363	Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations Kuzmin, D. and Klyushnev, N. Journal of Computational Physics 407 (2020) This work introduces a new type of constrained algebraic stabilization for continuous piecewise-linear finite element approximations to the equations of ideal magnetohydrodynamics (MHD). At the first step of the proposed flux-corrected transport (FCT) algorithm, the Galerkin element matrices are modified by adding graph viscosity proportional to the fastest characteristic wave speed. At the second step, limited antidiffusive corrections are applied and divergence cleaning is performed for the magnetic field. The limiting procedure developed for this stage is designed to enforce local maximum principles, as well as positivity preservation for the density and thermodynamic pressure. Additionally, it adjusts the magnetic field in a way which penalizes divergence errors without violating conservation laws or positivity constraints. Numerical studies for 2D test problems are performed to demonstrate the ability of the proposed algorithms to accomplish this task in applications to ideal MHD benchmarks. © 2020 Elsevier Inc.
  	view abstract	doi: 10.1016/j.jcp.2020.109230

• 2020 • 362	Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting Hajduk, H. and Kuzmin, D. and Kolev, T. and Tomov, V. and Tomas, I. and Shadid, J.N. Computers and Fluids 200 (2020) This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. The convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems. © 2020 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compfluid.2020.104451

• 2020 • 361	Modeling of viscoelastic structures with random material properties using time-separated stochastic mechanics Junker, P. and Nagel, J. International Journal for Numerical Methods in Engineering 121 308-333 (2020) Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations. © 2019 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.6210

• 2020 • 360	Numerical multi-level model for fiber-reinforced concrete - Multi-level validation based on an experimental study on high-strength concrete [Numerisches Mehrebenen-Modell für Stahlfaserbeton: Von der Faser- zur Bauteilebene: Mehrstufige Validierung anhand einer experimentellen Studie an hochfestem Faserbeton] Gudžulic, V. and Neu, G.E. and Gebuhr, G. and Anders, S. and Meschke, G. Beton- und Stahlbetonbau 115 146-157 (2020) Numerical multi-level model for fiber-reinforced concrete – Multi-level validation based on an experimental study on high-strength concrete. The contribution systematically examines the predictive capability of a numerical multi-level model for steel fiber reinforced concrete made of high-strength concrete by means of test series performed on the fiber as well as the structure level. The experimental study comprises pull-out tests of Dramix 3D fibers in high-strength concrete with different embedment lengths and inclinations to the crack surface as well as three-point bending tests on notched beams with three significantly different fiber contents. The numerical model is designed to directly track the influence of design parameters such as fiber type, fiber orientation, fiber content and concrete strength on the structural response. For this purpose, submodels on the single fiber level are combined into a crack bridging model, considering the fiber orientation and the fiber content, and are integrated into a finite element model for the purpose of numerical structural analysis. The validation of the models for hooked-end steel fibers shows that the interaction mechanisms between fiber and high-strength concrete are realistically captured for all investigated cases (fiber inclinations, embedment lengths). On the structural level, the load-displacement diagrams from the numerical simulations show a good agreement of the peak load as well as the post-peak behavior for all fiber contents. © 2020, Ernst und Sohn. All rights reserved.
  	view abstract	doi: 10.1002/best.201900067

• 2020 • 359	On mesh dependencies in finite-element-based damage prediction: application to sheet metal bending Sprave, L. and Schowtjak, A. and Meya, R. and Clausmeyer, T. and Tekkaya, A.E. and Menzel, A. Production Engineering 14 123-134 (2020) The properties of a local and a regularised gradient-enhanced continuum damage model are highlighted and both types of models are applied to the simulation of an air bending process. Constitutive relations are summarised for both Lemaitre-type models and a brief description of their implementation into Abaqus user material subroutines is given. With (several) material parameters obtained from a basic parameter identification process, an air bending experiment is simulated with different mesh densities. By means of the damage evolution as well as the distribution of representative damage and hardening variables, the mesh dependence of the local model in contrast to the mesh independence of the gradient-enhanced model is analysed for two air bending processes with different die width. © 2019, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-019-00937-9

• 2020 • 358	Structural reliability and durability assessment of reinforced concrete structures Freitag, S. and Kremer, K. and Edler, P. and Hofmann, M. and Meschke, G. Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019 2229-2236 (2020) In this paper, a concept for safety and durability assessment of reinforced concrete structures is presented. It is based on a multilevel modeling approach, where three different models are combined using simple linear elastic beam models for the reinforcement design, low fidelity nonlinear finite element models to compute the deformation at the full structural scale and finally high fidelity nonlinear finite element models to compute the crack widths at critical hot spots of the structure. The uncertainty of structural parameters is quantified by means of polymorphic uncertainty models combining stochastic and non-stochastic approaches. The multilevel approach is applied to the safety assessment and the crack widths prediction of a reinforced concrete beam structure. Copyright © 2019 European Safety and Reliability Association.
  	view abstract	doi: 10.3850/978-981-11-2724-30934-cd

• 2020 • 357	Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws Kuzmin, D. and Quezada de Luna, M. Journal of Computational Physics 411 (2020) This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard Galerkin approximation is transformed into a nonlinear high-resolution scheme which has the compact sparsity pattern of the piecewise-linear or multilinear subcell discretization. The representation of this scheme in terms of invariant domain preserving states makes it possible to prove the validity of local discrete maximum principles under CFL-like conditions. In contrast to predictor-corrector approaches based on the flux-corrected transport methodology, the proposed flux limiting strategy is monolithic, i.e., limited antidiffusive terms are incorporated into the well-defined residual of a nonlinear (semi-)discrete problem. A stabilized high-order Galerkin discretization is recovered if no limiting is performed. In the limited version, the compact stencil property prevents direct mass exchange between nodes that are not nearest neighbors. A formal proof of sparsity is provided for simplicial and box elements. The involved element contributions can be calculated efficiently making use of matrix-free algorithms and precomputed element matrices of the reference element. Numerical studies for Q2 discretizations of linear and nonlinear two-dimensional test problems illustrate the virtues of monolithic convex limiting based on subcell flux decompositions. © 2020 Elsevier Inc.
  	view abstract	doi: 10.1016/j.jcp.2020.109411

• 2020 • 356	The impact of post manufacturing treatment of functionally graded Ti6Al4V scaffolds on their surface morphology and mechanical strength Khrapov, D. and Koptyug, A. and Manabaev, K. and Léonard, F. and Mishurova, T. and Bruno, G. and Cheneler, D. and Loza, K. and Epple, M. and Surmenev, R. and Surmeneva, M. Journal of Materials Research and Technology 9 1866-1881 (2020) An ultrasonic vibration post-treatment procedure was suggested for additively manufactured lattices. The aim of the present research was to investigate mechanical properties and the differences in mechanical behavior and fracture modes of Ti6Al4V scaffolds treated with traditional powder recovery system (PRS) and ultrasound vibration (USV). Scanning electron microscopy (SEM) was used to investigate the strut surface and the fracture surface morphology. X-ray computed tomography (CT) was employed to evaluate the inner structure, strut dimensions, pore size, as well as the surface morphology of additively manufactured porous scaffolds. Uniaxial compression tests were conducted to obtain elastic modulus, compressive ultimate strength and yield stress. Finite element analysis was performed for a body-centered cubic (BCC) element-based model and for CT-based reconstruction data, as well as for a two-zone scaffold model to evaluate stress distribution during elastic deformation. The scaffold with PRS post treatment displayed ductile behavior, while USV treated scaffold displayed fragile behavior. Double barrel formation of PRS treated scaffold was observed during deformation. Finite element analysis for the CT-based reconstruction revealed the strong impact of surface morphology on the stress distribution in comparison with BCC cell model because of partially molten metal particles on the surface of struts, which usually remain unstressed. © 2019 The Authors.
  	view abstract	doi: 10.1016/j.jmrt.2019.12.019

• 2020 • 355	Three-field mixed finite element formulations for gradient elasticity at finite strains Riesselmann, J. and Ketteler, J.W. and Schedensack, M. and Balzani, D. GAMM Mitteilungen 43 (2020) Gradient elasticity formulations have the advantage of avoiding geometry-induced singularities and corresponding mesh dependent finite element solution as apparent in classical elasticity formulations. Moreover, through the gradient enrichment the modeling of a scale-dependent constitutive behavior becomes possible. In order to remain C0 continuity, three-field mixed formulations can be used. Since so far in the literature these only appear in the small strain framework, in this contribution formulations within the general finite strain hyperelastic setting are investigated. In addition to that, an investigation of the inf sup condition is conducted and unveils a lack of existence of a stable solution with respect to the L2-H1-setting of the continuous formulation independent of the constitutive model. To investigate this further, various discretizations are analyzed and tested in numerical experiments. For several approximation spaces, which at first glance seem to be natural choices, further stability issues are uncovered. For some discretizations however, numerical experiments in the finite strain setting show convergence to the correct solution despite the stability issues of the continuous formulation. This gives motivation for further investigation of this circumstance in future research. Supplementary numerical results unveil the ability to avoid singularities, which would appear with classical elasticity formulations. © 2019 The Authors. GAMM - Mitteilungen published by Wiley-VCH Verlag GmbH & Co. KGaA on behalf of Gesellschaft für Angewandte Mathematik und Mechanik
  	view abstract	doi: 10.1002/gamm.202000002

• 2020 • 354	Towards an understanding of grain boundary step in diamond cutting of polycrystalline copper Wang, Z. and Zhang, J. and Zhang, J. and Li, G. and Zhang, H. and ul Hassan, H. and Hartmaier, A. and Yan, Y. and Sun, T. Journal of Materials Processing Technology 276 (2020) Microstructural deformation at the grain level has an inherent impact on the achievable ultimate machining accuracy of polycrystalline materials. In the present work, numerical simulations and experiments of diamond cutting of polycrystalline copper are carried out to investigate the formation of surface step at grain boundaries on machined surface. Single crystal diamond cutting tool with straight cutting edge is chosen for experiments to mimic the tool geometry utilized in 2D crystal plasticity finite element simulations. Moreover, the same crystallography configuration of bi-crystal Cu is employed between experiments and simulations. Formation mechanisms of surface steps at grain boundaries are revealed by finite element simulations and corresponding experimental validation, as well as cross-sectional transmission electron microscope characterization. Finally, finite element simulations of orthogonal cutting of bi-crystal Cu are carried out to examine effects of both extrinsic cutting edge radius of diamond cutting tool and intrinsic misorientation angle of grain boundary on the propensity of grain boundary surface step formation. The present work provides theoretical guidelines on the strategy of suppressing grain boundary surface step formation for achieving superior surface finish of polycrystalline materials by diamond cutting. © 2019 Elsevier B.V.
  	view abstract	doi: 10.1016/j.jmatprotec.2019.116400

• 2019 • 353	A constitutive model for the sintering of suspension plasma-sprayed thermal barrier coating with vertical cracks Lv, B. and Mücke, R. and Zhou, D. and Fan, X. and Wang, T.J. and Guillon, O. and Vaßen, R. Journal of the American Ceramic Society 102 6202-6212 (2019) The degradation of mechanical properties due to sintering is one of the major issues during high temperature service of thermal barrier coating system for advanced gas turbines. In this study, a constitutive model was developed by the variational principle, based on the experimentally observed microstructure features of suspension plasma-sprayed thermal barrier coatings. The constitutive model was further implemented in finite element analysis software, in order to investigate the effect of vertical cracks. The evolution of microstructure during sintering, coating shrinkage and mechanical degradation were predicted. The numerical predictions of Young's modulus were generally in agreement with experimental results. Furthermore, the effect of vertical cracks on the strain tolerance and sintering resistance were discussed. It was confirmed that the introduction of vertical cracks contributed to the improvement of both properties. © 2019 The American Ceramic Society
  	view abstract	doi: 10.1111/jace.16491

• 2019 • 352	A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction Bertrand, F. and Moldenhauer, M. and Starke, G. Computational Methods in Applied Mathematics 19 663-679 (2019) The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a stable combination for incompressible linear elasticity computations. In this contribution, we extend the stress reconstruction procedure and resulting guaranteed a posteriori error estimator developed by Ainsworth, Allendes, Barrenechea and Rankin [2] and by Kim [18] to linear elasticity. In order to get a guaranteed reliability bound with respect to the energy norm involving only known constants, two modifications are carried out: (i) the stress reconstruction in next-to-lowest order Raviart-Thomas spaces is modified in such a way that its anti-symmetric part vanishes in average on each element; (ii) the auxiliary conforming approximation is constructed under the constraint that its divergence coincides with the one for the nonconforming approximation. An important aspect of our construction is that all results hold uniformly in the incompressible limit. Global efficiency is also shown and the effectiveness is illustrated by adaptive computations involving different Lamé parameters including the incompressible limit case. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.
  	view abstract	doi: 10.1515/cmam-2018-0004

• 2019 • 351	A scaled boundary finite element method for modelling wing crack propagation problems Zhang, P. and Du, C. and Birk, C. and Zhao, W. Engineering Fracture Mechanics 216 (2019) In this paper, a new shape function based on the scaled boundary finite element method (SBFEM) with side-face loading is used to study the problem of wing crack propagation. Crack contact is modelled by introducing the contact interface constraint condition by the Lagrange multiplier method. In the crack propagation process, the contact state of the crack surface at each step is obtained by an iterative method of determination and validation, and an accurate simulation for the frictional contact expansion process of compressed wing cracks is carried out. Polygon SBFEM remeshing technology is used to simulate the propagation of single and multiple wing cracks. The correctness and effectiveness of the new SBFEM shape function method in modelling wing crack propagation are verified using related experimental and numerical simulation results. The results indicate that under pressure, the wing crack propagates along the direction of the maximum circumferential stress during initial expansion, and the crack propagation angle is −70°32′, which is a pure type II crack. The crack then opens and gradually expands towards the pressure. In the considered wing crack problems, contact phenomena only occur on the initial crack surface during crack propagation. The contact force gradually decreases from the centre to the tips of the initial crack. As the crack expands, the contact force decreases, and the contact area of the crack gradually decreases. The friction coefficient has a strong influence on the crack propagation direction. The larger the friction coefficient, the closer the propagation direction is to the linear extension in the direction of the applied load. © 2019 Elsevier Ltd
  	view abstract	doi: 10.1016/j.engfracmech.2019.04.040

• 2019 • 350	Computational homogenisation of thermo-viscoplastic composites: Large strain formulation and weak micro-periodicity Berthelsen, R. and Menzel, A. Computer Methods in Applied Mechanics and Engineering 348 575-603 (2019) In this article, a first order two-scale finite element framework for fully coupled thermo-mechanical problems at finite deformations is considered. The scale bridging is achieved under application of Hill–Mandel condition based boundary conditions at the lower scale. Emphasis of the present article is on the extension of the concept of weak micro-periodicity to thermo-mechanically coupled problems. With this formulation at hand, uniform traction, respectively heat flux boundary conditions as well as the classic periodic boundary conditions are captured as well as a transition between them. The governing equations are summarised with a focus on the implementation of the weak periodic boundary conditions for thermo-mechanical problems. The performance of the proposed weak periodic boundary conditions in comparison to the classic boundary conditions is shown by means of simulations of a single representative volume element as well as by means of full multi-scale simulations. © 2019 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2018.12.032

• 2019 • 349	Experimental and numerical study of mechanical properties of multi-phase medium-Mn TWIP-TRIP steel: Influences of strain rate and phase constituents Benzing, J.T. and Liu, Y. and Zhang, X. and Luecke, W.E. and Ponge, D. and Dutta, A. and Oskay, C. and Raabe, D. and Wittig, J.E. Acta Materialia 177 250-265 (2019) In the current work we investigate the room temperature tensile properties of a medium-Mn twinning- and transformation-induced plasticity (TWIP-TRIP) steel from quasi-static to low-dynamic strain rates (ε˙ = 10−4 s−1 to ε˙ = 102 s−1). The multi-phase microstructure consists of coarse-grained recovered α'-martensite (inherited from the cold-rolled microstructure), multiple morphologies of ultrafine-grained (UFG) austenite (equiaxed, rod-like and plate-like), and equiaxed UFG ferrite. The multi-phase material exhibits a positive strain-rate sensitivity for yield and ultimate tensile strengths. Thermal imaging and digital image correlation allow for in situ measurements of temperature and local strain in the gauge length during tensile testing, but Lüders bands and Portevin Le Chatelier bands are not observed. A finite-element model uses empirical evidence from electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM), plus constitutive equations to dissect the microstructural influences of grain size, dislocation density and TWIP-TRIP driving forces on tensile properties. Calibration of tensile properties not only captures the strain rate sensitivity of the multi-phase TWIP-TRIP steel, but also provides opportunity for a complete parametric analysis by changing one variable at a time (phase fraction, grain size, strain-induced twin fraction and strain-induced ε-martensite fraction). An equivalent set of high-rate mechanical properties can be matched by changing either the austenite phase fraction or the ratio of twinning vs. transformation to ε-martensite. This experimental-computational framework enables the prediction of mechanical properties in multi-phase steels beyond the experimental regime by tuning variables that are relevant to the alloy design process. © 2019 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2019.07.036

• 2019 • 348	Fatigue behavior of HPC and FRC under cyclic tensile loading: Experiments and modeling Schäfer, N. and Gudžulić, V. and Timothy, J.J. and Breitenbücher, R. and Meschke, G. Structural Concrete 20 1265-1278 (2019) Systematic investigations of hardened cement paste, high-performance concrete and mortar with and without microfibers, subjected to static and cyclic tensile loadings, were conducted. The material degradation was investigated by means of microscopic analyses of the microcrack development. Notched specimens were subjected to a predefined number of load cycles. A nonsteady increase of microcracking with increasing load cycles was observed in high-strength concrete, whereas the addition of steel fibers lead to a steady increase of microcracks. High-strength mortar often showed premature failure, while addition of steel micro fibers allowed completion of the cyclic tests. To obtain a deeper insight into physical mechanisms governing fatigue and structural failure, high-performance concrete (HPC) and fiber-reinforced concrete (FRC) under static and cyclic tensile loadings have been modeled using cohesive interface finite elements, micromechanics, and a fiber-bundle model. Analysis of model predictions shows the significance of strength disorder and fiber properties on the structural behavior. © 2019 The Authors. Structural Concrete published by John Wiley & Sons Ltd on behalf of International Federation for Structural Concrete
  	view abstract	doi: 10.1002/suco.201900056

• 2019 • 347	FEM analysis of a multiferroic nanocomposite: comparison of experimental data and numerical simulation Labusch, M. and Lemke, V. and Schmitz-Antoniak, C. and Schröder, J. and Webers, S. and Wende, H. Archive of Applied Mechanics 89 1157-1170 (2019) In this contribution, we analyze the properties of two-phase magneto-electric (ME) composites. Such ME composite materials have raised scientific attention in the last decades due to many possible applications in a wide range of technical devices. Since the effective magneto-electric properties significantly depend on the microscopic morphology, we investigate in more detail the changes in the in-plane polarization due to an applied magnetic field. It was shown in previous works that it is possible to grow vertically aligned nanopillars of magnetostrictive cobalt ferrite in a piezoelectric barium titanate matrix by pulsed laser deposition. Based on x-ray linear dichroism, the displacements of titanate ions in the matrix material can be measured due to an applied magnetic field near the boundary of the interface between the matrix and the nanopillars. Here, we focus on (1–3) fiber-induced composites, based on previous experiments, where cobalt ferrite nanopillars are embedded in a barium titanate matrix. In the numerical simulations, we adjusted the boundary value problem to match the experimental setup and compare the results with previously made assumptions of the in-plane polarizations. A further focus is taken on the deformation behavior of the nanopillar over its whole height. Such considerations validate the assumption of the distortion of the nanopillars under an external magnetic field. Furthermore, we analyze the resulting magneto-electric coupling coefficient. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
  	view abstract	doi: 10.1007/s00419-019-01534-z

• 2019 • 346	Interrupted fatigue testing with periodic tomography to monitor porosity defects in wire + arc additive manufactured Ti-6Al-4V Biswal, R. and Zhang, X. and Shamir, M. and Al Mamun, A. and Awd, M. and Walther, F. and Khadar Syed, A. Additive Manufacturing 28 517-527 (2019) Porosity defects remain a challenge to the structural integrity of additive manufactured materials, particularly for parts under fatigue loading applications. Although the wire + arc additive manufactured Ti-6Al-4 V builds are typically fully dense, occurrences of isolated pores may not be completely avoided due to feedstock contamination. This study used contaminated wires to build the gauge section of fatigue specimens to purposely introduce spherical gas pores in the size range of 120–250 micrometres. Changes in the defect morphology were monitored via interrupted fatigue testing with periodic X-ray computed tomography (CT) scanning. Prior to specimen failure, the near surface pores grew by approximately a factor of 2 and tortuous fatigue cracks were initiated and propagated towards the nearest free surface. Elastic-plastic finite element analysis showed cyclic plastic deformation at the pore root as a result of stress concentration; consequently for an applied tension-tension cyclic stress (stress ratio 0.1), the local stress at the pore root became a tension-compression nature (local stress ratio −1.0). Fatigue life was predicted using the notch fatigue approach and validated with experimental test results. © 2019 The Authors
  	view abstract	doi: 10.1016/j.addma.2019.04.026

• 2019 • 345	Investigation on cutting edge preparation and FEM assisted optimization of the cutting edge micro shape for machining of nickel-base alloy Tiffe, M. and Aßmuth, R. and Saelzer, J. and Biermann, D. Production Engineering 13 459-467 (2019) The productivity and the tool life of cutting tools are majorly influenced by the cutting edge micro shape. The identification of optimized cutting edges is usually based on empirical knowledge or is carried out in iterative investigation steps. This paper presents an approach to predict optimal cutting edge micro shapes with the aid of finite-element-simulations of the chip formation. The approach is investigated for the machining of the nickel-base alloy Inconel 718. The cutting edges are prepared by pressurized air wet abrasive jet machining. Utilizing this method, the prepared cutting edges have a certain profile, which is considered for the modelling. By applying a model for tool wear the influence of the cutting edge micro shape on the tool life span is estimated. Subsequently, a statistical modelling provides the prediction of the tool wear rate for any possible parameter set within the investigated range. This is used to find an optimized cutting edge profile that minimizes the tool wear. An experimental investigation concludes the optimization procedure. © 2019, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-019-00900-8

• 2019 • 344	Modified mixed least-squares finite element formulations for small and finite strain plasticity Igelbüscher, M. and Schwarz, A. and Steeger, K. and Schröder, J. International Journal for Numerical Methods in Engineering 117 141-160 (2019) In this contribution, we propose mixed least-squares finite element formulations for elastoplastic material behavior. The resulting two-field formulations depending on displacements and stresses are given through the (Formula presented.) -norm minimization of the residuals of the first-order system of differential equations. The residuals are the balance of momentum and the constitutive equation. The advantage of using mixed methods for an elastoplastic material description lies in the direct approximation of the stresses as an unknown variable. In addition to the standard least-squares formulation, an extension of the least-squares functional as well as a modified formulation is done. The modification by means of a varied first variation of the functional is necessary to guarantee a continuous weak form, which is not automatically given within the elastoplastic least-squares approach. For the stress approximation, vector-valued Raviart-Thomas functions are chosen. On the other hand, standard Lagrange polynomials are taken into account for the approximation of the displacements. We consider classical J2 plasticity for a small and a large deformation model for the proposed formulations. For the description of the elastic material response, we choose for the small strain model Hooke's law and for finite deformations a hyperelastic model of Neo-Hookean type. The underlying plastic material response is defined by an isotropic von Mises yield criterion with linear hardening. © 2018 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.5951

• 2018 • 343	A new reverse engineering method to combine FEM and CFD simulation three-dimensional insight into the chipping zone during the drilling of Inconel 718 with internal cooling Oezkaya, E. and Biermann, D. Machining Science and Technology 1-18 (2018) The use of cooling lubricants in metal machining increases both the tool life and the quality of workpieces and improves the overall sustainability of production systems. In addition to fulfilling these main functions, the focus of machining processes is also related to the reduction of environmental pollution. This can for example be achieved by an optimized arrangement of the cutting tool cooling channels. Therefore, the active cutting edges of the tool should be effectively supplied with a sufficient amount of cooling lubricant. An analysis of the tribological stress is rather difficult because the complex contact zone is inaccessible. Hence, optical investigations are often limited to only observing the chip formation or analyzing the process without considering the influence of the chips. This article presents an innovative method, which enables a deeper three-dimensional insight into the chip formation zone during drilling with internal cooling channels, considering the cooling lubricant distribution and chip formation. The chip formation simulation based on the finite element method and the computational fluid dynamics flow simulation are combined. In this way, the differences between the different geometric models that do not allow any joint generation of numerical information due to missing interfaces are overcome. © 2018 Taylor & Francis Group, LLC
  	view abstract	doi: 10.1080/10910344.2017.1415933

• 2018 • 342	Computationally-efficient modeling of inelastic single crystal responses via anisotropic yield surfaces: Applications to shape memory alloys Hartl, D.J. and Kiefer, B. and Schulte, R. and Menzel, A. International Journal of Solids and Structures 136-137 38-59 (2018) Phenomenological constitutive models of inelastic responses based on the methods of classical plasticity provide several advantages, especially in terms of computational efficiency. For this reason, they are attractive for the analysis of complex boundary value problems comprising large computational domains. However, for the analysis of problems dominated by single crystal behavior (e.g., inclusion, granular interaction problems or inter-granular fracture), such approaches are often limited by the symmetry assumptions inherent in the stress invariants used to form yield-type criteria. On the other hand, the high computational effort associated with micro-mechanical or crystal plasticity-type models usually prevents their use in large structural simulations, multi-scale analyses, or design and property optimization computations. The goal of the present work is to establish a modeling strategy that captures micro-scale single-crystalline sma responses with sufficient fidelity at the computational cost of a phenomenological macro-scale model. Its central idea is to employ an anisotropic transformation yield criterion with sufficiently rich symmetry class—which can directly be adopted from the literature on plasticity theory—at the single crystal level. This approach is conceptually fundamentally different from the common use of anisotropic yield functions to capture tension-compression asymmetry and texture-induced anisotropy in poly-crystalline SMAs. In our model, the required anisotropy parameters are calibrated either from experimental data for single crystal responses, theoretical considerations or micro-scale computations. The model thus efficiently predicts single crystal behaviors and can be applied to the analysis of complex boundary value problems. In this work we consider the application of this approach to the modeling of shape memory alloys (SMAs), though its potential utility is much broader. Example analyses of SMA single crystals that include non-transforming precipitates and poly-crystalline aggregates are considered and the effects of both elastic and transformation anisotropy in these materials are demonstrated. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijsolstr.2017.12.002

• 2018 • 341	Coupled effect of crystallographic orientation and indenter geometry on nanoindentation of single crystalline copper Wang, Z. and Zhang, J. and Hassan, H.U. and Zhang, J. and Yan, Y. and Hartmaier, A. and Sun, T. International Journal of Mechanical Sciences 148 531-539 (2018) Surface pile-up topography is very significant for property extraction in nanoindentation tests. In the present work, we perform crystal plasticity finite element simulations of Berkovich nanoindentation of single crystalline copper with different crystallographic orientations, which derive quantitatively comparable mechanical properties and surface pile-up topographies with experimental data. Simulation results demonstrate that there is a coupled effect of crystallographic orientation of indented material and indenter geometry on surface pile-up behavior, due to the interaction between intrinsic dislocation slip events and extrinsic discrete stress distribution patterns. Based on the relative spatial orientation between crystallographic orientation of indented material and indenter geometry, a surface pile-up density factor mp is proposed to qualitatively characterize the propensity of surface pile-up behavior in nanoindentation tests of single crystalline copper. © 2018 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijmecsci.2018.09.007

• 2018 • 340	Development of forming and product properties of copper wire in a linear coil winding process Komodromos, A. and Lobbe, C. and Tekkaya, A.E. 2017 7th International Electric Drives Production Conference, EDPC 2017 - Proceedings 2017-December 1-7 (2018) Since electric motors are becoming more important in many application fields, e. g. hybrid electric vehicles, the optimization of the linear coil winding process is an important contribution to a higher productivity and flexibility. For the investigation of the forming behavior of the winding wire the material behavior is characterized in different experimental setups using wire diameters of 0.63 mm-3.35 mm. By comparing the results of tensile tests and compression tests, a tension-compression anisotropy of the wire behavior can be noticed. The Young's Modulus, measured in cyclic tensile tests from 99-116 GPa (dependent on the amount of strain), is used for the characterization of the elastic behavior of the copper wire. Subsequently, numerical investigations of the linear winding process in a case study for a rectangular bobbin are carried out in order to analyze the influence forming parameters have on the resulting properties of the wound coil. The wire tensile force represents a key parameter concerning the geometrical properties of the wound wire and the clearance between wire and bobbin. Numerical results show that the wire cross-section decreases through bending already at standard wire tensile forces. Additionally, the clearance between wire and bobbin increases with larger wire diameters. The aforementioned results serve as fundamentals for a comprehensive modeling of the linear winding process of noncircular coil bobbins with copper wire. © 2017 IEEE.
  	view abstract	doi: 10.1109/EDPC.2017.8328143

• 2018 • 339	Development of W-coating with functionally graded W/EUROFER-layers for protection of First-Wall materials Emmerich, T. and Qu, D. and Vaßen, R. and Aktaa, J. Fusion Engineering and Design 128 58-67 (2018) To protect First-Wall components, made of reduced activation ferritic martensitic steel, against the plasma of future fusion reactors, tungsten coatings are a feasible option. The difference in coefficient of thermal expansion between the coating and the steel substrate can be compensated using functionally graded material layers. Such layers were successfully produced by vacuum plasma spraying. This technique reduces, however, the hardness of the substrate surface near zone. Modified spraying parameters moderate the hardness loss. The parameters may, though, affect also the layer bonding toughness which is evaluated in this work by four point bending tests. Furthermore, the layers behavior on First-Wall Mock‐ups and under different thermal loads is investigated by finite element simulations. The measurement of the layer adhesion indicates that the layer adhesion decreases only for modified spraying parameters that do not reduce the substrate hardness. It follows also from the toughness calculation that without layer residual stresses the toughness values depend on coating thickness. In regard to the Mock‐up behavior the simulations show that intermediate steps are necessary during heating and cooling to prevent artificial stresses and inelastic deformation. It is, however, not possible to avoid stresses and inelastic deformation completely as they originate from the residual stresses. © 2018
  	view abstract	doi: 10.1016/j.fusengdes.2018.01.047

• 2018 • 338	Effective Diffusivity of Porous Materials with Microcracks: Self-Similar Mean-Field Homogenization and Pixel Finite Element Simulations Timothy, J.J. and Meschke, G. Transport in Porous Media 125 413-434 (2018) We investigate the influence of distributed microcracks on the overall diffusion properties of a porous material using the self-similar cascade continuum micromechanics model within the framework of mean-field homogenization and computational homogenization of diffusion simulations using a high-resolution pixel finite element method. In addition to isotropic, also anisotropic crack distributions are considered. The comparison of the results from the cascade continuum micromechanics model and the numerical simulations provides a deeper insight into the qualitative transport characteristics such as the influence of the crack density on the complexity and connectivity of crack networks. The analysis shows that the effective diffusivity for a disordered microcrack distribution is independent of the absolute length scale of the cracks. It is observed that the overall effective diffusivity of a microcracked material with the microcracks oriented in the direction of transport is not necessarily higher than that of a material with a random orientation of microcracks, independent of the microcrack density. © 2018, Springer Nature B.V.
  	view abstract	doi: 10.1007/s11242-018-1126-y

• 2018 • 337	Efficient stress–velocity least-squares finite element formulations for the incompressible Navier–Stokes equations Nisters, C. and Schwarz, A. Computer Methods in Applied Mechanics and Engineering 341 333-359 (2018) In this contribution three different mixed least-squares finite element methods (LSFEMs) are investigated with respect to accuracy and efficiency with simultaneous consideration of regular and adaptive meshing strategies. The deliberations are made for the incompressible Navier–Stokes equations. The generally known first-order div–grad system in terms of the (total) stress, velocity and pressure (SVP) formulation is the basis for two further div–grad least-squares formulations in terms of (total) stress and velocity (SV), whereby both formulations are derived from different fountainheads. The extended SV formulation is an enrichment of the known stress–velocity formulation proposed by Cai et al. (2004). The second SV formulation is based on the substitution of the pressure in the SVP formulation, thus it is based on a discontinuous pressure interpolation. Advantage of the SV formulations is a smaller system matrix size due to the reduction of the relevant degrees of freedom. Nevertheless, the approximation quality has to last the demand of the established least-squares formulations. The drawback of a poor mass conservation is well-investigated for the LSFEM and known to overcome by using high-order interpolations for all solution variables. Therefore, the main attention of this contribution is focused on accuracy, while aiming for high efficiency, which is intrinsic for the fundamental idea in here. In the light of efficient LSFEM solutions the advantage of the inherent a posteriori error estimator of the method is used for deliberations on different marking strategies in an h-type adaptive mesh refinement. © 2018 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2018.01.043

• 2018 • 336	Experimental and numerical investigation of the strain rate-dependent compression behaviour of a carbon-epoxy structure Schmack, T. and Filipe, T. and Deinzer, G. and Kassapoglou, C. and Walther, F. Composite Structures 189 256-262 (2018) The usage of fibre-reinforced composites in automotive body structures is still a rarity. The main goal in body structure development is to design lightweight structures as cost-efficient as possible. This research contributes to the approach of maximal material usage by considering the strength increase of a carbon-epoxy laminate with increasing strain rate. The objective was to substantiate the well-known material characteristic's strain rate dependency from a coupon level to realistic body structure component – experimentally and numerically. Hence, a special compression fixture was developed to obtain all necessary characteristic values of the investigated T700S DT120 prepreg system. The rectangular coupon specimens were loaded with quasi-static to intermediate strain rates (2×10-4 to 70s-1). A second compression fixture was developed to axial load omega cross-sectional specimens with strain rates from 2×10-4 to 5s-1. The experimental tests showed a significant increase of +23% and +21% in compression strength for rectangular coupon specimens and omega cross-sectional components, respectively. Furthermore, the numerical simulation showed the same increase in strength of +21% for omega cross-sectional components. This work has proven the necessity of considering the strain rate dependency of a composite material to accurately predict the maximum load capacity of a structure during a dynamic load event like a crash. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compstruct.2017.11.025

• 2018 • 335	Finite element-based software-in-the-loop for offline post-processing and real-time simulations Oveisi, A. and Sukhairi, T.A. and Nestorović, T. Structural Engineering and Mechanics 67 643-658 (2018) In this paper, we introduce a new framework for running the finite element (FE) packages inside an online Loop together with MATLAB. Contrary to the Hardware-in-the-Loop techniques (HiL), in the proposed Software-in-the-Loop framework (SiL), the FE package represents a simulation platform replicating the real system which can be out of access due to several strategic reasons, e.g., costs and accessibility. Practically, SiL for sophisticated structural design and multi-physical simulations provides a platform for preliminary tests before prototyping and mass production. This feature may reduce the new product's costs significantly and may add several flexibilities in implementing different instruments with the goal of shortlisting the most cost-effective ones before moving to real-time experiments for the civil and mechanical systems. The proposed SiL interconnection is not limited to ABAQUS as long as the host FE package is capable of executing user-defined commands in FORTRAN language. The focal point of this research is on using the compiled FORTRAN subroutine as a messenger between ABAQUS/CAE kernel and MATLAB Engine. In order to show the generality of the proposed scheme, the limitations of the available SiL schemes in the literature are addressed in this paper. Additionally, all technical details for establishing the connection between FEM and MATLAB are provided for the interested reader. Finally, two numerical sub-problems are defined for offline and online post-processing, i.e., offline optimization and closed-loop system performance analysis in control theory. © 2018 Techno-Press, Ltd.
  	view abstract	doi: 10.12989/sem.2018.67.6.643

• 2018 • 334	Fracture analysis of a metal to CFRP hybrid with thermoplastic interlayers for interfacial stress relaxation using in situ thermography Summa, J. and Becker, M. and Grossmann, F. and Pohl, M. and Stommel, M. and Herrmann, H.-G. Composite Structures 193 19-28 (2018) In this work a plane hybrid-structure composed of a metal and a carbon-fiber-reinforced-polymer (CFRP) constituent is introduced. Hereby an interlayer is inserted between the metal and the CFRP constituent, pursuing the task of stress relaxation. In order to study the effect of interfacial stress relaxation several thermoplastics are investigated. In situ passive thermography is used to assess the damage during quasi-static and fatigue mechanical loading. Thus, mechanical properties are correlated with corresponding damage-quantities from non-destructive testing (ndt). These results reveal that transversal cracking and mode-I delamination are the dominant failure processes, which strongly depend on the thermoplastic material. Additional finite element analysis describes strain-energy- and stressconcentrations, which coincide with the observed damage mechanisms and the origins of fracture. © 2018 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compstruct.2018.03.013

• 2018 • 333	Investigation of heat transfer in a copper-infiltrated tool steel based on measurement, microtomography, and numerical simulation Klein, S. and Weber, S. and Theisen, W. Materials and Design 156 42-51 (2018) Copper-infiltrated tool steels potentially combine the good mechanical properties of tool-steels and the superior electrical and thermal conductivity of copper. However, their effective properties greatly depend on the constitution of the components as well as their topology. In this work, the copper-infiltrated cold-work tool steel of type X245VCrMo9-4-4 is analyzed. The thermal conductivity (TC) of the composite and its components is measured and their topology is analyzed by means of X-ray microtomography (μCT). Using the digitized topology and the attained properties, numerical FE simulations were laid out, which allowed the detailed investigation of heat transfer in the material. The results indicate, that 1) the simulated thermal conductivity is very sensitive to the assumed thermal boundary conductance (TBC) 2) the TBC can be approximated by iteratively converging the simulation results to the measured TC 3) both components contribute to the effective thermal conductivity (1/6 steel + 5/6 copper) and act as a bypass for each other, preventing hot spots 4) small increases in the copper content increase the TC by shortening the effective heat conduction path. © 2018 Elsevier Ltd
  	view abstract	doi: 10.1016/j.matdes.2018.06.028

• 2018 • 332	Laminate-based modelling of single and polycrystalline ferroelectric materials – application to tetragonal barium titanate Dusthakar, D.K. and Menzel, A. and Svendsen, B. Mechanics of Materials 117 235-254 (2018) The present contribution deals with the development of a laminate-based model designed to study the single and polycrystalline tetragonal ferroelectric material behaviour. Laminate-based models are micromechanically motivated and consider the volume fraction of the distinct ferroelectric variants directly in their formulation. At first, a single crystal laminate-based model is established by considering the average strain and polarisation compatibility conditions. A suitable thermodynamic electric Gibbs energy and a rate-dependent dissipation equation are postulated to capture the dissipative hysteretic material response. The update of the inequality constrained volume fractions is solved by adopting a Fischer–Burmeister-type algorithm in combination with a Newton–Raphson scheme. Following the single crystal formulation, a homogenisation procedure based on random orientation of the individual grains in a polycrystalline aggregate is considered. The material properties and the polarisation switching response of the randomly oriented individual grains are averaged using a finite element framework in order to study the macroscopic polycrystalline behaviour. A parameter fitting procedure based on experimental data for single crystalline response, taken from the literature, is detailed and the material model as well as the algorithmic scheme are verified by solving representative boundary value problems. Moreover, the finite element based simulation results are compared with newly generated experimental hysteresis data for a barium titanate piezoceramic. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.mechmat.2017.10.005

• 2018 • 331	Multiple slip dislocation patterning in a dislocation-based crystal plasticity finite element method Grilli, N. and Janssens, K.G.F. and Nellessen, J. and Sandlöbes, S. and Raabe, D. International Journal of Plasticity 100 104-121 (2018) Dislocation structures forming during cyclic loading of fcc metals are fatigue damage precursors. Their specific structures are caused by the motion and interactions of dislocations. Depending on the load conditions, the grain orientation, the stacking fault energy, a variety of different dislocation structures appear in the material such as labyrinths, cells, veins and persistent slip bands. We present a continuum dislocation-based model for cyclic fatigue and incorporate it into a crystal plasticity finite element solver. A method for the simulation of dislocation junction formation is introduced, which reproduces the behaviour of discrete objects, such as dislocations, in a continuum framework. The formation of dislocation walls after 50 and 100 deformation cycles at 0.95% and 0.65% strain amplitude starting from an initial random dislocation distribution is predicted for 〈001〉 and 〈11¯0〉 oriented crystals. Simulations and cyclic tension-compression experiments of polycrystalline 316L stainless steel are performed to compare our model with another model based on edge and screw dislocation densities. The simulated dislocation structures and experimental results, obtained with the electron channeling contrast imaging technique, are compared using a 2D orientation distribution function of the dislocation structures. The dominant orientation of dislocation walls is predicted by the new model; it turns out to be perpendicular to the intersection line between the two slip planes involved in their formation and at an angle of around 45o from the loading axis. This agrees well with the experimental observations and represents a step forward for understanding the formation mechanism of these dislocation structures. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijplas.2017.09.015

• 2018 • 330	Numerical benchmarking of granular flow with shear dependent incompressible flow models Mandal, S. and Turek, S. and Schwarze, R. and Haustein, M. and Ouazzi, A. and Gladky, A. Journal of Non-Newtonian Fluid Mechanics 262 92-106 (2018) Dense granular materials are universal in nature and some common examples of this kind of materials in our daily lives are sand, rice, sugar etc. Research in this area is motivated by numerous applications encountered in industrial processes, such as hopper discharge, chute flow, moving beds, sandpipe flow, etc. and also in geophysics for the description and prediction of natural hazards like landslide and rock avalanches. Here, a continuum description of these granular flows is appropriate. Granular materials in liquid-like state show strong non-Newtonian behavior, which is typically described by phenomenological constitutive laws with local rheology. Very often, fluidization and flows of granular materials are localized in thin shear bands, whereas the granular material remains in solid-like state outside these bands. In this paper we establish a benchmark problem for granular materials, namely as Couette flow which is a very common example for granular materials in industrial application. We formulate the rheology for the continuum approach in the framework of the regularized version of a Bingham fluid and use advanced numerical methods regarding discretization as well as solution aspects, so that we can provide mesh independent results with two different software packages, Featflow and Openfoam, which can be used for validation and evaluation of the different methods and approaches. The authors thank the German Research Foundation DFG for funding under the grants TU 102/44-1 and SCHW 1168/6-1 within the pilot for transnational cooperation of the Dutch Technology Foundation STW and the DFG. This work was also supported by DAAD. © 2018 Elsevier B.V.
  	view abstract	doi: 10.1016/j.jnnfm.2018.03.015

• 2018 • 329	Predictive quality control of hybrid metal-CFRP components using information fusion Berger, D. and Zaiß, M. and Lanza, G. and Summa, J. and Schwarz, M. and Herrmann, H.-G. and Pohl, M. and Günther, F. and Stommel, M. Production Engineering 12 161-172 (2018) The paper presents an approach to determine the durability of hybrid metal-CFRP components combining the results of non-destructive testing (ndt) and finite element simulation The advantage of hybrid metal-CFRP components lies in the use of the properties of the materials used. CFRP parts with higher specific stiffness and strength are combined with metallic joining points, so that established joining processes for metal components can be applied to these lightweight components. In order to further promote the use of these hybrids in industry, it is necessary to guarantee a high level of component reliability through 100% quality control in order to avoid production-related defects. These defects such as delamination or fibre disorientation however vary in shape, size and position and lead to different effects on the part performance and reliability. Therefore the presented approach includes the application of non-destructive testing methods that are applied as in-line quality control measures in order to determine defect characteristics of the inspected parts. Due to the novelty of the component under test it is necessary to evaluate the individual criticality of detected defects and how they affect part performance during the testing procedure. Therefore the acquired ndt-data is used in finite element simulations where defect characteristics are added to the component model and whose effects on part reliability are evaluated. The generation of additional information combining non-destructive testing and simulation is referred to as data fusion. In order to evaluate the validity of the presented approach the determined part performances are compared to experimental mechanic tests. © 2018, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-018-0816-1

• 2018 • 328	Simulation based analysis and optimisation of the cutting edge micro shape for machining of nickel-base alloys Biermann, D. and Amuth, R. and Hess, S. and Tiffe, M. Procedia CIRP 67 284-289 (2018) The modification of the cutting edge micro shape by wet abrasive jet machining is utilized to increase the performance of cutting tools by means of productivity and tool life. However, for numerous cutting processes the optimal micro shape of cutting edges is still unknown. In this regard, the paper deals with a method to predict optimized cutting edge micro shapes using FE-Simulation. The method includes the consideration of the local process conditions like radius dependent cutting speeds in drilling processes depicted by the example of drilling a nickel-base alloy. In this paper first simulation analyses are compared to experimental investigations. In addition, predictions of the mechanical loads dependent on the applied cutting edge micro shapes are presented. © 2017 The Authors.
  	view abstract	doi: 10.1016/j.procir.2017.12.214

• 2018 • 327	Stress-velocity mixed least-squares FEMs for the time-dependent incompressible navier-stokes equations Schwarz, A. and Nisters, C. and Averweg, S. and Schröder, J. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10665 LNCS 137-144 (2018) In this article a mixed least-squares finite element method (LSFEM) for the time-dependent incompressible Navier-Stokes equations is proposed and investigated. The formulation is based on the incompressible Navier-Stokes equations consisting of the balance of momentum and the continuity equations. In order to obtain a first-order system the Cauchy stress tensor is introduced as an additional variable to the system of equations. From this stress-velocity-pressure approach a stress-velocity formulation is derived by adding a redundant residual to the functional without additional variables in order to strengthen specific physical relations, e.g. mass conservation. We account for implementation aspects of triangular mixed finite elements especially regarding the approximation used for H(div) × H1 and the discretization in time using the Newmark method. Finally, we present the flow past a cylinder benchmark problem in order to demonstrate the derived stress-velocity least-squares formulation. © Springer International Publishing AG 2018.
  	view abstract	doi: 10.1007/978-3-319-73441-5_14

• 2018 • 326	Testing of Ni-base superalloy single crystals with circular notched miniature tensile creep (CNMTC) specimens Cao, L. and Bürger, D. and Wollgramm, P. and Neuking, K. and Eggeler, G. Materials Science and Engineering A 712 223-231 (2018) The present work introduces a novel circular notched miniature tensile creep (CNMTC) specimen which is used to study the influence of notches on creep and of multiaxial stress states on microstructural evolution in Ni-based single crystal (SX) superalloys. It is briefly discussed how mild circular notches affect the stress state in the notch root of a tensile bar during elastic loading. Then the stress redistribution under creep conditions is calculated using the finite element method (FEM), assuming isotropic material behavior. Two series of interrupted creep experiments with the Ni-based single crystal superalloy ERBO1 (CMSX-4 type) were then performed at 950 °C, with flat uniaxial miniature tensile creep (FUMTC) and CNMTC <100> specimens, respectively. The evolution of cavities and microcracks in both types of specimens was carefully analyzed after 81, 169, and 306 h. In the uniaxial experiments, a growth of cast pores and the formation of new creep cavities were observed. These degradation processes were much less pronounced in the circular notched specimens. The results of the present work are discussed in the light of previous findings on the influence of multiaxial stress states on creep in single crystal superalloys. © 2017 Elsevier B.V.
  	view abstract	doi: 10.1016/j.msea.2017.11.102

• 2018 • 325	Variational approach to interface element modeling of brittle fracture propagation Khisamitov, I. and Meschke, G. Computer Methods in Applied Mechanics and Engineering 328 452-476 (2018) The paper proposes a variational approach to model brittle fracture propagation based on zero-thickness finite elements. Similar to the phase-field model for fracture, the problem of a fractured structure is variationally formulated by considering a minimization problem involving bulk and fracture surface energies. With the help of a damage variable used as an additional degree of freedom, the fracture propagates according to the values of the minimizers of the total potential energy. This damage variable is restricted to dimensionally reduced interface elements inserted between element boundaries. Crack opening is predicted when the elastic energy within the interface surface exceeds the critical energy release rate. The solution of the discretized system of equations is performed in a staggered scheme, solving first for the displacement field and then searching for the solution for the updated nodal damage variables. Selected numerical examples, including re-analyses of laboratory tests characterized by rather complex crack paths, are presented to demonstrate the performance of the proposed variational interface model. © 2017 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2017.08.031

• 2018 • 324	Viscoelasticity of short fiber composites in the time domain: from three-phases micromechanics to finite element analyses Breuer, K. and Schöneich, M. and Stommel, M. Continuum Mechanics and Thermodynamics 1-10 (2018) Micromechanical models can be used to calculate the mechanical properties of short glass fiber reinforced thermoplastics. In the present work, a three-step framework is used to validate a three-phases micromechanical model (RDI model) in the time domain, since the analysis of technical components by the finite element method is usually carried out in the time domain. The framework includes mechanical characterization, the implementation of the RDI model and a finite element analysis. The characterization delivers necessary information about the material phases of the composite. A dynamic mechanical analysis is performed to characterize the matrix material in order to obtain the linear viscoelastic properties. The mechanical properties of the matrix–fiber interphase are determined with an inverse calculation. In the second step, the RDI model is used to calculate the frequency depended effective stiffness of the composite. A new developed approach transforms the effective stiffness from the frequency domain into the time domain thus avoiding an explicit inverse Laplace–Carson transformation. In the third step, the RDI model is experimentally validated. © 2018 Springer-Verlag GmbH Germany, part of Springer Nature
  	view abstract	doi: 10.1007/s00161-018-0686-y

• 2017 • 323	A computational framework for modelling damage-induced softening in fibre-reinforced materials – Application to balloon angioplasty Polindara, C. and Waffenschmidt, T. and Menzel, A. International Journal of Solids and Structures 118-119 235-256 (2017) A computational framework for modelling damage-induced softening in fibre-reinforced materials is presented. The main aspect of this framework is the proposed non-local gradient-enhanced continuum damage formulation. At the material level, the elastic constitutive behaviour is defined by a hyperelastic functional including a volumetric and an isochoric contribution. The isochoric contribution is subdivided into three contributions associated to three different phases i=0,1,2. Phase 0 is represented by an incompressible neo-Hookean material, whereas phases 1 and 2 are represented by an exponential format that accounts for the stretching along two preferred anisotropy directions, i.e. two fibre families. Furthermore, a 1−di–type damage function, is introduced to reproduce the loss of stiffness in each phase i. Following the ideas discussed in (Dimitrijević and Hackl, 2008; Waffenschmidt et al. 2014) and references cited therein, the model is built around the enhancement of the local free energy function by means of terms that contain the referential gradients of the non-local damage variables ϕi. The inclusion of these terms ensures an implicit regularisation of the finite element implementation. A finite element implementation of the non-local gradient-enhanced continuum damage model is presented. To this end we develop an 8-noded Q1Q1P0 hexahedral element following a variational approach, in order to efficiently model the quasi-incompressible behaviour of the hyperelastic material. This element is implemented in Abaqus by means of a user subroutine UEL. Three boundary value problems are studied: an anisotropic plate with a hole, a balloon angioplasty and a full-3D artery-like tube. These computational experiments serve to illustrate the main capabilities of the proposed model. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijsolstr.2017.02.010

• 2017 • 322	A hybrid finite element and surrogate modelling approach for simulation and monitoring supported TBM steering Ninić, J. and Freitag, S. and Meschke, G. Tunnelling and Underground Space Technology 63 12-28 (2017) The paper proposes a novel computational method for real-time simulation and monitoring-based predictions during the construction of machine-driven tunnels to support decisions concerning the steering of tunnel boring machines (TBMs). The proposed technique combines the capacity of a process-oriented 3D simulation model for mechanized tunnelling to accurately describe the complex geological and mechanical interactions of the tunnelling process with the computational efficiency of surrogate (or meta) models based on artificial neural networks. The process-oriented 3D simulation model with updated model parameters based on acquired monitoring data during the advancement process is used in combination with surrogate models to determine optimal tunnel machine-related parameters such that tunnelling-induced settlements are kept below a tolerated level within the forthcoming process steps. The performance of the proposed strategy is applied to the Wehrhahn-line metro project in Düsseldorf, Germany and compared with a recently developed approach for real-time steering of TBMs, in which only surrogate models are used. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.tust.2016.12.004

• 2017 • 321	A multi-field finite element approach for the modelling of fibre-reinforced composites with fibre-bending stiffness Asmanoglo, T. and Menzel, A. Computer Methods in Applied Mechanics and Engineering 317 1037-1067 (2017) The implementation of an enhanced modelling approach for fibre-reinforced composites is presented which may, in addition to the directional dependency induced by the fibres, allow the capturing of the fibre-bending stiffness. The theoretical framework is based on the introduction of higher-order gradients of the motion function as additional arguments of the energy function such that size effects can be taken into account. However, the application of higher-order gradients within a finite element framework requires particular care with respect to continuity requirements. In this contribution the usage of a mixed-type multi-field finite element formulation and the fulfilment of the continuity requirement only in a weak sense is proposed. Based on a particular specification of the energy function representative boundary value problems are discussed to assess the model's properties. It is then shown that a model which is based on one additional invariant compared to the classic structural tensor approach allows, in principle, to incorporate effects which are due to the fibre-bending stiffness. © 2017 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2017.01.003

• 2017 • 320	A new monolithic Newton-multigrid-based FEM solution scheme for large strain dynamic poroelasticity problems Obaid, A. and Turek, S. and Heider, Y. and Markert, B. International Journal for Numerical Methods in Engineering 109 1103-1129 (2017) This paper presents a new efficient monolithic finite element solution scheme to treat the set of PDEs governing a 2D, biphasic, saturated theory of porous media model with intrinsically coupled and incompressible solid and fluid constituents for infinitesimal and large elastic deformation. Our approach, which inherits some of its techniques from CFD, is characterized by the following aspects: (1) it only performs operator evaluation with no additional Gateaux derivatives. In particular, the computations of the time-consuming material tangent matrix are not involved here; (2) it solves the non-linear dynamic problem with no restriction on the strength of coupling; (3) it is more efficient than the linear uvp solver discussed in previous works; (4) it requires weaker derivatives, and hence, lower-order FE can be tested; and (5) the boundary conditions are reduced, solution independent and more convenient to apply than in the old uvp formulation. For the purpose of validation and comparison, prototypical simulations including analytical solutions are carried out, and at the end, an adaptive time stepping procedure is introduced to handle the rapid change in the numbers of nonlinear iterations that may occur. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.5315

• 2017 • 319	A non-affine electro-viscoelastic microsphere model for dielectric elastomers: Application to VHB 4910 based actuators Thylander, S. and Menzel, A. and Ristinmaa, M. Journal of Intelligent Material Systems and Structures 28 627-639 (2017) Dielectric elastomers belong to a larger group of materials, the so-called electroactive polymers, which have the capability of transforming electric energy to mechanical energy through deformation. VHB 4910 is one of the most popular materials for applications of dielectric elastomers and therefore one of the most investigated. This paper includes a new micromechanically motivated constitutive model for dielectric elastomers that incorporates the nearly incompressible and viscous time-dependent behaviour often found in this type of material. A non-affine microsphere framework is used to transform the microscopic constitutive model to a macroscopic continuum counterpart. Furthermore the model is calibrated, through both homogeneous deformation examples and more complex finite element analysis, to VHB 4910. The model is able to capture both the purely elastic, the viscoelastic and the electro-viscoelastic properties of the elastomer and demonstrates the power and applicability of the electromechanically coupled microsphere framework. © SAGE Publications.
  	view abstract	doi: 10.1177/1045389X16651157

• 2017 • 318	A polytree-based adaptive approach to limit analysis of cracked structures Nguyen-Xuan, H. and Nguyen-Hoang, S. and Rabczuk, T. and Hackl, K. Computer Methods in Applied Mechanics and Engineering 313 1006-1039 (2017) We in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures. The key idea is to develop a general refinement algorithm based on a so-called polytree mesh structure. The method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones, which are considered as special cases. Also, polytree meshes are conforming and can be regarded as a generalization of quadtree meshes. For the aim of this paper, we restrict our main interest in plane-strain limit analysis to von Mises-type materials, yet its extension to a wide class of other solid mechanics problems and materials is completely possible. To avoid volumetric locking, we propose an approximate velocity field enriched with bubble functions using Wachspress coordinates on a primal-mesh and design carefully strain rates on a dual-mesh level. An adaptive mesh refinement process is guided by an L2-norm-based indicator of strain rates. Through numerical validations, we show that the present method reaches high accuracy with low computational cost. This allows us to perform large-scale limit analysis problems favorably. © 2016 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2016.09.016

• 2017 • 317	A relaxation-based approach to damage modeling Junker, P. and Schwarz, S. and Makowski, J. and Hackl, K. Continuum Mechanics and Thermodynamics 29 291-310 (2017) Material models, including softening effects due to, for example, damage and localizations, share the problem of ill-posed boundary value problems that yield mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior described, for example, by internal variables, at a spatial level. This can take account of the gradient of the internal variable to yield mesh-independent finite element results. In this paper, we present a new approach to damage modeling that does not use common field functions, inclusion of gradients or complex integration techniques: Appropriate modifications of the relaxed (condensed) energy hold the same advantage as other methods, but with much less numerical effort. We start with the theoretical derivation and then discuss the numerical treatment. Finally, we present finite element results that prove empirically how the new approach works. © 2016, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00161-016-0528-8

• 2017 • 316	A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy Viebahn, N. and Pimenta, P.M. and Schröder, J. Computational Mechanics 59 281-297 (2017) This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff–Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C1-continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C0-continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C1-continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works. © 2016, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00466-016-1343-6

• 2017 • 315	A Study on Microstructural Parameters for the Characterization of Granular Porous Ceramics Using a Combination of Stochastic and Mechanical Modeling Kulosa, M. and Neumann, M. and Boeff, M. and Gaiselmann, G. and Schmidt, V. and Hartmaier, A. International Journal of Applied Mechanics 9 (2017) To correlate the mechanical properties of granular porous materials with their microstructure, typically porosity is being considered as the dominant parameter. In this work, we suggest the average coordination number, i.e., the average number of connections that each grain of the porous material has to its neighboring grains, as additional - and possibly even more fundamental - microstructural parameter. In this work, a combination of stochastic and mechanical modeling is applied to study microstructural influences on the elastic properties of porous ceramics. This is accomplished by generating quasi-two-dimensional (2D) and fully three-dimensional (3D) representative volume elements (RVEs) with tailored microstructural features by a parametric stochastic microstructure model. In the next step, the elastic properties of the RVEs are characterized by finite element analysis. The results reveal that the average coordination number exhibits a very strong correlation with the Young's modulus of the material in both 2D and 3D RVEs. Moreover, it is seen that quasi-2D RVEs with the same average coordination number, but largely different porosities, only differ very slightly in their elastic properties such that the correlation is almost unique. This finding is substantiated and discussed in terms of the load distribution in microstructures with different porosities and average coordination numbers. © 2017 World Scientific Publishing Europe Ltd.
  	view abstract	doi: 10.1142/S1758825117500697

• 2017 • 314	A variational approach to the modelling of grooving in a three-dimensional setting Hackl, K. and Fischer, F.D. and Svoboda, J. Acta Materialia 129 331-342 (2017) We present a theory of thermal grooving, i.e. surface motion due to surface diffusion, based solely on geometrical and energetic arguments and a variational approach involving a thermodynamic extremal principle. The theory is derived for a fully three-dimensional setting. All interface and contact conditions at junction lines and points of the material aggregate are derived rigorously and without ambiguity. A finite element implementation of the model is employed. Numerical examples are presented and compared with experimental results from the literature. © 2017 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2017.01.064

• 2017 • 313	Adaptive crack modeling with interface solid elements for plain and fiber reinforced concrete structures Zhan, Y. and Meschke, G. Materials 10 (2017) The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense. © 2017 by the authors.
  	view abstract	doi: 10.3390/ma10070771

• 2017 • 312	An adaptive least-squares mixed finite element method for the Signorini problem Krause, R. and Müller, B. and Starke, G. Numerical Methods for Partial Differential Equations 33 276-289 (2017) We present and analyze a least squares formulation for contact problems in linear elasticity which employs both, displacements and stresses, as independent variables. As a consequence, we obtain stability and high accuracy of our discretization also in the incompressible limit. Moreover, our formulation gives rise to a reliable and efficient a posteriori error estimator. To incorporate the contact constraints, the first-order system least squares functional is augmented by a contact boundary functional which implements the associated complementarity condition. The bilinear form related to the augmented functional is shown to be coercive and therefore constitutes an upper bound, up to a constant, for the error in displacements and stresses in H1(Ω)d × H(div, Ω)d. This implies the reliability of the functional to be used as an a posteriori error estimator in an adaptive framework. The efficiency of the use of the functional as an a posteriori error estimator is monitored by the local proportion of the boundary functional term with respect to the overall functional. Computational results using standard conforming linear finite elements for the displacement approximation combined with lowest-order Raviart-Thomas elements for the stress tensor show the effectiveness of our approach in an adaptive framework for two-dimensional and three-dimensional Hertzian contact problems. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 276–289, 2017. © 2016 Wiley Periodicals, Inc.
  	view abstract	doi: 10.1002/num.22086

• 2017 • 311	Analytisch formulierte Näherungslösungen zur Grundwasserströmung bei einer Restwasserhaltung Perau, E. and Meteling, N. Geotechnik 40 2-14 (2017) Analytical approximate solution for ground water flow at a residual water drainage system. If excavations are conducted which go below the groundwater table, it makes sense to embed the pit wall in a less permeable soil stratum and to operate a residual water drainage system. With such a construction water flows under the pit walls and so a flow field arises which has to be determined for various calculations and stability verifications. For instance, hydraulic gradients, discharge velocities as well as potential heads and pore-water pressures have to be calculated. These values are needed to determine the earth and water pressure distribution. They can also be used for verifications in relation to hydraulic failure, internal erosion and failure of the earth support, and also for the calculation of groundwater influx. Using the Finite Element Method (FEM) a systematic parameter study is conducted as the basis for formulating analytical approximation solutions, including theoretical boundary cases. It is possible to optimize the parametric study for both plane and axis-symmetrical states with isotropic and anisotropic subsoil and to do this by defining the hydraulic problem as a parameterized boundary value problem. By evaluating the mathematical characteristics of the boundary value problem and conducting a dimensional analysis it is possible to reduce the number of parameters considerably. Copyright © 2017 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin
  	view abstract	doi: 10.1002/gete.201500032

• 2017 • 310	Automatic image-based stress analysis by the scaled boundary finite element method Saputra, A. and Talebi, H. and Tran, D. and Birk, C. and Song, C. International Journal for Numerical Methods in Engineering 109 697-738 (2017) Digital imaging technologies such as X-ray scans and ultrasound provide a convenient and non-invasive way to capture high-resolution images. The colour intensity of digital images provides information on the geometrical features and material distribution which can be utilised for stress analysis. The proposed approach employs an automatic and robust algorithm to generate quadtree (2D) or octree (3D) meshes from digital images. The use of polygonal elements (2D) or polyhedral elements (3D) constructed by the scaled boundary finite element method avoids the issue of hanging nodes (mesh incompatibility) commonly encountered by finite elements on quadtree or octree meshes. The computational effort is reduced by considering the small number of cell patterns occurring in a quadtree or an octree mesh. Examples with analytical solutions in 2D and 3D are provided to show the validity of the approach. Other examples including the analysis of 2D and 3D microstructures of concrete specimens as well as of a domain containing multiple spherical holes are presented to demonstrate the versatility and the simplicity of the proposed technique. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.5304

• 2017 • 309	Compressed Bi-crystal micropillars showing a sigmoidal deformation state – A computational study Toth, F. and Kirchlechner, C. and Fischer, F.D. and Dehm, G. and Rammerstorfer, F.G. Materials Science and Engineering A 700 168-174 (2017) It is the aim of this paper to show the mechanisms behind the experimental observations of rather smooth sigmoidal deformations in bi-crystal micropillar tests (in contrast to single crystal micro-compression tests) and to point out that the appearance of such deformation modes are a further reason for being careful when interpreting the force-axial displacement behavior in terms of stress-strain curves. Instabilities, i.e., buckling and subsequent post-buckling deformations, inhomogeneous strain fields and substantial deformations of the base as well as pronounced free surface effects are considered. The influences of imperfections and of friction as well as a possible clearance in the guidance of the loading device are taken into account, too. From these studies, the experimenter may get information how and with which limitations material parameters can be obtained from such compression tests in combination with simulations. © 2017 Elsevier B.V.
  	view abstract	doi: 10.1016/j.msea.2017.05.098

• 2017 • 308	Computational homogenisation for thermoviscoplasticity: application to thermally sprayed coatings Berthelsen, R. and Denzer, R. and Oppermann, P. and Menzel, A. Computational Mechanics 1-28 (2017) Metal forming processes require wear-resistant tool surfaces in order to ensure a long life cycle of the expensive tools together with a constant high quality of the produced components. Thermal spraying is a relatively widely applied coating technique for the deposit of wear protection coatings. During these coating processes, heterogeneous coatings are deployed at high temperatures followed by quenching where residual stresses occur which strongly influence the performance of the coated tools. The objective of this article is to discuss and apply a thermo-mechanically coupled simulation framework which captures the heterogeneity of the deposited coating material. Therefore, a two-scale finite element framework for the solution of nonlinear thermo-mechanically coupled problems is elaborated and applied to the simulation of thermoviscoplastic material behaviour including nonlinear thermal softening in a geometrically linearised setting. The finite element framework and material model is demonstrated by means of numerical examples. © 2017 Springer-Verlag GmbH Germany
  	view abstract	doi: 10.1007/s00466-017-1436-x

• 2017 • 307	Degradation in concrete structures due to cyclic loading and its effect on transport processes—Experiments and modeling Przondziono, R. and Timothy, J.J. and Weise, F. and Krütt, E. and Breitenbücher, R. and Meschke, G. and Hofmann, M. Structural Concrete 18 519-527 (2017) According to the objectives of the research group 1498, this paper deals with degradation effects in concrete structures that are caused by cyclic flexural loading. The goal is to determine their influence on the fluid transport processes within the material on the basis of experimental results and numerical simulations. The overall question was, to which extent the ingress of externally supplied alkalis and subsequently an alkali-silica reaction are affected by such modifications in the microstructure. Degradation in the concrete microstructure is characterized by ultrasonic wave measurements as well as by microscopic crack analysis. Furthermore, experiments on the penetration behavior of water into the investigated materials were performed. The penetration behavior into predamaged concrete microstructures was examined by the classical Karsten tube experiment, nuclear magnetic resonance method, and time domain reflectometry techniques. In order to create an appropriate model of the material's degradation on the water transport, the Darcy law was applied to describe the flow in partially saturated concrete. Material degradation is taken into account by an effective permeability that is dependent on the state of degradation. This effective permeability is obtained by the micromechanical homogenisation of the flow in an Representative Elementary Volume (REV) with distributed ellipsoidal microcracks embedded in a porous medium. The data gained in the microscopic crack analysis is used as input for the micromechanical model. Finite element simulations for unsaturated flow using the micromechanical model were compared with the experimental results showing good qualitative and quantitative agreement. © 2017 fib. International Federation for Structural Concrete
  	view abstract	doi: 10.1002/suco.201600180

• 2017 • 306	Efficient wave propagation simulation on quadtree meshes using SBFEM with reduced modal basis Gravenkamp, H. and Saputra, A.A. and Song, C. and Birk, C. International Journal for Numerical Methods in Engineering 110 1119-1141 (2017) We apply a combination of the transient scaled boundary finite element method (SBFEM) and quadtree-based discretization to model dynamic problems at high frequencies. We demonstrate that the current formulation of the SBFEM for dynamics tends to require more degrees of freedom than a corresponding spectral element discretization when dealing with smooth problems on regular domains. Thus, we improve the efficiency of the SBFEM by proposing a novel approach to reduce the number of auxiliary variables for transient analyses. Based on this improved SBFEM, we present a modified meshing procedure, which creates a quadtree mesh purely based on the geometry and allows arbitrary sizes and orders of elements, as well as an arbitrary number of different materials. The discretization of each subdomain is created automatically based on material parameters and the highest frequency of interest. The transition between regions of different properties is straightforward when using the SBFEM. The proposed approach is applied to image-based analysis with a particular focus on geological models. © 2016 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.5445

• 2017 • 305	Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture Shanthraj, P. and Svendsen, B. and Sharma, L. and Roters, F. and Raabe, D. Journal of the Mechanics and Physics of Solids 99 19-34 (2017) A finite-strain anisotropic phase field method is developed to model the localisation of damage on a defined family of crystallographic planes, characteristic of cleavage fracture in metals. The approach is based on the introduction of an undamaged configuration, and the inelastic deformation gradient mapping this configuration to a damaged configuration is microstructurally represented by the opening of a set of cleavage planes in the three fracture modes. Crack opening is modelled as a dissipative process, and its evolution is thermodynamically derived. To couple this approach with a physically-based phase field method for brittle fracture, a scalar measure of the overall local damage is introduced, whose evolution is determined by the crack opening rates, and weakly coupled with the non-local phase field energy representing the crack opening resistance in the classical sense of Griffith. A finite-element implementation of the proposed model is employed to simulate the crack propagation path in a laminate and a polycrystalline microstructure. As shown in this work, it is able to predict the localisation of damage on the set of pre-defined cleavage planes, as well as the kinking and branching of the crack resulting from the crystallographic misorientation across the laminate boundary and the grain boundaries respectively. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.jmps.2016.10.012

• 2017 • 304	Electro-chemical aspects of IPMCs within the framework of the theory of porous media Leichsenring, P. and Serdas, S. and Wallmersperger, T. and Bluhm, J. and Schröder, J. Smart Materials and Structures 26 (2017) Ionomeric polymer-metal composites (IPMCs) consist of an ionomer with bound anionic groups and mobile counterions. They are plated with noble impermeable metal cover layers. By application of an electric voltage, a transport of the mobile ions towards the respective electrode occurs. Due to local electrostatic and ionic forces, a local deformation of the IPMC can be observed. Therefore IPMCs are promising candidates for electrochemical transducers. In the present research, the chemo-electro-mechanical behavior of IPMCs is described within the framework of the theory of porous media. First, the field equations are derived with respect to the second law of thermodynamics. Second, a reduced set of equations for the chemo-electric behavior is formulated and discretized by applying the finite element method. In the numerical investigations a parametric study of the time and space dependent behavior is carried out in order to quantify the influence of different material compositions. Based on this study, the characteristic response of IPMC to the application of an electric voltage can be predicted. Concluding, the obtained computational framework is an excellent tool for the design of electrochemical transducers. © 2017 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/1361-665X/aa590e

• 2017 • 303	FEM study of analyzing the electrical resistance of brazed joint by the 4-wire technique for quality assurance Tillmann, W. and Sievers, N. and Henning, T. and Jakimenko, D. Measurement: Journal of the International Measurement Confederation 104 43-49 (2017) The validation of a brazed work piece requires lot of operating experiences in order to assure a sufficient joint quality for a reliable manufacturing process. In most cases, a quality assurance is only performed by destructive methods to measure the strength of the joint. Conventional non-destructive testing methods such as computer tomography, ultrasonic inspection, and magnetic particle inspection as well as other available optical and thermal methods are commonly not suitable for brazing applications in mass production. This is partly due to the fact that these methods are very expensive or even highly limited when it comes to the detection of critical imperfections. Hence, there is a high demand to investigate alternative non-destructive testing methods. The main focus of this feasibility study is the examination of the electrical resistance behavior of the brazed joint. In this regard, different positions of defects within the filler metal as well as different contact positions for the current supply and voltage measurement of the 4-wire technique are investigated by means of FEM-analyses. A key aspect is the evaluation of the particular voltage distribution within the brazed work pieces as a function of these variations and to generate significant potential differences for the measurement of brazed joints. The results will contribute the design of the resistance measurements on various component geometries to enable a precise quality inspection. © 2017
  	view abstract	doi: 10.1016/j.measurement.2017.03.015

• 2017 • 302	Fibre-reinforced composites with fibre-bending stiffness under azimuthal shear – Comparison of simulation results with analytical solutions Asmanoglo, T. and Menzel, A. International Journal of Non-Linear Mechanics 91 128-139 (2017) In Ref. [1], Spencer and Soldatos proposed an enhanced modelling approach for fibre-reinforced composites which accounts for the fibre-bending stiffness in addition to the directional dependency induced by the fibres. Although analytical solutions for simple geometries have been derived over the past years, often subject to specific assumptions such as small deformation kinematics, the application to more general and non-academic boundary value problems is desirable. Motivated by the latter, the numerical solution of the general system of partial differential equations by means of a multi-field finite element approach is proposed in Ref. [2] and the principal model properties are studied for a specific form of the elastic energy potential. In the present contribution a comparison of the numerical solution by means of the multi-field finite element approach against the analytical solution is presented for the azimuthal shear deformation of a tube-like structure. To this end, the general deformation pattern and especially the distribution of the stress and couple stress tensor are taken into account. We find that, although the analytical solution is derived subject to the assumption of small deformations, whereas the numerical solution is based on the finite strain counterpart of the theory, the simulation results are quasi identical, which verifies the numerical framework proposed. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijnonlinmec.2017.01.001

• 2017 • 301	Finite element analysis of combined forming processes by means of rate dependent ductile damage modelling Kiliclar, Y. and Vladimirov, I.N. and Wulfinghoff, S. and Reese, S. and Demir, O.K. and Weddeling, C. and Tekkaya, A.E. and Engelhardt, M. and Klose, C. and Maier, H.J. and Rozgic̀, M. and Stiemer, M. International Journal of Material Forming 10 73-84 (2017) Sheet metal forming is an inherent part of todays production industry. A major goal is to increase the forming limits of classical deep-drawing processes. One possibility to achieve that is to combine the conventional quasi-static (QS) forming process with electromagnetic high-speed (HS) post-forming. This work focuses on the finite element analysis of such combined forming processes to demonstrate the improvement which can be achieved. For this purpose, a cooperation of different institutions representing different work fields has been established. The material characterization is based on flow curves and forming limit curves for low and high strain rates obtained by novel testing devices. Further experimental investigations have been performed on the process chain of a cross shaped cup, referring to both purely quasi-static and quasi-static combined with electromagnetic forming. While efficient mathematical optimization algorithms support the new viscoplastic ductile damage modelling to find the optimum parameters based on the results of experimental material characterization, the full process chain is studied by means of an electro-magneto-mechanical finite element analysis. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine into the commercial finite element package LS-DYNA. © 2015 Springer-Verlag France
  	view abstract	doi: 10.1007/s12289-015-1278-z

• 2017 • 300	Functional NiTi grids for in situ straining in the TEM Schürmann, U. and Chluba, C. and Wolff, N. and Smazna, D. and Lima de Miranda, R. and Junker, P. and Adelung, R. and Quandt, E. and Kienle, L. Ultramicroscopy 182 10-16 (2017) In situ measurements are a pivotal extension of conventional transmission electron microscopy (TEM). By means of the shape memory alloy NiTi thin film Functional Grids were produced for in situ straining as alternative or at least complement of expensive commercial holders. Due to the martensite-austenite transition temperature straining effects can be observed by use of customary heating holders in the range of 50 to 100  °C. The grids can be produced in diversified designs to fit for different strain situations. Micro tensile tests were performed and compared with finite element simulations to estimate the applied forces on the sample and to predict the functionality of different grid designs. As a first example of this Functional Grid technology, we demonstrate the impact of applying a strain to a network of ZnO tetrapods. © 2017 Elsevier B.V.
  	view abstract	doi: 10.1016/j.ultramic.2017.06.003

• 2017 • 299	Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations Kuzmin, D. and Shadid, J.N. International Journal for Numerical Methods in Fluids (2017) This paper presents new linearity-preserving nodal limiters for enforcing discrete maximum principles in continuous (linear or bilinear) finite element approximations to transport problems with steep fronts. In the process of algebraic flux correction, the oscillatory antidiffusive part of a high-order base discretization is decomposed into a set of internodal fluxes and constrained to be local extremum dim inishing. The proposed nodal limiter functions are designed to be continuous and satisfy the principle of linearity preservation that implies the preservation of second-order accuracy in smooth regions. The use of limited nodal gradients makes it possible to circumvent angle conditions and guarantee that the discrete maximum principle holds on arbitrary meshes. A numerical study is performed for linear convection and anisotropic diffusion problems on uniform and distorted meshes in two space dimensions. © 2017 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/fld.4365

• 2017 • 298	Improving B1 Efficiency and Signal-to-Noise-Ratio of a Surface Coil by a High-Impedance-Surface RF Shield for 7-T Magnetic Resonance Imaging Chen, Z. and Solbach, K. and Erni, D. and Rennings, A. IEEE Transactions on Microwave Theory and Techniques 65 988-997 (2017) In this paper, we present a fundamental investigation to improve the B₁ efficiency and the signal-to-noise ratio (SNR) of a radio frequency (RF) surface coil for ultrahigh-field magnetic resonance imaging (MRI) by utilizing a high-impedance surface (HIS) as the RF shield. An analytical investigation indicates that a circular loop backed by a perfect magnetic conductor (PMC), which is the ideal case of an HIS, suggests an improved magnetic field compared with the case of a perfect electric conductor (PEC) and the case without any shield. This improvement is verified by a full-wave simulation, where the surface coil is modeled by an ideal impressed current model with azimuthal component (Jsurf,α = 1 A/m). The electromagnetic field is effectively shielded out behind the PEC and PMC shields compared with the case without any shield. Furthermore, the surface coil with uniform current distribution and the PMC shield is realized by a series resonant loop structure and a 2-D HIS structure, respectively. Since the normal component of the magnetic field is supported at the surface of an HIS, whereas suppressed by a conventional PEC, the B₁ field in the vicinity of the HIS shield is enhanced compared with the case with a PEC shield. Hence, an improvement on SNR and B₁ efficiency is achieved by utilizing an HIS shield, especially in the regions adjacent to the surface coil. It has been found that the improvement of B₁ efficiency is more prominent than the improvement of SNR due to different normalizations. The difference of peak SAR between considered shields, which is used for B₁ efficiency normalization, is considerably larger than the difference of the power loss within the phantom, which is used for the SNR normalization. The proposed approach is validated by full-wave finite-element method simulations and near-field measurements, which reveal good agreement with each other.
  	view abstract	doi: 10.1109/TMTT.2016.2631169

• 2017 • 297	Investigation on flow-induced vibrations of a steam turbine inlet valve considering fluid-structure interaction effects Domnick, C.B. and Benra, F.-K. and Brillert, D. and Dohmen, H.J. and Musch, C. Journal of Engineering for Gas Turbines and Power 139 (2017) The power output of steam turbines is controlled by steam turbine inlet valves. These valves have a large flow capacity and dissipate a huge amount of energy in throttled operation. The dissipation process generates strong pressure fluctuations resulting in high dynamic forces causing valve vibrations. A brief survey of the literature dealing with valve vibrations reveals that the vibrational problems and damages mostly occur in throttled operation when high speed jets, shocks, and shear layers are present. As previous investigations reveal that a feedback mechanism between the dynamic flow field and the vibrating valve plug exists, the vibrations are investigated with two-way coupled simulations. The fluid dynamics are solved with a scale-adaptive approach to resolve the pressure fluctuations generated by the turbulent flow. The finite element model (FEM) solving the structural dynamics considers both frictional effects at the valve packing and contact effects caused by the plug impacting on the valve bushing. As different flow topologies causing diverse dynamic loads exist, the fluid flow and the structural dynamics are simulated at different operating points. The simulations show that differences to the one-way-coupled approach exist leading to a change of the vibrational behavior. The physics behind the feedback mechanisms causing this change are analyzed and conclusions regarding the accuracy of the one-way-coupled approach are drawn. © 2017 by ASME.
  	view abstract	doi: 10.1115/1.4034352

• 2017 • 296	Investigations on chip flow control for coil edge machining: Untersuchungen zur Kontrolle der Spanabfuhr bei der Bandkantenbearbeitung Tiffe, M. and Vogel, F. and Biermann, D. and Geltz, N. Materialwissenschaft und Werkstofftechnik 48 5-11 (2017) Steel strips are frequently used in the metal working industry for the manufacturing of tubes and bearing sleeves. These steel strips are produced by cold and warm rolling and are commonly coiled up for transportation purposes. Moreover, the obtained coils are split into customized sizes. In order to use the steel strips for further processing the edges need to be machined with respect to deburring and joint preparation. Therefore, specialized machine tools are used which apply common turning inserts with a translational cutting motion. On the one hand this process is high efficient but on the other hand the process reliability is affected by the formation of long continuous chips. In order to meet the requirements for an increased process reliability investigations on chip flow control are carried out with the aid of the finite element method (FEM). The acquired results are presented in this article. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
  	view abstract	doi: 10.1002/mawe.201600733

• 2017 • 295	Linearity-preserving monotone local projection stabilization schemes for continuous finite elements Kuzmin, D. and Basting, S. and Shadid, J.N. Computer Methods in Applied Mechanics and Engineering 322 23-41 (2017) This paper presents some new tools for enforcing discrete maximum principles and/or positivity preservation in continuous piecewise-linear finite element approximations to convection-dominated transport problems. Using a linear first-order advection equation as a model problem, we construct element-level bilinear forms associated with first-order artificial diffusion operators and their two-scale counterparts. The underlying design philosophy is similar to that behind local projection stabilization (LPS) techniques and variational multiscale (VMS) methods. The difference lies in the structure of the local stabilization operator and in the way in which the resolved scales are detected. The proposed stabilization term penalizes the difference between the nodal values and cell averages of the finite element solution in a manner which guarantees monotonicity and linearity preservation. The value of the stabilization parameter is determined using a multidimensional limiter function designed to prevent unresolvable fine scale effects from creating undershoots or overshoots. The result is a nonlinear high-resolution scheme capable of resolving moving fronts and internal/boundary layers as sharp localized nonoscillatory features. The use of variational gradient recovery makes it possible to add high-order background dissipation leading to improved approximation properties in smooth regions. The numerical behavior of the constrained schemes is illustrated by a grid convergence study for stationary and time-dependent test problems in two space dimensions. © 2017 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2017.04.030

• 2017 • 294	Local characterization of light trapping effects of metallic and dielectric nanoparticles in ultra-thin Cu(In,Ga)Se2 solar cells via scanning near-field optical microscopy Song, M. and Yin, G. and Fumagalli, P. and Schmid, M. Proceedings of SPIE - The International Society for Optical Engineering 10114 (2017) Plasmonic and photonic nanoparticles have proven beneficial for solar cells in the aspect of light management. For improved exploitation of nanoparticles in solar cells, it is necessary to reveal the absorption enhancement mechanism from the nanoparticles. In this study, we investigated the nanoparticle-enhanced solar cells in near-field regime with optic and opto-electric scanning near-field optical microscopy (SNOM). The near-field distribution of regularly arranged silver and polystyrene nanoparticles produced by nanosphere lithography on Cu(In,Ga)Se2 (CIGSe) solar cells is characterized using a custom-built SNOM, which gives insight into the optical mechanism of light trapping from nanoparticles to solar cells. On the other hand, the photocurrent of CIGSe solar cells with and without nanoparticles is studied with an opto-electric SNOM by recording the photocurrent during surface scanning, further revealing the opto-electrical influences of the nanoparticles. In addition, finite element method simulations have been performed and agree with the results from SNOM. We found the dielectric polystyrene spheres are able to enhance the absorption and benefit the generation of charge carriers in the solar cells. Copyright © 2017 SPIE.
  	view abstract	doi: 10.1117/12.2253223

• 2017 • 293	Mass lumping for the optimal control of elliptic partial differential equations Rösch, A. and Wachsmuth, G. SIAM Journal on Numerical Analysis 55 1412-1436 (2017) The finite element discretization of a control constrained elliptic optimal control problem is studied. Control and state are discretized by higher order finite elements. The inequality constraints are only posed in the Lagrange points. The computational effort is significantly reduced by a new mass lumping strategy. The main contribution is the derivation of new a priori error estimates up to order h4 on locally refined meshes. Moreover, we propose a new algorithmic strategy to obtain such highly accurate results. The theoretical findings are illustrated by numerical examples. © 2017 Society for Industrial and Applied Mathematics.
  	view abstract	doi: 10.1137/16M1074473

• 2017 • 292	Material flow analysis for the incremental sheet-bulk gearing by rotating tools Wernicke, S. and Sieczkarek, P. and Grodotzki, J. and Gies, S. and Khalifa, N.B. and Tekkaya, A.E. ASME 2017 12th International Manufacturing Science and Engineering Conference, MSEC 2017 collocated with the JSME/ASME 2017 6th International Conference on Materials and Processing 1 (2017) The manufacturing of gear elements by forming offers advantages regarding the resulting mechanical properties of the functional components. One possible approach is offered by the incremental sheet-bulk metal forming of gears using a linear motion punch. This method is highly flexible in terms of shape and position of the functional elements to be produced, but inefficient from an economical point of view due to the high process time. This paper presents a new sheet-bulk gear forming process using rotating tools in order to speed up the manufacturing process of load-Adapted gears. Here, different concepts with rotating tools being synchronized and nonsynchronized to the workpiece are investigated to form highstrength, load-Adapted gears made of bainitic steel BS600. The focus is on the analysis of the occurring material flow which is examined by means of finite element analysis and microstructural investigations to ensure the manufacture of fully functional geared components by this sheet-bulk metal forming process. ©2017 ASME.
  	view abstract	doi: 10.1115/MSEC20173029

• 2017 • 291	On the Design, Characterization and Simulation of Hybrid Metal-Composite Interfaces Kießling, R. and Ihlemann, J. and Pohl, M. and Stommel, M. and Dammann, C. and Mahnken, R. and Bobbert, M. and Meschut, G. and Hirsch, F. and Kästner, M. Applied Composite Materials 24 251-269 (2017) Multi-material lightweight designs are a key feature for the development of innovative and resource-efficient products. In the development of a hybrid composite, the interface between the joined components has to be considered in detail as it represents a typical location of the initialization of failure. This contribution gives an overview of the simulative engineering of metal-composite interfaces. To this end, several design aspects on the microscale and macroscale are explained and methods to model the mechanical behavior of the interface within finite element simulations. This comprises the utilization of cohesive elements with a continuum description of the interface. Likewise, traction-separation based cohesive elements, i.e. a zero-thickness idealization of the interface, are outlined and applied to a demonstration example. Within these finite element simulations, the constitutive behavior of the connected components has to be described by suitable material models. Therefore, inelastic material models at large strains are formulated based on rheological models. © 2016 Springer Science+Business Media Dordrecht
  	view abstract	doi: 10.1007/s10443-016-9526-z

• 2017 • 290	On the influence of microcantilever pre-crack geometries on the apparent fracture toughness of brittle materials Brinckmann, S. and Matoy, K. and Kirchlechner, C. and Dehm, G. Acta Materialia 136 281-287 (2017) Focused ion beam machined microcantilevers are frequently used for fracture mechanics analysis of inhomogeneous solids at the micrometer scale. A finite element method study about the influence of the pre-crack geometry on the apparent fracture toughness is provided. We discuss the influence of material bridges and the effect of rounded pre-crack corners when two dimensional models are employed to evaluate the fracture toughness. We conclude with a guideline for introducing an optimized pre-crack. © 2017 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2017.07.014

• 2017 • 289	On the numerical implementation of thermomechanically coupled distortional hardening Bartels, A. and Mosler, J. International Journal of Plasticity 96 182-209 (2017) In contrast to the by now classic isotropic and kinematic hardening, the more general framework of distortional hardening characterised by an evolution of the yield surface's shape can capture the effect of texture evolution on the macroscopic response. Although different distortional hardening models can indeed be found in the literature, efficient numerical implementations of such models are still missing. This statement proves particularly true within a thermomechanically coupled framework which is important for most technologically relevant processes - such as for deep drawing. Accordingly, this paper deals with an efficient finite element formulation for distortional hardening within a thermomechanically coupled framework. As a first step towards this target, the recently advocated isothermal distortional hardening framework Shi et al. (2014) is extended to the thermomechanically coupled setting. In order to avoid an over-estimation of the temperature increase due to plastic deformation, the initial yield stress is decomposed into a classic dissipative part and a non-classic energetic part. By doing so, the restrictions imposed by thermodynamical principles are fulfilled and simultaneously realistic temperature predictions are obtained. For the resulting model, an efficient numerical implementation is proposed. By developing a suitable time integration scheme for the evolution equations of the fourth-order tensor describing the distortional hardening, a return-mapping scheme for updating the internal variables is derived which shows the same numerical complexity as a return-mapping scheme for purely isotropic hardening. This efficient return-mapping scheme is finally incorporated into a thermomechanically coupled finite element formulation, and the resulting set of equations is fully implicitly and monolithically solved by means of a Newton-type iteration. Several numerical complex examples demonstrate the capabilities of the distortional hardening model as well as the robustness and efficiency of the numerical formulation. © 2017 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijplas.2017.05.003

• 2017 • 288	On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations Schröder, J. and Viebahn, N. and Wriggers, P. and Auricchio, F. and Steeger, K. Computational Mechanics 1-14 (2017) In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075–1092, 2005, Comput Mech 52:1153–1167, 2013). © 2017 Springer-Verlag Berlin Heidelberg
  	view abstract	doi: 10.1007/s00466-017-1415-2

• 2017 • 287	Perovskite Nanopillar Array Based Tandem Solar Cell Raja, W. and Schmid, M. and Toma, A. and Wang, H. and Alabastri, A. and Proietti Zaccaria, R. ACS Photonics 4 2025-2035 (2017) One of the promising approaches to improve the efficiency of conventional single-crystalline silicon (c-Si) solar cells is their integration in a tandem arrangement. In this perspective, inorganic-organic perovskites are an ideal blend of materials to combine with c-Si owing to their complementary light absorption characteristics. Even though interesting and promising combinations of perovskite/c-Si-based solar cells have been presented, their overall efficiency has been limited by the photocurrent reduction occurring in both perovskite and silicon due mostly to reflection and parasitic losses. Here, we envision and model a new design strategy for an efficient light-to-current conversion through the use of a nanopillar array based perovskite/c-Si tandem solar cell. The optical-electrical performance of the proposed architecture is analyzed by a 3D finite-element numerical model. In particular, we have searched for the best optical enhancement conditions through the tuning of the cell geometrical parameters, demonstrating the importance of optical resonances. Afterward, we have evaluated the electrical response of the optimized structures in a four-terminal (4-T) configuration by studying the current-voltage characteristics and power conversion efficiency. In particular, the introduced solar cell yields a conversion efficiency of 27%, with contributions of 18.5% and 8.51% from perovskite and c-Si, respectively. We have compared our proposed nanopatterned design with its planar counterpart characterized by the same quantity of active material, obtaining a relative efficiency enhancement of 21%. Importantly, the conversion efficiency of our proposed design surpasses the efficiency of single-junction perovskite and c-Si solar cells, and, similarly, it represents a new achievement for 4-T perovskite/c-Si tandem solar cells. © 2017 American Chemical Society.
  	view abstract	doi: 10.1021/acsphotonics.7b00406

• 2017 • 286	Pre- and post-buckling behavior of bi-crystalline micropillars: Origin and consequences Kirchlechner, C. and Toth, F. and Rammerstorfer, F.G. and Fischer, F.D. and Dehm, G. Acta Materialia 124 195-203 (2017) Compression of micropillars is routinely used to measure the material response under uniaxial load. In bi-crystalline pillars an S-shaped grain-boundary together with an S-shaped pillar is often observed after deformation raising the question of its origin and consequences for stress-strain materials data. In addition to dislocation and grain-boundary based mechanisms, this observation can be caused by buckling and subsequent post-buckling deformation. Deviations from the classical pre- and post-buckling deformation behavior are assigned to imperfections, which are categorized in extrinsic and intrinsic imperfections in this work. In the present paper, the S-shaped actual deformation state is particularly promoted by an intrinsic imperfection, caused by a material heterogeneity (due to the bi-crystal arrangement). This kind of deformation behavior is investigated by micro-compression experiments on 7 × 7 × 21 μm3 sized bi-crystal copper pillars with nearly elastic (axial Young's modulus) homogeneity and identical Schmid factors for both grain orientations. Complementary finite element simulations are performed, in which also the role of friction and of an extrinsic imperfection in the form of initial misalignment of the loading on the S-shape are considered. There, a material model describing the flow stress distribution caused by a dislocation pile-up at the grain-boundary is applied. Finally, suggestions to prevent buckling and, thus, transversal post-buckling displacements during micropillar compression tests are given with the goal to extract engineering stress-strain curves. © 2016 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2016.10.075

• 2017 • 285	Prediction of plasticity and damage initiation behaviour of C45E + N steel by micromechanical modelling Wu, B. and Vajragupta, N. and Lian, J. and Hangen, U. and Wechsuwanmanee, P. and Münstermann, S. Materials and Design 121 154-166 (2017) For large-scale engineering applications, macroscopic phenomenological damage mechanics models with less complexity are usually applied due to their high computational efficiency and simple implementation procedures in finite element simulations. Compared with micromechanical models, however, they also have a significant disadvantage, namely the lack of microstructure sensitivity. This work aims to develop a method to integrate the influence of microstructural features into the parameter calibration of a stress-state-dependent damage mechanics model (the modified Bai-Wierzbicki model) for a C45E + N steel. For this purpose, virtual experiments are performed on an artificial microstructure model to derive the plasticity and damage initiation behaviour for the investigated material. A crystal plasticity model for ferrite along with an empirical strain hardening law for pearlite are assigned to the corresponding constituents in the artificial microstructure model to define their material properties. Nanoindentation tests and numerical analysis are used to calibrate the parameters of the crystal plasticity model. By applying different boundary conditions to the artificial microstructure model, both the plasticity and the damage initiation behaviour under different stress states are calibrated by the virtual experiments. In addition, this approach is also applied to investigating the influence of microstructure on plasticity and damage initiation. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.matdes.2017.02.032

• 2017 • 284	Prismatic semi-analytical elements for the simulation of linear elastic problems in structures with piecewise uniform cross section Krome, F. and Gravenkamp, H. and Birk, C. Computers and Structures 192 83-95 (2017) This work addresses the computation of stiffness matrices for general prismatic structures with an arbitrary cross section. The presented approach is based on the scaled boundary finite element method (SBFEM), a semi-analytical method, which can be used to model structures by only discretizing the boundary of a domain. For prismatic structures, the process is further simplified, as only the cross section of the structure has to be discretized. Thus, a particular semi-analytical finite element is constructed for bounded and unbounded domains. The proposed approach leads to a frequency-dependent stiffness matrix. This stiffness matrix can easily be coupled to other prismatic SBFEM domains or general SBFEM domains. Necessary modifications to include forces along the scaling direction, such as body loads, are addressed. The results of the proposed approach are compared to those of traditional FEM models obtained using commercially available software. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compstruc.2017.06.015

• 2017 • 283	Recurrent neural networks and proper orthogonal decomposition with interval data for real-time predictions of mechanised tunnelling processes Freitag, S. and Cao, B.T. and Ninić, J. and Meschke, G. Computers and Structures (2017) A surrogate modelling strategy for predictions of interval settlement fields in real time during machine driven construction of tunnels, accounting for uncertain geotechnical parameters in terms of intervals, is presented in the paper. Artificial Neural Network and Proper Orthogonal Decomposition approaches are combined to approximate and predict tunnelling induced time variant surface settlement fields computed by a process-oriented finite element simulation model. The surrogate models are generated, trained and tested in the design (offline) stage of a tunnel project based on finite element analyses to compute the surface settlements for selected scenarios of the tunnelling process steering parameters taking uncertain geotechnical parameters by means of possible ranges (intervals) into account. The resulting mappings of time constant geotechnical interval parameters and time variant deterministic steering parameters onto the time variant interval settlement field are solved offline by optimisation and online by interval analyses approaches using the midpoint-radius representation of interval data. During the tunnel construction, the surrogate model is designed to be used in real-time to predict interval fields of the surface settlements in each stage of the advancement of the tunnel boring machine for selected realisations of the steering parameters to support the steering decisions of the machine driver. © 2017 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compstruc.2017.03.020

• 2017 • 282	Reliable a posteriori error estimation for state-constrained optimal control Rösch, A. and Siebert, K.G. and Steinig, S. Computational Optimization and Applications 1-42 (2017) We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introduce an adaptation strategy for the regularisation parameter. © 2017 Springer Science+Business Media New York
  	view abstract	doi: 10.1007/s10589-017-9908-7

• 2017 • 281	Segmented and mathematical model for 3D FEM tapping simulation to predict the relative torque before tool production Oezkaya, E. and Biermann, D. International Journal of Mechanical Sciences 128-129 695-708 (2017) The conventional tapping tool development consists of costly investigative experiments. The development time and cost can be significantly reduced, if these test were replaced by virtual analyses, before the tool prototypes are fabricated. Compared to turning, milling and drilling, in which many valid simulative methods have been established, the tapping process has been given rather little research attention. In this paper an approach is presented, which could be used during the design phases, to predict the relative torque, so that resources, energy and cost can be saved. Based on a simulated reference model, which is in good agreement with corresponding experimental results, the problem of a long computing time could be solved by using a proper segmentation method, which offers a process simulation along the whole chamfer length. With an according mathematical model, the discontinuous torque curve could be summarized to a total load cycle. © 2017 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijmecsci.2017.04.011

• 2017 • 280	Sensitivity of structural response in context of linear and non-linear buckling analysis with solid shell finite elements Radau, L. and Gerzen, N. and Barthold, F.-J. Structural and Multidisciplinary Optimization 55 2259-2283 (2017) The paper is concerned with the sensitivity analysis of structural responses in context of linear and non-linear stability phenomena like buckling and snapping. The structural analysis covering these stability phenomena is summarised. Design sensitivity information for a solid shell finite element is derived. The mixed formulation is based on the Hu-Washizu variational functional. Geometrical non-linearities are taken into account with linear elastic material behaviour. Sensitivities are derived analytically for responses of linear and non-linear buckling analysis with discrete finite element matrices. Numerical examples demonstrate the shape optimisation maximising the smallest eigenvalue of the linear buckling analysis and the directly computed critical load scales at bifurcation and limit points of non-linear buckling analysis, respectively. Analytically derived gradients are verified using the finite difference approach. © 2016 Springer-Verlag Berlin Heidelberg
  	view abstract	doi: 10.1007/s00158-016-1639-3

• 2017 • 279	Simulation based evaluation of time-variant loadings acting on tunnel linings during mechanized tunnel construction Ninić, J. and Meschke, G. Engineering Structures 135 21-40 (2017) In the design of machine driven tunnels, the loadings acting on the segmental lining are often adopted according to simplified assumptions, which improperly reflect the actual loading on the linings developing during the construction of a bored tunnel. A coupled 3D Finite Element model of the tunnel advancement process including the ring-wise installation of the lining and the hardening process of the grouting material serves as the basis for the analysis of the actual spatio-temporal evolution of the loading on the lining during tunnel construction. The distribution of the loadings in the different construction phases is calculated using a modified surface-to-surface contact condition imposed between the solidifying grouting material in the tail gap and the lining elements. An extensive parametric study investigates the influence of the initial grouting pressure, the pressure gradient, the temporal stiffness evolution, the soil permeability as well as the interface conditions between the grouting material and the tunnel shell on the temporal evolution of the loading on linings. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.engstruct.2016.12.043

• 2017 • 278	Size- and density-controlled deposition of Ag nanoparticle films by a novel low-temperature spray chemical vapour deposition method—research into mechanism, particle growth and optical simulation Liu, Y. and Plate, P. and Hinrichs, V. and Köhler, T. and Song, M. and Manley, P. and Schmid, M. and Bartsch, P. and Fiechter, S. and Lux-Steiner, M.C. and Fischer, C.-H. Journal of Nanoparticle Research 19 (2017) Ag nanoparticles have attracted interest for plasmonic absorption enhancement of solar cells. For this purpose, well-defined particle sizes and densities as well as very low deposition temperatures are required. Thus, we report here a new spray chemical vapour deposition method for producing Ag NP films with independent size and density control at substrate temperatures even below 100 °C, which is much lower than for many other techniques. This method can be used on different substrates to deposit Ag NP films. It is a reproducible, low-cost process which uses trimethylphosphine (hexafluoroacetylacetonato) silver as a precursor in alcoholic solution. By systematic variation of deposition parameters and classic experiments, mechanisms of particle growth and of deposition processes as well as the low decomposition temperature of the precursor could be explained. Using the 3D finite element method, absorption spectra of selected samples were simulated, which fitted well with the measured results. Hence, further applications of such Ag NP films for generating plasmonic near field can be predicted by the simulation. © 2017, Springer Science+Business Media Dordrecht.
  	view abstract	doi: 10.1007/s11051-017-3834-6

• 2017 • 277	Tool wear-dependent process analysis by means of a statistical online monitoring system Finkeldey, F. and Hess, S. and Wiederkehr, P. Production Engineering 11 677-686 (2017) Simulating milling processes can provide numerous optimization possibilities regarding process stability and surface quality. In tool and die manufacturing often long-running processes are necessary. In contrast to very time-consuming Finite-Element-based approaches, geometric physically-based simulation systems allow predictions for such processes because of their relatively short runtime. The machining of hardened material and varying engagement conditions between the tool and the workpiece provoke a gradually increasing influence of tool wear on the cutting edges. To consider these alterations while simulating milling processes, different approaches can be used. Because of the complex characteristics of tool wear, methods, which result in an increased simulation runtime, have to be used for the geometric modeling of tool wear. In this paper, a novel approach for monitoring a milling process is presented, which utilizes an online-selection of pre-calculated simulation data to predict the process stability for different states of tool wear. To achieve this, measured data are compared to simulated data, which result from offline simulation conductions for each defined state of tool wear. As tool wear changes when the process is progressing, different simulation data for different states of tool wear have to be selected to ensure a valid stability prediction. © 2017, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-017-0773-0

• 2016 • 276	A fast three-dimensional model for strip rolling Overhagen, C. and Mauk, P.J. Key Engineering Materials 716 566-578 (2016) Rolling Models have come a long way from the first empirical relations about forward slip and bite conditions to their current state, which allows local quantities to be calculated in two and three dimensions. In this paper, state-of-The-Art of analytical modelling of the rolling process is shown with a fully three-dimensional rolling model for hot and cold strip rolling with stress distributions in the longitudinal, vertical and lateral directions. For this purpose, von Karman's strip approach is extended to account for the stress gradient in lateral direction, as was already shown in different papers. The stress gradient in the vertical (through-Thickness) direction is introduced by a modern implementation of Orowan's inhomogeneous deformation theory. The local stress distributions are compared to results from Finite-Element Calculations obtained with modern FEM codes. It will be shown, under which circumstances expensive FEM calculations can be replaced by simpler models like the one proposed here, which are more time and cost-effective without a significant loss in result precision. The rolling model is extended with a Finite Element Beam Model for work and backup roll deformation, as well as local work roll flattening and thermal crown for hot rolling. The Effects of those features on stress distribution and exit strip profile are shown for hot and cold rolling. © 2016 Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.716.566

• 2016 • 275	A finite element model for propagating delamination in laminated composite plates based on the Virtual Crack Closure method Marjanović, M. and Meschke, G. and Vuksanović, D. Composite Structures 150 8-19 (2016) In the paper, a simple and efficient algorithm to track a moving delamination front of arbitrary shape, using a laminated finite plate element model in conjunction with the Virtual Crack Closure Technique (VCCT), is proposed. The solution requires the calculation of the virtually closed area in front of the delamination, which is approximated by means of a 6-node-polygon, the delamination opening behind this front and the reaction forces in the nodes at the delamination front. These quantities are calculated in a local coordinate system (LCS) defined in the nodes along the delamination front. Using the proposed algorithm, arbitrary meshes composed of 4- and 9-node quadrilateral finite elements can be considered. The proposed model is developed in the context of a layered finite element plate model. To prevent interlaminar penetration of adjacent layers in the delaminated region, an algorithm recently proposed by Marjanović et al. (2015) is adopted. The model performance is demonstrated by re-analyses of the Double-Cantilever-Beam problem, for which analytical solutions exist, and by transient analyses of laminated composite plates with propagating delamination fronts. © 2016 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compstruct.2016.04.044

• 2016 • 274	A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations Pierce, D.M. and Unterberger, M.J. and Trobin, W. and Ricken, T. and Holzapfel, G.A. Biomechanics and Modeling in Mechanobiology 15 229-244 (2016) The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress. © 2015, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s10237-015-0685-x

• 2016 • 273	A new mixed finite-element approach for the elastoplastic analysis of Mindlin plates Kutlu, A. and Meschke, G. and Omurtag, M.H. Journal of Engineering Mathematics 99 137-155 (2016) The objective of this paper is to develop an accurate and efficient solution procedure for elastoplastic problems in structural mechanics in the framework of a two-field mixed variational principle. A novel solution algorithm is proposed and applied to the elastoplastic analysis of Mindlin plates. The Hellinger–Reissner principle is adopted to obtain the global finite-element equations of the problem. Instead of a static condensation, the stress-type field variables are preserved during the solution. According to the proposed approach, the strain increments within a nonlinear solution step are obtained directly at the nodal points from matrix operations instead of gradients of a displacement field. In the present implementation, the von Mises yield criterion with linear hardening is adopted. For the integration of the elastoplastic constitutive rate equations at the nodal points, a 3D fully implicit algorithm is employed. A layered approach is followed to enable the resolution of the plastic strains through the plate thickness. The mixed formulation of the Mindlin plate theory is shear-locking free by construction. The proposed solution strategy is verified by solving several benchmark problems that demonstrate the high accuracy and convergence rate of the presented layered mixed formulation for elastoplastic analyses. © 2015, Springer Science+Business Media Dordrecht.
  	view abstract	doi: 10.1007/s10665-015-9825-7

• 2016 • 272	A non-rigid registration method for the efficient analysis of shape deviations in production engineering applications Schweinoch, M. and Schäfer, R. and Sacharow, A. and Biermann, D. and Buchheim, C. Production Engineering 10 137-146 (2016) A common requirement in production engineering applications is the comparison of designed and as-built parts. Due to manufacturing influences and geometric changes incorporated during physical prototyping, there may exist significant deviations between these shapes. In order to compensate the manufacturing influences and to incorporate geometric changes into the virtual design, a detailed analysis of the deviations is required. The designed (or reference) shape is usually given in terms of a CAD data set, while the as-built (or test) geometry is acquired by digitization of the physically manufactured prototype. Given these two geometries, one is faced with the problem of determining points of correspondence between them. This is also referred to as registration. In rigid registration, correspondences are determined by first aligning the two geometries rigidly using a best-fit approach. Subsequently, the correspondences between the aligned geometries are determined by finding for a point of one shape the closest surface point on the other. While several efficient rigid registration methods exist, they do not account for shape deviations, resulting in inaccurate correspondences when applied to such geometries. Non-rigid registration methods, conversely, do not search for a global best-fit alignment, but instead affect a deformation of the one geometry onto the other, allowing for an improved correspondence calculation. Most published state-of-the-art non-rigid registration methods are not necessarily applicable to production engineering scenarios due to, among others, the typical data sizes and the required level of accuracy in the correspondence determination. A further hindrance is their lack of shop-floor applicability, attributable to their calculation times as well as to the expertise that their application requires on behalf of the user. This paper presents a non-rigid registration method for the efficient calculation of correspondences in production engineering scenarios. By combination of several established methods from the field of geometric modeling, the test shape is iteratively deformed onto the reference shape. When the deformed test shape satisfiably approximates the reference geometry, correspondences are determined by projection. The procedure is applied to the problem of springback behavior, which arises in sheet metal forming. A validation of the method is achieved by comparing the calculated correspondences with the ideal correspondences, as determined by finite element simulation. © 2016, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-016-0660-0

• 2016 • 271	A phase field model for damage in elasto-viscoplastic materials Shanthraj, P. and Sharma, L. and Svendsen, B. and Roters, F. and Raabe, D. Computer Methods in Applied Mechanics and Engineering 312 167-185 (2016) A phase field method for brittle fracture is formulated for a finite strain elasto-viscoplastic material using a novel obstacle phase field energy model. The obstacle energy model results in a crack profile with compact support, and thus gives a physically realistic description of the material behaviour at the vicinity of the crack tip. The resulting variational inequality is discretised by a finite element method, and is efficiently solved using a reduced space NEWTON method. The solution accuracy and numerical performance of this method is compared with a conventional phase field energy model for brittle fracture through representative examples, and a significant reduction in the numerical solution cost is demonstrated. © 2016 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2016.05.006

• 2016 • 270	Accurate springback prediction in deep drawing using pre-strain based multiple cyclic stress-strain curves in finite element simulation Ul Hassan, H. and Traphöner, H. and Güner, A. and Tekkaya, A.E. International Journal of Mechanical Sciences 110 229-241 (2016) The focus of this work is the accurate prediction of springback in deep drawing for DP600 material. A novel method is used for the characterization of material which leads to simultaneous generation of multiple cyclic stress-strain curves with different magnitude of plastic strains in a single experiment. An enhanced finite element simulation model is also presented which is capable of application of these multiple pre-strain based cyclic stress-strain curves in a single simulation. After each increment, the elements are grouped based on their pre-strain levels independent of the element location and assigned the relevant stress-strain curve. Simulations are performed with the Yoshida Uemori (YU) model, Chaboche-Roussilier (CR) model and an isotropic hardening model for the prediction of springback for hat geometry and tunnel geometry. The maximum deviation between the geometries of experiment and the springback simulation for hat and tunnel geometry for model with multiple cyclic stress-strain curves is 0.8 mm and 1.6 mm respectively in contrast to the deviation of 1.8 mm and 4.2 mm for the simulation model with single cyclic stress-strain curve respectively. It is shown that the simulation model with multiple cyclic stress-strain curves predicts the springback more accurately than the other models with single stress-strain curve. © 2016 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijmecsci.2016.03.014

• 2016 • 269	Adaptive coarse spaces for FETI-DP in three dimensions Klawonn, A. and Kühn, M. and Rheinbach, O. SIAM Journal on Scientific Computing 38 A2880-A2911 (2016) An adaptive coarse space approach including a condition number bound for dual primal finite element tearing and interconnecting (FETI-DP) methods applied to three dimensional problems with coefficient jumps inside subdomains and across subdomain boundaries is presented. The approach is based on a known adaptive coarse space approach enriched by a small number of additional local edge eigenvalue problems. These edge eigenvalue problems serve to make the method robust and permit a condition number bound which depends only on the tolerance of the local eigenvalue problems and some properties of the domain decomposition. The introduction of the edge eigenvalue problems thus turns a well-known condition number indicator for FETI-DP and balancing domain decomposition by constraints (BDDC) methods into a condition number estimate. Numerical results are presented for linear elasticity and heterogeneous materials supporting our theoretical findings. The problems considered include those with random coefficients and almost incompressible material components. © 2016 Axel Klawonn, Martin Kühn, Oliver Rheinbach.
  	view abstract	doi: 10.1137/15M1049610

• 2016 • 268	Advanced finite element modeling of excavation and advancement processes in mechanized tunneling Alsahly, A. and Stascheit, J. and Meschke, G. Advances in Engineering Software 100 198-214 (2016) Mechanized tunneling is characterized by complex interactions between the shield machine and the surrounding ground during the TBM advancement process. In this paper, a new computational framework is developed to enable an efficient and realistic three-dimensional modeling of the tunneling process for arbitrary alignments using the finite element method. A new steering algorithm for the advancement of the Tunnel Boring Machine (TBM) for arbitrary alignments during shield tunneling is incorporated in the proposed model. This algorithm simulates the shield behavior and accordingly provides the numerical model with the required information to keep the TBM on track during the simulation. However, the utilization of this algorithm is only possible using a finite element discretization which adapts to the actual motion path of the shield machine. For this purpose, a re-meshing technique is proposed in order to automate the process of mesh generation in the vicinity of the tunnel face, denoted as the region of interest, within the advancing process. The combination of a computational steering algorithm and a 3D automatic adaptive mesh generation procedure form a novel framework for process oriented finite element simulations of the mechanized tunnel construction process. The applicability of the proposed modeling technique for predicting the shield behavior and the soil-tunnel interactions during tunneling along curved alignments is demonstrated by means of selected examples. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.advengsoft.2016.07.011

• 2016 • 267	Advanced Simulation-based Design of High Performance Machining Processes Biermann, D. and Bleckmann, T. and Schumann, S. and Iovkov, I. Procedia CIRP 46 165-168 (2016) The development of high performance machining processes is a key aspect to achieve higher productivity, efficiency and performance in modern production systems. In order to reduce the corresponding effort and costs, simulation systems are one possibility to support the design and the optimization of manufacturing processes. In this article, three different application examples with respect to milling, grinding and deep-hole drilling operations are presented. In this context, both finite-element and geometric-kinematic simulation approaches are applied to model the different challenging issues of the corresponding machining process. © 2016 The Authors.
  	view abstract	doi: 10.1016/j.procir.2016.03.167

• 2016 • 266	Anwendungen einer Näherungslösung für die Grundwasserströmung bei Restwasserhaltung Perau, E. and Meteling, N. Bautechnik 93 636-646 (2016) Application of an approximate solution for groundwater flow at a residual water drainage system. If excavations go below the groundwater table, a proven option is to embed the pit wall in a less permeable soil stratum and to operate a residual water drainage system. As an underflow of the pit walls occurs in these constructions the flow field has to be determined for various calculations and stability verifications. For instance, hydraulic gradients, discharge velocities as well as potential heads and pore-water pressures have to be calculated. These values are necessary to determine the earth and water pressure distribution. They can also be used for the verification of hydraulic failure, internal erosion and failure of the earth support, as well as for the calculation of groundwater influx. By defining the hydraulic problem as a parameterized boundary value problem and using the Finite Element Method (FEM) an analytical approximate solution was formulated. This solution is valid for both plane and axisymmetric state with isotropic and anisotropic subsoil. It is used for the calculation of the hydraulic head distribution on the level of the wall toe and along the inner surface of the wall. These approximate solutions are evaluated for the verification against hydraulic heave and for the calculation of the maximum gradient at the change of layer in area of the excavation pit and the determination of the required embedment depth. Copyright © 2016 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin
  	view abstract	doi: 10.1002/bate.201600037

• 2016 • 265	Comparison of fatigue life assessment by analytical, experimental and damage accumulation modelling approach for steel SAE 1045 Imran, M. and Siddique, S. and Guchinsky, R. and Petinov, S. and Walther, F. Fatigue and Fracture of Engineering Materials and Structures 39 1138-1149 (2016) Fatigue life assessment for two-phase steel SAE 1045 has been carried out by experimental and simulation techniques. Analytical approach, termed as fatigue lifetime calculation, was employed making use of a load increase testing procedure and constant amplitude tests equipped with measurement techniques – plastic strain amplitude, change in temperature and change in electrical potential difference. The predicted fatigue life has been validated by constant amplitude tests and compared with fatigue life estimation by microstructure-based simulation. Simulation has been carried out over the complete cross section of the specimen. The simulation uses damage accumulation in the gage section of the specimen culminating in the macro-crack propagation, taking into account the inhomogeneous fatigue resistance of the material element. The results show that at the initial intervals of high cycle fatigue range at relatively higher stress amplitudes, the experimental and simulation results are in agreement; whereas in the (high cycle fatigue) region at relatively low stress amplitudes, the simulation results were found more optimistic and the corresponding fatigue scatter is also increased. Each scatter is attributed to the relatively small number of analysed models of the material structure. Scanning electron microscope was used to determine volume fraction of the microstructure for simulation. Fatigue fracture surface analysis shows that crack initiated from internal defect of material and crack propagation is driven by silicon oxide inclusion. © 2016 Wiley Publishing Ltd.
  	view abstract	doi: 10.1111/ffe.12426

• 2016 • 264	Computational modelling of wear – application to structured surfaces of elastoplastic tools Berthelsen, R. and Wilbuer, H. and Holtermann, R. and Menzel, A. GAMM Mitteilungen 39 210-228 (2016) Sheet bulk metal forming processes are applied in order to produce tailored workpieces at high quality. Thereby, effort is made to optimise frictional and wear behaviour by designing the structures of the contact surfaces. Numerical process analysis can evoke a deeper under-standing of the functionality of such surface structures. In this contribution, a finite element framework for the simulation of wear and the determination of effective frictional behaviour of structured surfaces at finite deformations is proposed. The modelling of wear is realised by pre- and postprocessing of an underlying representative contact problem at the meso-scale. Thereby, elasto-plastic material behaviour is assumed. A number of simulations with different parameterisations of a sinusoidal contact surface are carried out in order to demonstrate the influence of surface topology, which additionally depends on the state of wear, on the effective frictional behaviour. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). Copyright © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/gamm.201610013

• 2016 • 263	Crystal plasticity modeling of size effects in rolled multilayered Cu-Nb composites Jia, N. and Raabe, D. and Zhao, X. Acta Materialia 111 116-128 (2016) We present size-dependent crystal plasticity finite element simulations of the deformation microstructure, plastic flow and texture evolution in multilayered Cu-Nb composites during cold rolling. The model is based on a constitutive framework incorporating thermally activated dislocation slip, mechanical twinning and non-crystallographic shear banding. It also accounts for the dislocation density evolution and its dependence on initial grain size. By performing a series of quadricrystal simulations considering characteristic heterophase microstructures, the underlying micromechanics and texture of the composites are explored. Significant shear banding occurs in both phases, primarily determined by their initial orientations. For each phase, the activation of shear banding is also affected by the mechanical properties and orientations of the adjacent phase. For composites with an initial single layer thickness of 35 μm or 4 μm, the layer thickness reduction after rolling is non-uniform and the typical rolling textures for bulk pure metals develop in the respective phases. For the 75 nm initial single layer thickness composite, both phases are reduced uniformly in thickness and the initial orientations prevail. The predictions agree well with experimental observations in cold-rolled Cu-Nb thin films. The simulations reveal that for the composites with initial single layer thickness of micrometer scale, dislocation slip is the dominant deformation mechanism although shear banding increasingly carries the deformation at larger strains. For the samples with initial single layer thickness of a few tens of nanometers, shear banding and dislocation slip are the dominant mechanisms. This transition in deformation characteristics leads to different textures in micrometer- and nanometer-scaled multilayers. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.actamat.2016.03.055

• 2016 • 262	Deep drawing of high-strength tailored blanks by using tailored tools Mennecart, T. and Ul Hassan, H. and Güner, A. and Khalifa, N.B. and Hosseini, M. Materials 9 (2016) In most forming processes based on tailored blanks, the tool material remains the same as that of sheet metal blanks without tailored properties. A novel concept of lightweight construction for deep drawing tools is presented in this work to improve the forming behavior of tailored blanks. The investigations presented here deal with the forming of tailored blanks of dissimilar strengths using tailored dies made of two different materials. In the area of the steel blank with higher strength, typical tool steel is used. In the area of the low-strength steel, a hybrid tool made out of a polymer and a fiber-reinforced surface replaces the steel half. Cylindrical cups of DP600/HX300LAD are formed and analyzed regarding their formability. The use of two different halves of tool materials shows improved blank thickness distribution, weld-line movement and pressure distribution compared to the use of two steel halves. An improvement in strain distribution is also observed by the inclusion of springs in the polymer side of tools, which is implemented to control the material flow in the die. Furthermore, a reduction in tool weight of approximately 75%can be achieved by using this technique. An accurate finite element modeling strategy is developed to analyze the problem numerically and is verified experimentally for the cylindrical cup. This strategy is then applied to investigate the thickness distribution and weld-line movement for a complex geometry, and its transferability is validated. The inclusion of springs in the hybrid tool leads to better material flow, which results in reduction of weld-line movement by around 60%, leading to more uniform thickness distribution. © 2016 by the authors.
  	view abstract	doi: 10.3390/ma9020077

• 2016 • 261	Depsim: Numerical 3D-simulation of the water, gas and solid phase in a landfill Schmuck, S. and Werner, D. and Widmann, R. and Ricken, T. International Journal of Sustainable Development and Planning 11 694-699 (2016) The model depSIM is a dump simulation model, which allows a detailed and time-scaled focus into the complex processes of a landfill. Description of the mechanical model: The biological, chemical and physical processes in the waste body are closely connected with each other and can be described mechanically. Therefore, a number of differential equations are needed and implemented in the model. The porous media body is examined under the acceptance of a compressible gas phase, a materially incompressible solid state, an organic phase and a liquid phase. For the verification of the numerical model the long-time behaviour (100 years) was simulated. Further details about the model and the mechanical background are summarized in Robeck, Ricken et Widmann: A finite element simulation model of biological conversion processes in landfills [1]. Use potentials: The developed model allows a differentiated, time wise and locally calculation and representation of the temperature, the organic conversion rate, the local pressure ratios and the gas current speeds. There were several case studies with the depSIM model in Germany which show the correlation between the temperature, gas production and gas potential. Therefore three different landfills were evaluated. Here, in the correlation between measured temperature in the landfill body and the temperature in the model was shown. The average divergence between both was less than 2 degree. By the detailed calculation of the gas speeds in every point of the dump an essential improvement arises compared with conventional arithmetic models for gas forecast and gas capture. These forecast models are based on estimated initial parameters. This allows only forecasts for a complete dump or a dump segment, but allows no coupled calculation of the relevant parameters. The model depSIM offers a spatially differentiated consideration of the gas production. However, just a spatially exact, quantitative forecast of the gas production is necessary for dump operator and authorities. The right forecast is elementary for the right dimensioning of the gas collection system and gas treatment and the possible use in combined heat and power units. All gas streams can be shown with the simulation model along the dump surface spatially and time wise differentiated. This allows a locally differentiated dump gas management with a division in areas with active or passive gas collection or to estimate the feasibility of a methane oxidation layer. © 2016 WIT Press.
  	view abstract	doi: 10.2495/SDP-V11-N5-694-699

• 2016 • 260	Detection of damage to reinforced-concrete structures using piezoelectric smart aggregates Stojić, D. and Nestorović, T. and Marković, N. and Cvetković, R. and Stojić, N. Gradjevinar 68 371-380 (2016) The implementation of active monitoring systems to diagnose damage to reinforced concrete structures using piezoelectric smart aggregates, and based on wave propagation, ranks among the world's most advanced research activities. Original models, with parametric analysis of the damage index variation problem, depending on the size, position and orientation of cracks, are presented in the paper. Numerical modelling of wave propagation in reinforced concrete is conducted using the explicit finite element method, which is highly effective for this purpose.
  	view abstract	doi: 10.14256/JCE.1372.2015

• 2016 • 259	Development of carbon fibre-reinforced plastic (CFRP) crash absorbers with stable crushing behaviour considering the connection to the bumper system Szlosarek, R. and Bombis, F. and Mühler, M. and Kröger, M. and Karall, T. Materialwissenschaft und Werkstofftechnik 47 1099-1108 (2016) Crash absorbers made of fibre-reinforced plastics becoming more and more popular to reduce the mass in the front section of cars. Various research projects analysed the high specific energy absorption and the stable crushing behaviour of this material, however without examining the connection to other car body components. This paper focuses on the connection of the crash absorbers to the bumper system, particularly regarding to the crushing behaviour. An initial step focused on the development of a crash absorber made of carbon-fibre-reinforced plastic, which shows similar energy absorption compared to absorbers made of aluminium. A following step investigated various connection concepts using a drop tower. These first connection concepts resulted in unstable crushing behaviour. The finite element simulation of the tests delivered additional information about the reasons for the insufficient crushing behaviour. Subsequently, a simulation of various connection concepts turned out suitable connection concepts. A final drop tower test investigated the best connection concept. The developed connection system shows similar to the unmodified crash absorber stable crushing behaviour. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
  	view abstract	doi: 10.1002/mawe.201600634

• 2016 • 258	Effect of the stiffness of bone substitutes on the biomechanical behaviour of femur for core decompression Tran, T.N. and Kowalczyk, W. and Hohn, H.P. and Jäger, M. and Landgraeber, S. Medical Engineering and Physics 38 911-916 (2016) Core decompression is the most common procedure for treatment of the early stages of osteonecrosis of the femoral head. The purpose of this study was to compare the biomechanical performance of four different bone graft substitutes combined with core decompression. Subject-specific finite element models generated from computed tomography (CT) scan data were used for a comprehensive analysis. Two different contact conditions were simulated representing states of osseointegration at the interface. Our results showed that the use of a low-stiffness bone substitute did not increase the risk of femoral fracture in the early postoperative phase, but resulted in less micromotion and interfacial stresses than high-stiffness bone substitutes. © 2016 IPEM
  	view abstract	doi: 10.1016/j.medengphy.2016.05.008

• 2016 • 257	Electromagnetic Field Analysis of a Dipole Coil Element with Surface Impedance Characterized Shielding Plate for 7-T MRI Chen, Z. and Solbach, K. and Erni, D. and Rennings, A. IEEE Transactions on Microwave Theory and Techniques 64 972-981 (2016) In this paper, we systematically investigate the electromagnetic (EM) field of a stripline dipole coil element backed by various shielding plates, which are characterized by surface impedance. The initial analysis is based on a 2-D finite-element-method model, where the considered surface impedance was categorized in terms of magnitude and phase. It has been demonstrated that the shielding plate can be approximately modeled by the magnitude of a complex surface impedance if the absolute EM field distribution is considered. Additionally, as the magnitude of the surface impedance increases, the magnetic and electric fields excited by the stripline tend to distribute in a broader manner. Thus, the transversal homogeneity of the B1 field of a stripline coil can be improved by a shielding plate with a high surface impedance, which has been verified by 3-D models based on single-and multi-coil elements. For the experimental validation, two shielding plates-a copper-plated substrate and a high-impedance surface, which exhibits a small and large surface impedance, respectively-are considered. An excellent agreement of field distributions between numerical simulation and measurement has been observed. © 1963-2012 IEEE.
  	view abstract	doi: 10.1109/TMTT.2016.2518168

• 2016 • 256	Experimental and numerical investigation of increased formability in combined quasi-static and high-speed forming processes Kiliclar, Y. and Demir, O.K. and Engelhardt, M. and Rozgić, M. and Vladimirov, I.N. and Wulfinghoff, S. and Weddeling, C. and Gies, S. and Klose, C. and Reese, S. and Tekkaya, A.E. and Maier, H.J. and Stiemer, M. Journal of Materials Processing Technology 237 254-269 (2016) The formability of deep drawing can be extended by combining it with a subsequent high-speed forming method such as electromagnetic forming. However, up to now, no sufficient systematic understanding of the underlying principles or of a successful design of such coupled processes has been gained. Hence, in this work, a methodology for the analysis and design of such process chains is presented. This approach comprises a new method for the experimentally based determination of quasi-static and high-speed forming limits along close to proportional strain paths, a constitutive visco-plastic, anisotropic material model with a rate dependent ductile damage formulation, which allows for the accurate numerical prediction of forming limits for complicated forming operations under a largely varying strain rate, and finally the actual application of both to a combined quasi-static and high-speed forming operation. In doing so, material areas are identified that are deep drawn up to a degree immediately before necking occurs and then electromagnetically be formed beyond the quasi-static forming limit without damage. This proves that an extension of formability is here achieved due to a change in strain rate rather than in the strain path. © 2016 Elsevier B.V.
  	view abstract	doi: 10.1016/j.jmatprotec.2016.06.007

• 2016 • 255	Failure by fracture in sheet-bulk metal forming Isik, K. and Wernicke, S. and Silva, M.B. and Martins, P.A.F. and Tekkaya, A.E. Journal of Strain Analysis for Engineering Design 51 387-394 (2016) This article investigates the possibility of failure by crack-opening mode III (out-of-plane shearing) in sheet-bulk metal forming processes. The investigation makes use of experimentally and theoretically determined fracture-forming limits of aluminium AA1050-H111 sheets with 1 mm thickness, experimental tests in incremental ploughing with a roll-tipped tool and numerical simulation using a commercial finite element programme. Results show that incremental ploughing of thin sheets with a roll-tipped tool under large indentation depths gives rise to transverse cracks that are triggered at the upper groove surface and propagate downward across thickness along an inclined direction to the sheet surface. In contrast to sheet-metal forming processes that only fail by fracture in crack-opening modes I and II, sheet-bulk metal forming processes present the unique ability of failing in all three possible crack-opening modes, namely, in mode III that is typical of bulk metal-forming processes. © Institution of Mechanical Engineers.
  	view abstract	doi: 10.1177/0309324716639773

• 2016 • 254	Finite element model updating using simulated annealing hybridized with unscented Kalman filter Astroza, R. and Nguyen, L.T. and Nestorović, T. Computers and Structures 177 176-191 (2016) This paper proposes a method for finite element (FE) model updating of civil structures. The method is a hybrid global optimization algorithm combining simulated annealing (SA) with the unscented Kalman filter (UKF). The objective function in the optimization problem can be defined in the modal, time, or frequency domains. The algorithm improves the accuracy, convergence rate, and computational cost of the SA algorithm by local improvements of the accepted candidates though the UKF. The proposed methodology is validated using a mathematical function and numerically simulated response data from linear and nonlinear FE models of realistic three-dimensional structures. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.compstruc.2016.09.001

• 2016 • 253	Finite element simulation of coating-induced heat transfer: application to thermal spraying processes Berthelsen, R. and Tomath, D. and Denzer, R. and Menzel, A. Meccanica 51 291-307 (2016) Thermal spraying is a widely applied coating technique. The optimisation of the thermal spraying process with respect to temperature or temperature induced residual stress states requires a numerical framework for the simulation of the coating itself as well as of the quenching procedure after the application of additional material. This work presents a finite element framework for the simulation of mass deposition due to coating by means of thermal spraying combined with the simulation of nonlinear heat transfer of a rigid heat conductor. The approach of handling the dynamic problem size is highlighted with focus on the thermodynamical consistency of the derived model. With the framework implemented, numerical examples are employed and material parameters are fitted to experimental data of steel as well as of tungsten-carbide–cobalt-coating. © 2015, Springer Science+Business Media Dordrecht.
  	view abstract	doi: 10.1007/s11012-015-0236-7

• 2016 • 252	Finite element simulation of rate-dependent magneto-active polymer response Haldar, K. and Kiefer, B. and Menzel, A. Smart Materials and Structures 25 (2016) This contribution is concerned with the embedding of constitutive relations for magneto-active polymers (MAP) into finite element simulations. To this end, a recently suggested, calibrated, and validated material model for magneto-mechanically coupled and rate-dependent MAP response is briefly summarized in its continuous and algorithmic settings. Moreover, the strongly coupled field equations of finite deformation magneto-mechanics are reviewed. For the purpose of numerical simulation, a finite element model is then established based on the usual steps of weak form representation, discretization and consistent linearization. Two verifying inhomogeneous numerical examples are presented in which a classical 'plate with a hole' geometry is equipped with MAP properties and subjected to different types of time-varying mechanical and magnetic loading. © 2016 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/0964-1726/25/10/104003

• 2016 • 251	GPGPU-based rising bubble simulations using a MRT lattice Boltzmann method coupled with level set interface capturing Safi, M.A. and Turek, S. Computers and Fluids 124 170-184 (2016) A multiphase Lattice Boltzmann (LB) scheme coupled with a level set interface capturing model is used for the simulation of multiphase flows, and in particular, rising bubbles under moderate and high density and viscosity ratios. We make use of consistent time integration and force discretization schemes in particular for pressure forces along with using multiple relaxation time (MRT) form of the collision in the LB equation which enables us to preserve stability and accuracy for high density and critical Eo numbers. We first present the solution for the standard test of a static bubble in order to show the accuracy of the solution with respect to the Laplace law for pressure and also the spurious velocity level. We present quantitative benchmark computations and error analysis for the 2D rising bubble test cases being further validated against high precision finite element solutions in Hysing et al. (2009). Furthermore, by applying efficient multi-core and many core general purpose GPU (GPGPU) implementations outlines, we demonstrate that the desired parallel scaling characteristics of general LBM solutions are well preserved for the proposed coupled computations. The presented implementations are shown to outperform the available GPU-based phase-field LBM solvers in terms of computational time, turning the scheme into a desirable choice for massive multiphase simulations in three dimensions. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compfluid.2015.06.001

• 2016 • 250	Granular media-based tube press hardening Chen, H. and Güner, A. and Ben Khalifa, N. and Tekkaya, A.E. Journal of Materials Processing Technology 228 145-159 (2016) Press hardening process can benefit the formability of 22MnB5 in high temperature and high strength as a final product. It is widely used for weight reduction of car body without sacrifice of its crashworthiness. Nevertheless, not only strength but also stiffness is important for some vehicle components. Press hardening of tube using granular media is the possible technology to realize the press hardening process for tubular components, which have much higher stiffness as compared to sheet metal parts. To choose appropriate granular media, instrumented die compaction test and high pressure direct shear test were established to characterize the material property of granular material. A hot tensile test was used to determine the formability of 22MnB5 tube material. Interaction between granular media and tube material including friction coefficient and heat transfer coefficient was measured by shear test and heat transfer test. Based on these works, a thermal-mechanical coupled finite element model was used to analyses the process. In validation experiment, a T-shape specimen was formed and quenched. Process parameters such as loading force, interfacial friction, and tube geometry were also investigated via numerical and experimental research for a better understanding of the process. The interfacial friction between granular media and tube showed significant effects to the forming result. These effects were represented by process parameters such as friction coefficient, tube length, types of granular media. A multi-type granular media brought out higher pressure transfer effect and also reduced interfacial friction force, which showed better formability. © 2015 Elsevier B.V.
  	view abstract	doi: 10.1016/j.jmatprotec.2015.03.028

• 2016 • 249	Hardware-Based efficiency advances in the EXA-DUNE project Bastian, P. and Engwer, C. and Fahlke, J. and Geveler, M. and Göddeke, D. and Iliev, O. and Ippisch, O. and Milk, R. and Mohring, J. and Müthing, S. and Ohlberger, M. and Ribbrock, D. and Turek, S. Lecture Notes in Computational Science and Engineering 113 3-23 (2016) We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the EXA-DUNE project, part of the DFG priority program 1648 Software for Exascale Computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on the DUNE platform and the FEAST library. In this contribution, we focus on node-level performance and accelerator integration, which will complement the provenMPI-level scalability of the framework. The higher-level aspects of the EXADUNE project, in particular multiscale methods and uncertainty quantification, are detailed in the companion paper (Bastian et al., Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE. In: Proceedings of the SPPEXA Symposium, 2016). © Springer International Publishing Switzerland 2016.
  	view abstract	doi: 10.1007/978-3-319-40528-5_1

• 2016 • 248	Hydrogen diffusion and trapping in Ti-modified advanced high strength steels Winzer, N. and Rott, O. and Thiessen, R. and Thomas, I. and Mraczek, K. and Höche, T. and Wright, L. and Mrovec, M. Materials and Design 92 450-461 (2016) The influence of Ti on hydrogen diffusion and trapping in various advanced high strength steels was investigated. Electrochemical hydrogen permeation tests were performed on various model steels, with and without Ti, with benchmark tests performed using a commercial steel variant. The hydrogen trapping parameters for each steel were determined by fitting the permeation curves with a finite element model based on the McNabb and Foster equations using least squares minimisation. The influence of Ti on the hydrogen trapping parameters was greatly dependent on microstructure, with ferrite-containing grades being most affected. The results are inconsistent with hydrogen trapping by TiC particles, but consistent with trapping by boundaries between neighbouring ferrite and martensite grains. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.matdes.2015.12.060

• 2016 • 247	In Situ Characterization of Ultrathin Films by Scanning Electrochemical Impedance Microscopy Estrada-Vargas, A. and Bandarenka, A. and Kuznetsov, V. and Schuhmann, W. Analytical Chemistry 88 3354-3362 (2016) Control over the properties of ultrathin films plays a crucial role in many fields of science and technology. Although nondestructive optical and electrical methods have multiple advantages for local surface characterization, their applicability is very limited if the surface is in contact with an electrolyte solution. Local electrochemical methods, e.g., scanning electrochemical microscopy (SECM), cannot be used as a robust alternative yet because their methodological aspects are not sufficiently developed with respect to these systems. The recently proposed scanning electrochemical impedance microscopy (SEIM) can efficiently elucidate many key properties of the solid/liquid interface such as charge transfer resistance or interfacial capacitance. However, many fundamental aspects related to SEIM application still remain unclear. In this work, a methodology for the interpretation of SEIM data of "charge blocking systems" has been elaborated with the help of finite element simulations in combination with experimental results. As a proof of concept, the local film thickness has been visualized using model systems at various tip-to-sample separations. Namely, anodized aluminum oxide (Al2O3, 2-20 nm) and self-assembled monolayers based on 11-mercapto-1-undecanol and 16-mercapto-1-hexadecanethiol (2.1 and 2.9 nm, respectively) were used as model systems. (Figure Presented). © 2016 American Chemical Society.
  	view abstract	doi: 10.1021/acs.analchem.6b00011

• 2016 • 246	Incipient and repeatable plastic flow in incremental sheet-bulk forming of gears Sieczkarek, P. and Wernicke, S. and Gies, S. and Martins, P.A.F. and Tekkaya, A.E. International Journal of Advanced Manufacturing Technology 86 3091-3100 (2016) This paper analyses the differences between incipient and repeatable material flow in the incremental sheet-bulk metal forming (SBMF) of gears produced by indentation along the direction perpendicular to the sheet thickness. The underfilling of the punch cavity during the first indentation, which prevents the production of sound disk gears, is explained on the basis of constrained material flow under material strain hardening. A solution based on the utilization of a tailored disk blank is proposed to overcome this defect. The geometry of the tailored disk blank is determined by means of finite element analysis, and the overall methodology involved material characterization and experimentation with DC04 mild steel. The discussion on the extent of the plastic deformation region under constrained and free-material flow during indentation is complemented by experimental results obtained with a flat punch in rectangular sheet blanks of aluminium EN AW-1050A. © 2016, Springer-Verlag London.
  	view abstract	doi: 10.1007/s00170-016-8442-6

• 2016 • 245	Investigations of ductile damage during the process chains of toothed functional components manufactured by sheet-bulk metal forming Isik, K. and Gerstein, G. and Schneider, T. and Schulte, R. and Rosenbusch, D. and Clausmeyer, T. and Nürnberger, F. and Vucetic, M. and Koch, S. and Hübner, S. and Behrens, B.-A. and Tekkaya, A.E. and Merklein, M. Production Engineering 10 5-15 (2016) Sheet-bulk metal forming processes combine conventional sheet forming processes with bulk forming of sheet semi-finished parts. In these processes the sheets undergo complex forming histories. Due to in- and out-of-plane material flow and large accumulated plastic strains, the conventional failure prediction methods for sheet metal forming such as forming limit curve fall short. As a remedy, damage models can be applied to model damage evolution during those processes. In this study, damage evolution during the production of two different toothed components from DC04 steel is investigated. In both setups, a deep drawn cup is upset to form a circumferential gearing. However, the two final products have different dimensions and forming histories. Due to combined deep drawing and upsetting processes, the material flow on the cup walls is three-dimensional and non-proportional. In this study, the numerical and experimental investigations for those parts are presented and compared. Damage evolution in the process chains is simulated with a Lemaitre damage criterion. Microstructural analysis by scanning electron microscopy is performed in the regions with high mechanical loading. It is observed that the evolution of voids in terms of void volume fraction is strongly dependent on the deformation path. The comparison of simulation results with microstructural data shows that the void volume fraction decreases in the upsetting stage after an initial increase in the drawing stage. Moreover, the concurrent numerical and microstructural analysis provides evidence that the void volume fraction decreases during compression in sheet-bulk metal forming. © 2016, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-016-0656-9

• 2016 • 244	Investigations on the Initial Stress Evolution During Atmospheric Plasma Spraying of YSZ by In Situ Curvature Measurement Mutter, M. and Mauer, G. and Mücke, R. and Vaßen, R. and Back, H.C. and Gibmeier, J. Journal of Thermal Spray Technology 25 672-683 (2016) The residual stresses within plasma-sprayed coatings are an important factor that can influence the lifetime as well as the performance in operation. The investigation of stresses evolving during deposition and post-deposition cooling for atmospheric plasma spraying of yttria-stabilized zirconia coatings using in situ measurement of the samples curvature is a powerful tool for identifying the factors that contribute to stress generation. Under various spray conditions, the first deposition pass leads to a significantly larger increase in samples curvature than the subsequent passes. It is shown in this work that the amount of curvature change at the onset of spraying is significantly influenced by the spray conditions, as well as by the substrate material. More information on the origin of this steep curvature increase at the onset of spraying was obtained by single splat experiments, which yielded information on the splat bonding behavior under various conditions. A comparison of the compressive yield strength for different substrate materials indicated the influence of substrate residual stress relaxation. Residual stress measurements using the incremental hole-drilling method and x-ray diffraction confirmed that the coating deposition affects the substrate residual stress level. The yield strength data were combined with the substrate near-surface temperature during deposition, obtained by finite element simulations, and with the measured residual stress-profile. This revealed that residual stress relaxation is the key factor for the initial curvature increase. © 2016, ASM International.
  	view abstract	doi: 10.1007/s11666-016-0398-4

• 2016 • 243	Local sheet thickening by in-plane swaging Wernicke, S. and Sieczkarek, P. and Martins, P.A.F. and Tekkaya, A.E. International Journal of Mechanical Sciences 119 59-67 (2016) This paper presents a new sheet-bulk forming process to locally pile-up material in thin sheets for subsequent forming or joining operations. An analytical solution is proposed for explaining the influence of the major process parameters, estimating the thickening of the pile-up material and determining the normal and thrust forces applied by the tools. The approach is built upon the slip-line field theory under plane strain assumptions and results are compared against finite element predictions and experimental results using Aluminium EN AW-1050A (EN 573-3) sheets with 3 mm thickness. The last part of the paper introduces a modified tool geometry that is able to control the pile-up material for subsequent mechanical fastening operations. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.ijmecsci.2016.10.003

• 2016 • 242	Modeling of Microstructure Evolution with Dynamic Recrystallization in Finite Element Simulations of Martensitic Steel Baron, T.J. and Khlopkov, K. and Pretorius, T. and Balzani, D. and Brands, D. and Schröder, J. Steel Research International 87 37-45 (2016) A metallurgical material description of the flow behavior for finite element (FE) simulations was developed. During hot compression tests, the dynamic microstructure evolution is modeled on the example of high-strength martensitic steel MS-W 1200. Compression tests at 900-1000 °C with a strain rate of 0.1 s-1 on fine-grain and coarse-grain samples were performed. An analysis of the flow behavior identified a strong correlation between the dynamic recrystallization kinetics and the initial microstructure. The regression analysis has been used to determine correction factors of the new model to describe the dynamic recrystallization. A good agreement between FE simulation and measurement shows the validity of the new model. A metallurgical material description of the flow behavior for finite element (FE) simulations is developed. During hot compression tests, the dynamic microstructure evolution is modeled on the example of high-strength martensitic steel MS-W 1200. An analysis of the flow behavior identifies a strong correlation between the dynamic recrystallization kinetics and the initial microstructure. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/srin.201400576

• 2016 • 241	Modelling and simulation of thermal effects in internal traverse grinding of hardened bearing steel Biermann, D. and Holtermann, R. and Menzel, A. and Schumann, S. CIRP Annals - Manufacturing Technology 65 321-324 (2016) Internal traverse grinding with electro-plated cBN wheels combines the advantages of both internal hard turning and internal grinding, enabling a high material removal rate along with a high surface quality. The drawback, however, is a high thermal load on the workpiece, resulting in shape and dimension errors of the finished part. This paper deals with the compensation of these manufacturing errors with a hybrid simulation system. It combines thermo-mechanically coupled finite element models on both meso- and macro-scale with a scale-bridging kinematic simulation system, enabling the prediction of the resulting temperatures and the development of corresponding simulation-based compensation strategies. © 2016 CIRP
  	view abstract	doi: 10.1016/j.cirp.2016.04.005

• 2016 • 240	Multilevel computational model for failure analysis of steel-fiber-reinforced concrete structures Zhan, Y. and Meschke, G. Journal of Engineering Mechanics 142 (2016) A multilevel modeling framework for the failure analyses of structures made of steel-fiber-reinforced concrete (SFRC), which allows researchers to follow the effects of design parameters such as fiber type, distribution, and orientation from the scale of fiber-matrix interaction to the structural behavior, is proposed. The basic ingredient at the level of single fibers is an analytical model for the prediction of the pullout response of straight or hooked-end fibers. For an opening crack in a specific SFRC composite, the fiber bridging effect is computed via the integration of the pullout response of all fibers intercepting the crack, taking anisotropic fiber orientations into consideration. For the finite-element analysis of the failure behavior of SFRC structures, interface solid elements are used to represent cracks. The softening behavior of opening cracks is governed by cohesive tractions and the fiber bridging effect. The use of an implicit/explicit integration scheme enhances the computational robustness considerably. Numerical analyses of selected benchmark problems demonstrate that the model is able to predict the structural response for different fiber cocktails in good agreement with experimental results. © 2016 American Society of Civil Engineers.
  	view abstract	doi: 10.1061/(ASCE)EM.1943-7889.0001154

• 2016 • 239	NCP function-based dual weighted residual error estimators for Signorini's problem Rademacher, A. SIAM Journal on Scientific Computing 38 A1743-A1769 (2016) In this paper, we consider goal-oriented adaptive finite element methods for Signorini's problem. The basis is a mixed formulation, which is reformulated as nonlinear variational equality using a nonlinear complementarity function. For a general discretization, we derive error identities w.r.t. a possible nonlinear quantity of interest in the displacement as well as in the contact forces, which are included as Lagrange multiplier, using the dual weighted residual method. Afterwards, a numerical approximation of the error identities is introduced. We exemplify the results for a low order mixed discretization of Signorini's problem. The theorectical findings and the numerical approximation scheme are finally substantiated by some numerical examples. © 2016 Society for Industrial and Applied Mathematics.
  	view abstract	doi: 10.1137/15M1033873

• 2016 • 238	Nonlinear Kalman Filters for Model Calibration of Soil Parameters for Geomechanical Modeling in Mechanized Tunneling Nguyen, L.T. and NestoroviC, T. Journal of Computing in Civil Engineering 30 (2016) This work shows that nonlinear Kalman filters can be applied very effectively for the calibration of geomaterial parameters for geomechanical modeling in mechanized tunneling, using tunneling-induced settlements and horizontal displacements. The data curves measured along tunnel excavation steps, which exhibit a nonlinear relationship with respect to soil parameters and are prone to measurement inaccuracies, are utilized in combination with finite element modeling to estimate the underlying soil parameters, using a sequential inference framework: the nonlinear Kalman filtering. The paper shows the comparative performance of the two types of nonlinear Kalman filters that are effective for the identification of soil parameters in terms of convergence speed and accuracy: the extended Kalman filter (EKF) and the sigma-point Kalman filter (SPKF). The effectiveness of the two Kalman filters for inverse analysis is demonstrated through computer simulations for identifying a number of important constitutive parameters of the hardening soil model in the context of mechanized tunneling. © 2015 American Society of Civil Engineers.
  	view abstract	doi: 10.1061/(ASCE)CP.1943-5487.0000495

• 2016 • 237	Numerical Determination of Process Values Influencing the Surface Integrity in Grinding Holtermann, R. and Schumann, S. and Zabel, A. and Biermann, D. and Menzel, A. Procedia CIRP 45 39-42 (2016) Internal traverse grinding with electroplated cBN wheels using high-speed process conditions combines high material removal rates and a high surface quality of the workpiece in one single grinding stroke. In order to capture the macroscopic and mesoscopic thermo-mechanical loads onto the workpiece during internal traverse grinding, numerical simulations are conducted at the two scales. This results in a hybrid approach coupling two finite element models with a geometric kinematic simulation. The article focuses on the influence of multiple grain engagements onto a surface layer region using a two-dimensional chip formation simulation. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.
  	view abstract	doi: 10.1016/j.procir.2016.02.072

• 2016 • 236	Numerical treatment of a geometrically nonlinear planar Cosserat shell model Sander, O. and Neff, P. and Bîrsan, M. Computational Mechanics 57 817-841 (2016) We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton’s method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear. © 2016, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00466-016-1263-5

• 2016 • 235	Optimal control for reinitialization in finite element level set methods Basting, C. and Kuzmin, D. and Shadid, J.N. International Journal for Numerical Methods in Fluids 84 292-305 (2016) A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first-order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE-based reinitialization techniques. © 2016 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/fld.4348

• 2016 • 234	Optimization of artificial ground freezing in tunneling in the presence of seepage flow Marwan, A. and Zhou, M.-M. and Zaki Abdelrehim, M. and Meschke, G. Computers and Geotechnics 75 112-125 (2016) Artificial ground freezing is an environmentally friendly technique to provide temporary excavation support and groundwater control during tunnel construction under difficult geological and hydrological ground conditions. Evidently, groundwater flow has a considerable influence on the freezing process. Large seepage flow may lead to large freezing times or even may prevent the formation of a closed frozen soil body. For safe and economic design of freezing operations, this paper presents a coupled thermo-hydraulic finite element model for freezing soils integrated within an optimization algorithm using the Ant Colony Optimization (ACO) technique to optimize ground freezing in tunneling by finding the optimal positions of the freeze pipe, considering seepage flow. The simulation model considers solid particles, liquid water and crystal ice as separate phases, and the mixture temperature and liquid pressure as primary field variables. Through two fundamental physical laws and corresponding state equations, the model captures the most relevant couplings between the phase transition associated with latent heat effect, and the liquid transport within the pores. The numerical model is validated by means of laboratory results considering different scenarios for seepage flow. As demonstrated in numerical simulations of ground freezing in tunneling in the presence of seepage flow connected with the ACO optimization algorithm, the optimized arrangement of the freeze pipes may lead to a substantial reduction of the freezing time and of energy costs. © 2016.
  	view abstract	doi: 10.1016/j.compgeo.2016.01.004

• 2016 • 233	Probabilistic lifetime model for atmospherically plasma sprayed thermal barrier coating systems Nordhorn, C. and Mücke, R. and Mack, D.E. and Vaßen, R. Mechanics of Materials 93 199-208 (2016) Calculations of atmospherically plasma sprayed thermal barrier coating durability were facilitated by the development of a numerical lifetime model including probabilistic fracture mechanical analyses of thermally induced topcoat stress field evolutions. The stress distributions were determined in finite element analyses taking into account oxide scale growth and topcoat sintering as transient degradation effects. The influence of interface microstructure was investigated by implementing two different interface approximation functions. Subsequent fracture mechanical analyses of subcritical crack growth were performed at numerous different and permanently assigned abstract crack positions. A comparison of the transient energy release rate to its critical value, which depends on crack length and therefore position, results in statistical distributions of system lifetime as a function of simulated thermal cycling conditions. The model was calibrated by presetting an experimental lifetime distribution which was determined in thermal cycling experiments performed at a burner rig facility. The associated cycle-dependent calibration parameter reflects the effect of fracture toughness increase for increasing crack lengths. Experimental reference values for system lifetime were found to be reproduced by the lifetime model. The stress field inversion directly correlated to oxide scale growth rate was identified as the main failure mechanism. The expectation values and standard deviations of the calculated lifetime distributions were found to be in accordance to the experimentally obtained lifetime data and the data scattering typically observed in thermal cycling. © 2015 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.mechmat.2015.11.002

• 2016 • 232	Robust numerical schemes for an efficient implementation of tangent matrices: Application to hyperelasticity, inelastic standard dissipative materials and thermo-mechanics at finite strains Tanaka, M. and Balzani, D. and Schröder, J. Lecture Notes in Applied and Computational Mechanics 81 1-23 (2016) In this contribution robust numerical schemes for an efficient implementation of tangent matrices in finite strain problems are presented and their performance is investigated through the analysis of hyperelastic materials, inelastic standard dissipative materials in the context of incremental variational formulations, and thermo-mechanics. The schemes are based on highly accurate and robust numerical differentiation approaches which use non-real numbers, i.e., complex variables and hyper-dual numbers. The main advantage of these approaches are that, contrary to the classical finite difference scheme, no round-off errors in the perturbations due to floating-point arithmetics exist within the calculation of the tangent matrices. This results in a method which is independent of perturbation values (in case of complex step derivative approximations if sufficiently small perturbations are chosen). An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of hyperelastic, finite strain elastoplastic, and thermo-elastoplastic boundary value problems, the performance of the proposed approaches is analyzed. © Springer International Publishing Switzerland 2016.
  	view abstract	doi: 10.1007/978-3-319-39022-2_1

• 2016 • 231	Simulation of balloon angioplasty in residually stressed blood vessels—Application of a gradient-enhanced fibre damage model Polindara, C. and Waffenschmidt, T. and Menzel, A. Journal of Biomechanics 49 2341-2348 (2016) In this contribution we study the balloon angioplasty in a residually stressed artery by means of a non-local gradient-enhanced fibre damage model. The balloon angioplasty is a common surgical intervention used to extend or reopen narrowed blood vessels in order to restore the continuous blood flow in, for instance, atherosclerotic arteries. Inelastic, i.e. predominantly damage-related and elastoplastic processes are induced in the artery during its inflation resulting in an irreversible deformation. As a beneficial consequence, provided that the inelastic deformations do not exceed a specific limit, higher deformations can be obtained within the same pressure level and a continuous blood flow can be guaranteed. In order to study the mechanical response of the artery in this scenario, we make use of the non-local gradient-enhanced model proposed in Waffenschmidt et al. (2014). In this contribution, we extend this model to make use of an incompressible format in connection with a Q1Q1P0 finite element implementation. The residual stresses in the artery are also taken into account following the framework presented in Waffenschmidt (2015). From the results it becomes apparent that, when the artery is subjected to radial stresses beyond the physiological range, damage evolution is triggered in the collagen fibres. The impact of the residual stresses on the structural response and on the circumferential stress distribution along the thickness of the arterial wall is also studied. It is observed that the residual stresses have a beneficial effect on the mechanical response of the arterial wall. © 2016 Elsevier Ltd
  	view abstract	doi: 10.1016/j.jbiomech.2016.01.037

• 2016 • 230	Springback prediction and reduction in deep drawing under influence of unloading modulus degradation ul Hassan, H. and Maqbool, F. and Güner, A. and Hartmaier, A. and Ben Khalifa, N. and Tekkaya, A.E. International Journal of Material Forming 9 619-633 (2016) Springback is considered as one of the major problems in deep drawing of high-strength steels (HSS) and advanced high-strength steels (AHSS) which occurs during the unloading of part from the tools. With an ever increasing demand on the automotive manufactures for the production of lightweight automobile structures and increased crash performance, the use of HSS and AHSS is becoming extensive. For the accurate prediction of springback, unloading behavior of dual phase steels DP600, DP1000 and cold rolled steel DC04 for the deep drawing process is investigated and a strategy for the reduction of springback based on variable blankholder force is also presented. Cyclic tension compression tests and LS-Opt software are used for the identification of material parameters for Yoshida-Uemori (YU) model. Degradation of the Young’s modulus is found to be 28 and 26 and 14 % from the initial Young’s modulus for DP600, DP1000 and for the DC04 respectively for the saturated value. A finite element model is generated in LS-DYNA based on the kinematic hardening material model, namely Yoshida-Uemori (YU) model. The validation of numerical simulations is also carried out by the real deep drawing experiments. The springback could be predicted with the maximum deviation of 1.1 mm for these materials. For DP1000, the maximum springback is reduced by 24.5 %, for DP600 33.3 and 48.7 % for DC04 by the application of monotonic blankholder force instead of a constant blankholder force of 80 kN. It is concluded that despite the reduction of Young’s modulus, the springback can be reduced for these materials by increasing the blankholder force only in last 13 % of the punch travel. © 2015, Springer-Verlag France.
  	view abstract	doi: 10.1007/s12289-015-1248-5

• 2016 • 229	Strong discontinuity approaches: An algorithm for robust performance and comparative assessment of accuracy Cazes, F. and Meschke, G. and Zhou, M.-M. International Journal of Solids and Structures 96 355-379 (2016) The Strong Discontinuity Approach (SDA) is a popular method to incorporate cracks as displacement discontinuities into finite elements. In the first part of the paper, different SDA formulations (denoted as SOS, KOS and SKON) are assessed numerically based upon different error norms including a norm to evaluate the variational consistency of SDA elements. Results are compared with analytical solutions as well as with results from interface elements and the element erosion technique for cohesionless cracks. In the second part of the paper, a new method to improve the computational robustness of SDA analyses is proposed. In addition to using arc-length control to solve the nonlinear equation system, a sequential un- and reloading scheme is proposed with the crack state frozen during unloading to avoid, that more than one new crack segment is activated within an increment. The performance of the algorithm is demonstrated by numerical analyses of a tension test on a dog-bone shaped specimen by means of different variants of the SDA and, for comparison, also using interface elements. © 2016
  	view abstract	doi: 10.1016/j.ijsolstr.2016.05.016

• 2016 • 228	Structural Transitions in a Quasi-1D Wigner Solid on Liquid Helium Beysengulov, N.R. and Rees, D.G. and Lysogorskiy, Y. and Galiullin, N.K. and Vazjukov, A.S. and Tayurskii, D.A. and Kono, K. Journal of Low Temperature Physics 182 28-37 (2016) We present a detailed study of structural transitions of an electron system on liquid helium in quasi-1D confinement geometry. The structural transitions are experimentally observed as current oscillations in transport measurements with changing electrostatic confinement parameters. Finite element modelling and Monte Carlo simulations were used to investigate the electron configuration. With increasing electron density, the single chain of electrons splits into a two-, three- and so on row configuration. A proliferation of defects accompanies each structural transition. We find a good agreement between the observed current modulation and the evolution of the electron row configuration predicted by our calculations. © 2015, Springer Science+Business Media New York.
  	view abstract	doi: 10.1007/s10909-015-1344-4

• 2016 • 227	Towards control of viscous effects in acrylic-based actuator applications Thylander, S. and Menzel, A. and Ristinmaa, M. Smart Materials and Structures 25 (2016) Dielectric elastomers offer clear advantages over more traditional and conventional materials when soft, lightweight, noiseless actuator applications with large deformations are considered. However, the viscous time-dependent behaviour associated with most elastomers limit the number of possible applications. For this purpose, the possibility of controlling the viscous response by regulating the applied electric potential is explored. The constitutive model chosen is calibrated to fit the electro-viscoelastic response of an acrylic elastomer often used in dielectric elastomer actuators. The response of both homogeneous deformation examples and inhomogeneous finite element boundary value problems, chosen to mimic existing applications, are presented. Control of both force and displacement quantities are successfully achieved. © 2016 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/0964-1726/25/9/095034

• 2015 • 226	A deflation based coarse space in dual-primal feti methods for almost incompressible elasticity Gippert, S. and Klawonn, A. and Rheinbach, O. Lecture Notes in Computational Science and Engineering 103 573-581 (2015) A new coarse space for FETI-DP domain decomposition methods for mixed finite element discretizations of almost incompressible linear elasticity problems in 3D is presented. The mixed finite element discretization uses continuous piecewise triquadratic displacements and discontinuous piecewise constant pressures. The piecewise constant pressure variables are statically condensated on the element level. The new coarse space is significantly smaller than earlier known coarse spaces for FETI-DP or BDDC methods for the equations of almost incompressible elasticity or Stokes’ equations. For discretizations with discontinuous pressure elements it is well-known that a zero net flux condition on each subdomain is needed to ensure a good condition number. Usually, this constraint is enforced for each vertex, edge, and face of each subdomain separately. Here, a coarse space is discussed where all vertex and edge constraints are treated as usual but where all faces of each subdomain contribute only a single constraint. This approach is presented within a deflation based framework for the implementation of coarse spaces into FETI-DP methods. © Springer International Publishing Switzerland 2015.
  	view abstract	doi: 10.1007/978-3-319-10705-9_56

• 2015 • 225	A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions Meschke, G. and Leonhart, D. Computer Methods in Applied Mechanics and Engineering 290 438-465 (2015) In computational simulations of hydraulic fracturing problems, consideration of interactions between the propagating fracture zone and the fluid flow through the porous material requires an appropriate up-scaling procedure from the spatial scale of the local crack, which usually is much smaller compared to the scale of typical finite elements in poromechanics problems. This scale transition refers to both the displacement field (discontinuity across cracks) as well as to the fluid flow (accelerated flow within cracks and the interaction with the flow in the bulk material). To resolve the small and the large scale portion of the solution, the Generalized Finite Element Method (GFEM) exploiting the partition of unity property of shape functions is used. Accordingly, the displacements u and the liquid pressure p<inf>l</inf> are locally enriched to better resolve their distribution in the vicinity of cracks by means of an additive decomposition into a large and a small scale part. As far as the representation of cracks is concerned, the Extended Finite Element Method (XFEM) is used by enriching the displacement field by means of a jump function as well as crack tip functions. In the framework of the GFEM physically motivated enrichment functions for the local enrichment of the C1 discontinuity of the liquid pressure field across cracks are proposed in the paper. The space and time variant analytical solutions obtained from the 1D transient response of saturated porous materials subjected to the liquid pressure within the crack are applied as enrichment functions to locally improve the approximation of the liquid pressure field at discontinuities. Applying these space and time variant functions, which are the exact solutions of the pressure field in the vicinity of cracks, as local enrichment functions lead to a significant improvement in the local approximation of the pressure field at discontinuities. The new GFEM model is formulated in a poromechanics framework for fully saturated porous materials. Representative analyses demonstrate the improvement of the solution quality compared to existing FEM and XFEM models. © 2015 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2015.03.005

• 2015 • 224	A grooved in-plane torsion test for the investigation of shear fracture in sheet materials Yin, Q. and Soyarslan, C. and Isik, K. and Tekkaya, A.E. International Journal of Solids and Structures 66 121-132 (2015) Abstract The grooved in-plane torsion test is proposed as a shear fracture test for sheet materials. Unlike conventional simple shear tests, which are prone to incipient cracking at the free edges, this test uses radially continuous specimens, as firstly introduced by Marciniak and Kołodziejski (1972). In order to control the fracture position, a radial groove is cut out which allows to keep the fracture away from the clamping area. Thus, this test is able to create material fracture under ideal shear conditions i.e., the condition of vanishing triaxiality at the observable region of the test. Accordingly, the recent shear extended damage and fracture models for the selected material classes can be validated and/or quantified. With the help of finite element analysis (FEA), the corresponding fracture strains for the steel DP1000 were investigated using the proposed shear test and, additionally, three tensile tests conducted on notched specimens which cause fracture at moderate to high triaxialities. These are used to fit the fracture loci of some shear enhanced fracture criteria which have recently been proposed in the literature. The FEA shows that the proposed test provides fracture development under constantly zero triaxiality and zero Lode parameter conditions. Moreover, among the selected criteria, the model proposed by Lou et al. (2012) delivers the best results for selected experimental set. The developed test is ideally suitable for fracture parameter identification of sheet materials which do not show pronounced in-plane anisotropy, e.g. dual phase steels. Furthermore, this test is not limited to metallic materials. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.ijsolstr.2015.03.032

• 2015 • 223	A mechanical model for dissolution-precipitation creep based on the minimum principle of the dissipation potential Klinge, S. and Hackl, K. and Renner, J. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2015) In contrast to previous approaches that consider dissolution-precipitation creep as a multi-stage process and only simulate its governing subprocess, the present model treats this phenomenon as a single continuous process. The applied strategy uses the minimum principle of the dissipation potential according to which a Lagrangian consisting of elastic power and dissipation is minimized. Here, the elastic part has a standard form while the assumption for dissipation stipulates the driving forces to be proportional to two kinds of velocities: The material-transport velocity and the boundary-motion velocity. A Lagrange term is included to impose mass conservation. Two ways of solution are proposed. The strong form of the problem is solved analytically for a simple case. The weak form of the problem is used for a finite-element implementation and for simulating more complex cases. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
  	view abstract	doi: 10.1098/rspa.2014.0994

• 2015 • 222	A modified extended finite element method approach for design sensitivity analysis Barthold, F.-J. and Materna, D. International Journal for Numerical Methods in Engineering 104 209-234 (2015) This paper describes a modified extended finite element method (XFEM) approach, which is designed to ease the challenge of an analytical design sensitivity analysis in the framework of structural optimisation. This novel formulation, furthermore labelled YFEM, combines the well-known XFEM enhancement functions with a local sub-meshing strategy using standard finite elements. It deviates slightly from the XFEM path only at one significant point but thus allows to use already derived residual vectors as well as stiffness and pseudo load matrices to assemble the desired information on cut elements without tedious and error-prone re-work of already performed derivations and implementations. The strategy is applied to sensitivity analysis of interface problems combining areas with different linear elastic material properties. © 2015 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.4930

• 2015 • 221	An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces Sokolov, A. and Ali, R. and Turek, S. Journal of Computational and Applied Mathematics 289 101-115 (2015) Abstract In this article we present a new implicit numerical scheme for reaction-diffusion-advection equations on an evolving in time hypersurface Γ(t). The partial differential equations are solved on a stationary quadrilateral, resp., hexahedral mesh. The zero level set of the time dependent indicator function ø(t) implicitly describes the position of Γ(t). The dominating convective-like terms, which are due to the presence of chemotaxis, transport of the cell density and surface evolution may lead to the non-positiveness of a given numerical scheme and in such a way cause appearance of negative values and give rise of nonphysical oscillations in the numerical solution. The proposed finite element method is constructed to avoid this problem: implicit treatment of corresponding discrete terms in combination with the algebraic flux correction (AFC) techniques make it possible to obtain a sufficiently accurate solution for reaction-diffusion-advection PDEs on evolving surfaces. © 2015 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cam.2015.03.002

• 2015 • 220	An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity Ostwald, R. and Bartel, T. and Menzel, A. Computer Methods in Applied Mechanics and Engineering 293 232-265 (2015) We extend a newly introduced framework for the simulation of shape memory alloys undergoing martensite-austenite phase-transformations by allowing for the evolution of individual plastic deformations in each phase considered. The goal is to obtain a generalised model which will facilitate the reflection of the characteristic macroscopic behaviour of SMA as well as TRIP steels. Particularly, we show that the incorporation of plasticity effects interacting with phase-transformations allows to capture the typical multi-cyclic stress-strain responses. As a basis, we use a scalar-valued phase-transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The incorporation of plasticity phenomena is established by enhancing the deviatoric contributions of the Helmholtz free energy functions of the material phases considered, where the plastic driving forces acting in each phase are derived from the overall free energy potential of the mixture. The resulting energy landscape of the constitutive model is obtained from the contributions of the individual constituents, where the actual energy barriers are computed by minimising parametric intersection curves of elliptic paraboloids. With the energy barriers at hand, we use a statistical physics based approach to determine the resulting evolution of volume fractions due to acting thermo-mechanical loads. Though the model allows to take into account an arbitrary number of solid phases of the underlying material, we restrict the investigations to the simulation of phase-transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar-valued model is embedded into a computational micro-sphere formulation in order to simulate three-dimensional boundary value problems. The systems of evolution equations are solved in a staggered manner, where a newly proposed, physically motivated plasticity inheritance law accounts for the inheritance of plastic deformations due to evolving phases. © 2015 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2015.04.008

• 2015 • 219	Analysis of a combined CG1-DG2 method for the transport equation Becker, R. and Bittl, M. and Kuzmin, D. SIAM Journal on Numerical Analysis 53 445-463 (2015) In this paper, we introduce a reduced discontinuous Galerkin method in which the space of continuous piecewise-linear functions (CG1) is enriched with discontinuous piecewisequadratics (DG2). The resultant finite element approximation is continuous at the vertices of the mesh and discontinuous across edges/faces. We analyze the properties of the CG1-DG2 discretization in the context of a steady linear transport equation. The presented a priori error estimate shows that the discontinuous enrichment stabilizes the continuous coarse-scale component and delivers optimal convergence rates. Numerical studies for steady and unsteady convection problems confirm this result. © 2015 Society for Industrial and Applied Mathematics.
  	view abstract	doi: 10.1137/13093683X

• 2015 • 218	Analytical investigation of structurally stable configurations in shape memory alloy-actuated plates Peraza Hernandez, E.A. and Kiefer, B. and Hartl, D.J. and Menzel, A. and Lagoudas, D.C. International Journal of Solids and Structures 69-70 442-458 (2015) Strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface-like engineering structures. Shape memory alloys (SMAs) are active materials that provide a significant amount of strain under large stresses, a characteristic of great utility in such morphing structures. In this work, an analytical approach to approximate the deformation of plates with SMA constituents is developed via the Rayleigh-Ritz method. An additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field. The total potential energy is then calculated using the displacement field, loading conditions, and constitutive relations for the plate layer(s) composed of SMA wire meshes, dense SMA films, and/or elastic material. The unknown coefficients are then found via minimization of the total potential energy. This approach provides closed-form expressions for the approximate deformation of the plates including multistable configurations. The response of circular SMA-based plates is studied herein. The results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate Gaussian curvature is determined by the direction of the temperature gradient. An alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape. The obtained closed-form expressions show good agreement with detailed non-linear finite element analysis simulations. The proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of SMA-based plates under given loading conditions. Knowledge of such stable configurations is very valuable in the design of SMA-based morphing structures. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.ijsolstr.2015.05.007

• 2015 • 217	Challenges in the Modeling of Wound Healing Mechanisms in Soft Biological Tissues Valero, C. and Javierre, E. and García-Aznar, J.M. and Menzel, A. and Gómez-Benito, M.J. Annals of Biomedical Engineering 43 1654-1665 (2015) Numerical models have become one of the most powerful tools in biomechanics and mechanobiology allowing highly detailed simulations. One of the fields in which they have broadly evolved during the last years is in soft tissue modeling. Particularly, wound healing in the skin is one of the processes that has been approached by computational models due to the difficulty of performing experimental investigations. During the last decades wound healing simulations have evolved from numerical models which considered only a few number of variables and simple geometries to more complex approximations that take into account a higher number of factors and reproduce more realistic geometries. Moreover, thanks to improved experimental observations, a larger number of processes, such as cellular stress generation or vascular growth, that take place during wound healing have been identified and modeled. This work presents a review of the most relevant wound healing approximations, together with an identification of the most relevant criteria that can be used to classify them. In addition, and looking towards the actual state of the art in the field, some future directions, challenges and improvements are analyzed for future developments. © 2014, Biomedical Engineering Society.
  	view abstract	doi: 10.1007/s10439-014-1200-8

• 2015 • 216	Comparison of phenomenological and laminate-based models for rate-dependent switching in ferroelectric continua Dusthakar, D.K. and Menzel, A. and Svendsen, B. GAMM Mitteilungen 38 147-170 (2015) The purpose of the current work is the comparison of a phenomenological and a laminate-based model for rate-dependent switching in ferroelectric single crystals. To this end, the phenomenological model formulation of [1] is considered. In this model, the polarization vector is treated as an internal variable. The evolution of the polarization determines the remanent strain; dependence of energy storage on its direction results in generally transverse isotropic material behavior. This is compared here with a laminate-based model in which the volume fractions of ferroelectric variants are treated as internal variables. The evolution of these volume fractions determines in turn the remanent strain and polarization as volume averages of corresponding ferroelectric variant quantities. Besides a comparison of the respective model formulations, the phenomenological and laminate models are compared in the context of numerical simulation examples. It turns out that both modeling frameworks nicely recapture the underlying dissipative and rate-dependent effects, which is represented by means of simulated butterfly curves and hysteresis loops under homogeneous loading conditions as well as by finite element simulations. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/gamm.201510008

• 2015 • 215	Computation of non-linear magneto-electric product properties of 0-3 composites Schröder, J. and Labusch, M. and Keip, M.-A. and Kiefer, B. and Brands, D. and Lupascu, D.C. GAMM Mitteilungen 38 8-24 (2015) The magneto-electric (ME) coupling of multiferroic materials is of high interest for a variety of advanced applications like in data storage or sensor technology. Since the ME coupling of single-phase multiferroics is too low for technical applications, the manufacturing of composite structures becomes relevant. These composites generate the effective ME coupling as a strain-induced product property. Several experiments on composite multiferroics showed remarkable ME coefficients that are orders of magnitudes higher than those of single-phase materials. The present paper investigates the arising effective product properties of two-phase ME composites by simulating the coupling behavior using a two-scale finite element (FE2) homogenization approach. By means of this method, microstructures with different volume fractions of the individual phases and associated macroscopic ME coupling coefficients are considered. We investigate the influence of different magnetization states by means of the non-linear dissipative magnetostriction material model originally established in [1]. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/gamm.201510002

• 2015 • 214	Computation of three-dimensional fracture parameters at interface cracks and notches by the scaled boundary finite element method Saputra, A.A. and Birk, C. and Song, C. Engineering Fracture Mechanics 148 213-242 (2015) This paper presents the computations of fracture parameters including stress intensity factors and T-stress of three-dimensional cracks and notches by the scaled boundary finite element method. The singular stress field along the crack front is approximated by a singularity at a point through a semi-analytical solution. The solution is expressed as a matrix power function which allows direct extraction of the fracture parameters based on their definitions. No singular element or asymptotic solution is required for the extraction process. The numerical examples presented which include bimaterial interface cracks and V-notches illustrate the accuracy and versatility of the proposed approach. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.engfracmech.2015.09.006

• 2015 • 213	Computed tomography for characterization of fatigue performance of selective laser melted parts Siddique, S. and Imran, M. and Rauer, M. and Kaloudis, M. and Wycisk, E. and Emmelmann, C. and Walther, F. Materials and Design 83 661-669 (2015) Components manufactured by maturing additive manufacturing techniques like selective laser melting (SLM) find potential competence in several applications especially in automotive and aerospace industries as well as in medical applications like customized implants. The manufactured parts possess better, or at least comparable, yield strength and tensile strength values accompanied with a reduced fracture strain. Though their fatigue performance in the as-built condition is impaired due to surface roughness, it can be sufficiently improved by post-process surface treatments. Even then, there exists a high fatigue scatter due to remnant porosity. Characterization of remnant porosity is necessary for a reliable component design to be employed for cyclic applications. Computed tomography has been used in this study to evaluate the influence of porosity-incited stress concentration on the corresponding fatigue scatter. Microscopic analysis, tensile tests, fatigue tests with continuous load increase and constant amplitudes as well as finite element analysis have been used for this purpose. Critical pore characteristics and a modification in the process scanning strategy have been recommended so that the components can be reliably used in fatigue-loaded applications. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.matdes.2015.06.063

• 2015 • 212	Coordinate-invariant phase field modeling of ferro-electrics, part I: Model formulation and single-crystal simulations Schrade, D. and Keip, M.-A. and Thai, H. and Schröder, J. and Svendsen, B. and Müller, R. and Gross, D. GAMM Mitteilungen 38 102-114 (2015) An electro-mechanically coupled phase field model for ferroelectric domain evolution is introduced. Based on Gurtin's concept of a microforce balance, a generalized Ginzburg-Landau evolution equation is derived from the second law of thermodynamics. The thermodynamic potential is formulated for transversely isotropic material behavior by adopting a coordinateinvariant formulation. The model is reduced to 2D and implemented into a finite element framework. The numerical simulations concern the microstructure evolution in mechanically clamped BaTiO3 single-crystals. In the second part of this contribution Keip et al. [1], the poling behavior of ferroelectric composites and polycrystals is investigated with regard to size effects and the influence of a discontinuous order parameter field across grain boundaries. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/gamm.201510005

• 2015 • 211	Determination of the thermal load distribution in internal traverse grinding using a geometric-kinematic simulation Schumann, S. and Siebrecht, T. and Kersting, P. and Biermann, D. and Holtermann, R. and Menzel, A. Procedia CIRP 31 322-327 (2015) During grinding processes, numerous grains interact with the workpiece material producing mechanical and thermal loads on the surface. In the field of thermal simulation of grinding processes, a widely used approach is to substitute numerous cutting edges by a single moving distributed heat source of a specific geometrical shape referring to the theory of Carslaw and Jaeger. This heat source is then moved across the modelled workpiece according to the specific kinematics of the grinding process. The geometrical shape of the substituted heat source can usually be determined using different approaches, e. g., predefined distribution functions or, more precisely, based on measurements of the shear stress within the contact zone. Referring to the state of the art, it is not possible to measure the shear stress within the contact zone during internal traverse grinding with roughing and finishing zone because of its very complex engagement conditions and the non-rectangular shape of its contact zone. In this work, a novel approach to determining a heat source distribution based on a geometric-kinematic simulation for internal traverse grinding is presented. This simulation identifies the ideal geometrical interaction of workpiece and grinding wheel. For this purpose, the specific material removal rate for each grain is calculated and accumulated with respect to the contact zone resulting in a three-dimensional thermal load distribution. This heat source can be used in finite element simulations to determine the thermal load on the workpiece. © 2015 The Authors. Published by Elsevier B.V.
  	view abstract	doi: 10.1016/j.procir.2015.03.020

• 2015 • 210	Electrochemical strain microscopy time spectroscopy: Model and experiment on LiMn2O4 Amanieu, H.-Y. and Thai, H.N.M. and Luchkin, S.Yu. and Rosato, D. and Lupascu, D.C. and Keip, M.-A. and Schröder, J. and Kholkin, A.L. Journal of Applied Physics 118 (2015) Electrochemical Strain Microscopy (ESM) can provide useful information on ionic diffusion in solids at the local scale. In this work, a finite element model of ESM measurements was developed and applied to commercial lithium manganese (III,IV) oxide (LiMn<inf>2</inf>O<inf>4</inf>) particles. ESM time spectroscopy was used, where a direct current (DC) voltage pulse locally disturbs the spatial distribution of mobile ions. After the pulse is off, the ions return to equilibrium at a rate which depends on the Li diffusivity in the material. At each stage, Li diffusivity is monitored by measuring the ESM response to a small alternative current (AC) voltage simultaneously applied to the tip. The model separates two different mechanisms, one linked to the response to DC bias and another one related to the AC excitation. It is argued that the second one is not diffusion-driven but is rather a contribution of the sum of several mechanisms with at least one depending on the lithium ion concentration explaining the relaxation process. With proper fitting of this decay, diffusion coefficients of lithium hosts could be extracted. Additionally, the effect of phase transition in LiMn<inf>2</inf>O<inf>4</inf> is taken into account, explaining some experimental observations. © 2015 AIP Publishing LLC.
  	view abstract	doi: 10.1063/1.4927747

• 2015 • 209	Enhancement of Lemaitre model to predict cracks at low and negative triaxialities in sheet metal forming Isik, K. and Doig, M. and Richter, H. and Clausmeyer, T. and Tekkaya, A. E. Key Engineering Materials 639 427-434 (2015) Advanced high strength steels are still one of the best alternatives for light weight design in the automotive industry. Due to their good performances like high strength and high energy absorption, those steel grades are excellent for body in white components. Because of their restricted ductility, which sometimes leads to the formation of cracks without or low necking during forming operations, conventional forming limit diagrams may fall short. As a remedy, an enhanced variant of the Lemaitre continuum mechanical damage model (CDM) is presented in this work. Previous model extensions of the Lemaitre model improved the damage prediction for the shear and compression dominated stress states by introducing an additional weighting factor for the influence of compression on damage evolution, the so called crack closure parameter h. However, the possible range of the fracture behavior predicted by such models for low and negative stress triaxialities is limited. In this work, the Lemaitre CDM has been enhanced by considering the maximal shear stress to predict the fracture occurrence under shear. Previous models for the effect of void closure on damage evolution are reviewed and a novel model enhancement taking into account the maximal shear stresses is described. The determination of the damage model parameters is presented for a dual phase steel. For this particular material, the response of model enhancement on the failure prediction is discussed for a test part. © (2015) Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.639.427

• 2015 • 208	Experimental and simulative investigations of tribology in sheet-bulk metal forming Beyer, F. and Blum, H. and Kumor, D. and Rademacher, A. and Willner, K. and Schneider, T. Key Engineering Materials 639 283-290 (2015) Friction has a considerable influence in metal forming both in economic and technical terms. This is especially true for sheet-bulk metal forming (SBMF). The contact pressure that occurs here can be low making Coulomb's friction law advisable, but also very high so that Tresca's friction law is preferable. By means of an elasto-plastic half-space model rough surfaces have been investigated, which are deformed in such contact states. The elasto-plastic half-space model has been verified and calibrated experimentally. The result is the development of a constitutive friction law, which can reproduce the frictional interactions for both low and high contact pressures. In addition, the law gives conclusion regarding plastic smoothening of rough surfaces. The law is implemented in the framework of the finite element method (FEM). However, compared to usual friction relations the tribological interplay presented here comes with the disadvantage of rising numerical effort. In order to minimise this drawback, a model adaptive finite element simulation is performed additionally. In this approach, contact regions are identified, where a conventional friction law is applicable, where the newly developed constitutive friction law should be used, or where frictional effects are negligible. The corresponding goal-oriented indicators are derived based on the "dual-weighted-residual" (DWR) method taking into account both the model and the discretisation error. This leads to an efficient simulation that applies the necessary friction law in dependence of contact complexity. © 2015 Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.639.283

• 2015 • 207	Failure mechanisms of microbolometer thermal imager sensors using chip-scale packaging Elßner, M. and Vogt, H. Microelectronics Reliability 55 1901-1905 (2015) This paper analyzes relevant failure mechanisms for microbolometer thermal imager sensors that are assembled with a small size and low cost chip scale package. The analyses focus on device specific elements like the bolometer sensor structures, the longtime stability of the sensor and its performance, and the stability of the hermetic chip scale package. Executed reliability tests showed a high reliability of the sensor and the package without hard failures. The package survived harsh environmental accelerated stress tests and showed only a slight reduction of the shear strength through void formation and small cracks within the lead frame that could be verified through FEM simulations. The stress on the bolometers is investigated by thermomechanical FEM simulations. Executed reliability tests showed no enlargement in the number of defect pixel. The sensor performance showed a longtime drift and temperature dependence through outgassing processes inside the package leading to a significant performance reduction. Thus this effect is investigated more closely and possible countermeasures are proposed. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.microrel.2015.07.040

• 2015 • 206	FETI-DP methods with an adaptive coarse space Klawonn, A. and Radtke, P. and Rheinbach, O. SIAM Journal on Numerical Analysis 53 297-320 (2015) A coarse space is constructed for the dual-primal finite element tearing and interconnecting (FETI-DP) domain decomposition method applied to highly heterogeneous problems by solving local generalized eigenvalue problems. For certain problems with highly varying coefficients, e.g., from multiscale simulations, the coefficient jump will appear in the condition number bound even if standard techniques such as scaling and the weighting of constraints are used. The FETI-DP theory is revisited and two central estimates are identified where the dependency on the coefficient contrast can enter the condition number bound. The first is a Poincaré inequality and the second an extension theorem. These estimates are replaced by local eigenvalue problems. Enriching the FETI-DP coarse space by a few numerically computed eigenvectors yields independence of the contrast of the coefficients even in challenging situations. © 2015 Axel Klawonn, Patrick Radtke, Oliver Rheinbach.
  	view abstract	doi: 10.1137/130939675

• 2015 • 205	Fiber-matrix interphase in applied short glass fiber composites determined by a nano-scratch method Schöneich, M. and Zamanzade, M. and Stommel, M. Composites Science and Technology 119 100-107 (2015) The fiber-matrix interphase in composites is defined as the intersection region between fibers and the matrix material. It shows altered matrix material properties. In dependency of the matrix material or the fiber coating, this phase is created by interdiffusion processes at the macromolecular scale driven by thermodynamic forces. Especially for FE simulations of composites and the validation of multi-scale material modeling approaches, the information about the existing interphase becomes important. Thus, the present study analyses the interphase in applied short glass fiber reinforced thermoplastics. For the identification of the interphase thickness, the nano-scratch method provides admissible results. This methodology is improved and adapted to the use in short fiber composite specimens. Thereby, the measured range of interphase thickness represents the inhomogeneity of the interphase. To assure that the measured interphase is not mainly constituted by the sizing of the glass fiber, incineration tests are performed additionally. The comparison of the interphase and the sizing thickness shows a significant thicker interphase. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compscitech.2015.10.004

• 2015 • 204	Finite element discretization of state-constrained elliptic optimal control problems with semilinear state equation Neitzel, I. and Pfefferer, J. and Rösch, A. SIAM Journal on Control and Optimization 53 874-904 (2015) We study a class of semilinear elliptic optimal control problems with pointwise state constraints. The purpose of this paper is twofold. First, we present convergence results for the finite element discretization of this problem class similarly to known results with finite-dimensional control space, thus extending results that are-for control functions-only available for linear-quadratic convex problems. We rely on a quadratic growth condition for the continuous problem that follows from second order sufficient conditions. Second, we show that the second order sufficient conditions for the continuous problem transfer to its discretized version. This is of interest, for example, when considering questions of local uniqueness of solutions or the convergence of solution algorithms such as the SQP method. © 2015 Society for Industrial and Applied Mathematics.
  	view abstract	doi: 10.1137/140960645

• 2015 • 203	Geometrically nonlinear transient analysis of delaminated composite and sandwich plates using a layerwise displacement model with contact conditions Marjanović, M. and Vuksanović, D. and Meschke, G. Composite Structures 122 67-81 (2015) In the paper, a computational model for the transient response of laminated composite and sandwich plates with existing zones of partial delamination, subjected to dynamic pulse loading is proposed. Laminated composite and sandwich plates are modeled using the extended version of the Generalized Laminated Plate Theory. For the numerical solution, the finite element method with layered finite elements is used. Delamination between individual layers is considered as discontinuities in the displacement field using Heaviside step functions. Since the status of delaminated layers may change in dynamic loading conditions, leading to the so-called "breathing" phenomenon, contact conditions allowing for the opening/closing of delaminated layers are proposed. Nonlinear kinematics in the sense of small strains and moderately large rotations is accounted for according to the von Kármán assumptions. The material of the individual layers is assumed as orthotropic and linearly elastic. The governing spatial-temporal partial differential equations are integrated in time by means of the implicit Newmark's method. After verification of the proposed model for intact plates, the effect of the size and the position of embedded delamination zones on the transient response of geometrical nonlinearity of composite and sandwich plates is investigated numerically by means of a number of numerical applications. © 2014 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compstruct.2014.11.028

• 2015 • 202	Heat input modeling and calibration in dry NC-milling processes Schweinoch, M. and Joliet, R. and Kersting, P. and Zabel, A. Production Engineering 9 495-504 (2015) Due to friction and material deformation in the shear zone, workpieces in NC-milling processes are subjected to heat input and thermal loading. Ongoing geometric changes as well as time-varying contact and cutting conditions result in an inhomogeneous temperature field that is constantly in flux. Such thermally loaded workpieces often exhibit complex and transient thermomechanical deformations, which may result in erroneous material removal with respect to the desired shape. In order to meet critical manufacturing tolerances, it is therefore necessary to avoid and compensate these effects. Predicting the deformation exhibited by a thermally loaded workpiece is a problem of linear thermoelasticity, which can be solved by use of the finite element (FE) method. A prerequisite to this is the accurate calculation of the temperature field that results within the workpiece material during the course of the milling process. Although the FE method may be used for this as well, the practical application to realistic milling processes is limited due to the required computational resources. This paper presents a fast geometric process simulation for the prediction of cutting forces, heat input and thermal loading in dry NC milling. The temperature field of the workpiece is continuously updated, such that it is possible to determine the temperature of any material point at any point in time of the milling process. Individual models comprising the simulation system are described in detail, along with the experiments that are required to calibrate them. The accuracy of the geometric process simulation is validated by comparison with experimental data for a non-trivial milling process. © 2015, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-015-0621-z

• 2015 • 201	Hybrid mpi/openmp parallelization in feti-dp methods Klawonn, A. and Lanser, M. and Rheinbach, O. and Stengel, H. and Wellein, G. Lecture Notes in Computational Science and Engineering 105 67-84 (2015) We present an approach to hybrid MPI/OpenMP parallelization in FETIDP methods using OpenMP with PETScCMPI in the finite element assembly and using the shared memory parallel direct solver Pardiso in the FETI-DP solution phase. Our approach thus uses OpenMP parallelization on subdomains and MPI in between subdomains. We investigate the efficiency of this approach for a benchmark problem from two dimensional nonlinear hyperelasticity. We observe good scalability for up to four threads for each MPI rank on a state-of-the-art Ivy Bridge architecture and incremental improvements for up to ten OpenMP threads for each MPI rank. © Springer International Publishing Switzerland 2015
  	view abstract	doi: 10.1007/978-3-319-22997-3_4

• 2015 • 200	Hybrid surrogate modelling for mechanised tunnelling simulations with uncertain data Freitag, S. and Cao, B.T. and Ninić, J. and Meschke, G. International Journal of Reliability and Safety 9 154-173 (2015) For numerical reliability analyses of engineering structures, highly efficient computational models are required, in particular if numerical simulations of construction processes are to be performed in real time during the construction. Adopting process-oriented finite element simulations in mechanised tunnelling as a specific field of application, surrogate models are proposed to substitute inevitable expensive complex finite element simulations with uncertain parameters. The focus in this paper is laid on the uncertainty of geotechnical and tunnelling process parameters described by stochastic numbers, intervals and interval stochastic numbers. A new hybrid surrogate modelling concept is presented, which is based on combining artificial neural networks and the proper orthogonal decomposition method. Thereby, uncertain time variant surface settlements of several monitoring points are predicted by recurrent neural networks. Based on these predictions, the complete surface settlement field of each time step is computed using the gappy proper orthogonal decomposition approach. The hybrid surrogate model is applied for reliability analyses of a mechanised tunnelling process, where limit states at multiple surface positions are evaluated. Copyright © 2015 Inderscience Enterprises Ltd.
  	view abstract	doi: 10.1504/IJRS.2015.072717

• 2015 • 199	Identification of fully coupled anisotropic plasticity and damage constitutive equations using a hybrid experimental-numerical methodology with various triaxialities Yue, Z.M. and Soyarslan, C. and Badreddine, H. and Saanouni, K. and Tekkaya, A.E. International Journal of Damage Mechanics 24 683-710 (2015) A hybrid experimental-numerical methodology is presented for the parameter identification of a mixed nonlinear hardening anisotropic plasticity model fully coupled with isotropic ductile damage accounting for microcracks closure effects. In this study, three test materials are chosen: DP1000, CP1200, and AL7020. The experiments involve the tensile tests with smooth and notched specimens and two types of shear tests. The tensile tests with smooth specimens are conducted in different directions with respect to the rolling direction. This helps to determine the plastic anisotropy parameters of the material when the ductile damage is still negligible. Also, in-plane torsion tests with a single loading cycle are used to determine separately the isotropic and kinematic hardening parameters. Finally, tensile tests with notched specimens and Shouler and Allwood shear tests are used for the damage parameters identification. These are conducted until the final fracture with the triaxiality ratio• lying between 0 and 1 / 3 (i.e. 0• 1/3). The classical force-displacement curves are chosen as the experimental responses. However, for the tensile test with notched specimens, the distribution of displacement components is measured using a full field measurement technique (ARAMIS system). These experimental results are directly used by the identification methodology in order to determine the values of material parameters involved in the constitutive equations. The inverse identification methodology combines an optimization algorithm which is coded within MATLAB together with the finite element (FE) code ABAQUS/Explicit. After optimization, good agreement between experimental and numerically predicted results in terms of force-displacement curves is obtained for the three studied materials. Finally, the applicability and validity of the determined material parameters are proved with additional validation tests. © 2014 The Author(s) Reprints and permissions.
  	view abstract	doi: 10.1177/1056789514546578

• 2015 • 198	Influence of isotropic and anisotropic material models on the mechanical response in arterial walls as a result of supra-physiological loadings Schmidt, T. and Pandya, D. and Balzani, D. Mechanics Research Communications 64 29-37 (2015) As accepted in the literature, arterial tissues have in principle anisotropic material properties. Although some very special situations in arteries exist where isotropic constitutive models may approximate the real material behavior with sufficient accuracy, the larger part of analyses requires an anisotropic model. In particular for overstretched arteries, as e.g. a result of a balloon angioplasty, an accurate representation of the complex softening phenomena is important and then the consideration of anisotropy may be necessary. However, a variety of publications found in the literature, where such supra-physiological loading situations are analyzed to optimize e.g. stent designs, consider isotropic models. Therefore, in this contribution, the response of an isotropic and an anisotropic material model is compared in numerical calculations where arteries are subjected to supra-physiological loading. The constitutive formulations include the typical nonlinear stiffening of the fiber response as well as softening due to microscopic damage. In detail, the isotropic and the anisotropic model are adjusted to the same experimental stress-stretch curves of different arterial layers and then both models are applied to finite element simulations of overstretched arterial walls. As it turns out a significant difference is obtained for both calculations showing the importance of anisotropic models for these loading situations. © 2015 Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.mechrescom.2014.12.008

• 2015 • 197	Integration of plasmonic Ag nanoparticles as a back reflector in ultra-thin Cu(In,Ga)Se2 solar cells Yin, G. and Steigert, A. and Andrae, P. and Goebelt, M. and Latzel, M. and Manley, P. and Lauermann, I. and Christiansen, S. and Schmid, M. Applied Surface Science 355 800-804 (2015) Integration of plasmonic Ag nanoparticles as a back reflector in ultra-thin Cu(In,Ga)Se2 (CIGSe) solar cells is investigated. X-ray photoelectron spectroscopy results show that Ag nanoparticles underneath a Sn:In2O3 back contact could not be thermally passivated even at a low substrate temperature of 440 °C during CIGSe deposition. It is shown that a 50 nm thick Al2O3 film prepared by atomic layer deposition is able to block the diffusion of Ag, clearing the thermal obstacle in utilizing Ag nanoparticles as a back reflector in ultra-thin CIGSe solar cells. Via 3-D finite element optical simulation, it is proved that the Ag nanoparticles show the potential to contribute the effective absorption in CIGSe solar cells. © 2015 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.apsusc.2015.07.195

• 2015 • 196	Inverse analysis for heterogeneous materials and its application to viscoelastic curing polymers Klinge, S. and Steinmann, P. Computational Mechanics 55 603-615 (2015) This contribution aims at achieving two important goals: First, it outlines a numerical inverse homogenization strategy able to recover material parameters of the microstructure by using results of macroscopic tests. Second, it considers parameter identification for viscoelastic heterogeneous materials, which is a step providing the basis for the further extension toward the general treatment of dissipative processes. The approach proposed couples the Levenberg–Marquardt method with the multiscale finite element method. In this combination, the former is a gradient-based optimization strategy used to minimize a merit function while the latter is a numerical homogenization technique needed to solve the direct problem. The specific example studied in the paper deals with the investigation of a composite consisting of a viscoelastic curing polymer and a nonlinear elastic material. It proposes a three-step procedure for the evaluation of its material parameters and discusses the accuracy and the uniqueness of the solution. © 2015, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00466-015-1126-5

• 2015 • 195	Investigations on the formation of straightness deviation in MQL deep-hole drilling of thin-walled aluminium components: Experimental and simulation-based analysis of thermomechanical effects in deep-hole drilling using single-lip drills and twist drills Biermann, D. and Iovkov, I. Production Engineering 9 527-535 (2015) One of the most challenging machining operation, particularly with regard to the difficult chip evacuation, is the deep-hole drilling process. Due to the high length-to-diameter ratio of the drill holes and of the tools no complete dry machining is possible, thus minimum quantity lubrication is used to provide a lubrication film at the contact surface of the tribological partners and to ensure a reliable chip removal capability. This paper presents a fundamental comparison of the in-process heat input into the workpiece and the resulting straightness deviations for two different tool concepts-a single-lip drill and a twist drill. In particular, the deep-hole drilling of components with small wall thicknesses, down to a minimum value of sw = 1mm, was analysed to gather information about the mechanisms leading to straightness deviations. Due to the conclusions, particularly using a single-lip drill, a novel experimental approach for the determination of the force distribution over the drill radius was developed. It enables the incremental force measurement along the cutting edge and has been used to generate input data for a finite element analysis of the tool deflection and the contact conditions between tool and workpiece. The results indicate that the single-lip drill is a competitive alternative to the twist drill, but the asymmetric cutting edge design and the required guide pad support limit its productivity, in particular with regard to the heat input and the straightness deviation in the manufacturing of drill holes in thin-walled workpieces. © 2015, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-015-0632-9

• 2015 • 194	Model size and boundary conditions for geohydraulic calculation of a residual-water drainage system using the FEM Perau, E. and Meteling, N. Geotechnik 38 46-55 (2015) It is rational, in excavations in the subsoil beneath the groundwater table, to embed the pit wall in a less permeable soil stratum and operate a residual-water drainage system. The Finite Element Method (FEM) can be used to determine both the influx of groundwater and the potentials and pore-water pressures relevant for various analyses of stability. Such numerical calculations require the selection of a model size and the assumption of certain boundary conditions, however. The influence of these on the results of the calculation are examined in this paper. A study has been performed for the cases of plane and axis-symmetrical states with isotropic and anisotropic subsoil, and is firstly optimised by formulating the task as a parameterised boundary value problem. Evaluation of the mathematical characteristics of the boundary value problem and dimensional analysis are then used to reduce the number of parameters. Finally, conclusions concerning the necessary model size and boundary conditions are drawn on the basis of the parameter study, and recommendations then provided for the user. Copyright © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin.
  	view abstract	doi: 10.1002/gete.201400028

• 2015 • 193	Model update and real-time steering of tunnel boring machines using simulation-based meta models Ninić, J. and Meschke, G. Tunnelling and Underground Space Technology 45 138-152 (2015) A method for the simulation supported steering of the mechanized tunneling process in real time during construction is proposed. To enable real-time predictions of tunneling induced surface settlements, meta models trained a priori from a comprehensive process-oriented computational simulation model for mechanized tunneling for a certain project section of interest are introduced. For the generation of the meta models, Artificial Neural Networks (ANN) are employed in conjunction with Particle Swarm Optimization (PSO) for the model update according to monitoring data obtained during construction and for the optimization of machine parameters to keep surface settlements below a given tolerance. To provide a rich data base for the training of the meta model, the finite element simulation model for tunneling is integrated within an automatic data generator for setting up, running and postprocessing the numerical simulations for a prescribed range of parameters. Using the PSO-ANN for the inverse analysis, i.e. identification of model parameters according to monitoring results obtained during tunnel advance, allows the update of the model to the actual geological conditions in real time. The same ANN in conjunction with the PSO is also used for the determination of optimal steering parameters based on target values for settlements in the forthcoming excavation steps. The paper shows the performance of the proposed simulation-based model update and computational steering procedure by means of a prototype application to a straight tunnel advance in a non-homogeneous soil with two soil layers separated by an inclined boundary. © 2014 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.tust.2014.09.013

• 2015 • 192	Modeling of anisotropic wound healing Valero, C. and Javierre, E. and García-Aznar, J.M. and Gómez-Benito, M.J. and Menzel, A. Journal of the Mechanics and Physics of Solids 79 80-91 (2015) Biological soft tissues exhibit non-linear complex properties, the quantification of which presents a challenge. Nevertheless, these properties, such as skin anisotropy, highly influence different processes that occur in soft tissues, for instance wound healing, and thus its correct identification and quantification is crucial to understand them. Experimental and computational works are required in order to find the most precise model to replicate the tissues' properties. In this work, we present a wound healing model focused on the proliferative stage that includes angiogenesis and wound contraction in three dimensions and which relies on the accurate representation of the mechanical behavior of the skin. Thus, an anisotropic hyperelastic model has been considered to analyze the effect of collagen fibers on the healing evolution of an ellipsoidal wound. The implemented model accounts for the contribution of the ground matrix and two mechanically equivalent families of fibers. Simulation results show the evolution of the cellular and chemical species in the wound and the wound volume evolution. Moreover, the local strain directions depend on the relative wound orientation with respect to the fibers. © 2015 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.jmps.2015.03.009

• 2015 • 191	Modeling ultrasonic waves in elastic waveguides of arbitrary cross-section embedded in infinite solid medium Gravenkamp, H. and Birk, C. and Van, J. Computers and Structures 149 61-71 (2015) An approach is presented to model elastic waveguides of arbitrary cross-section coupled to infinite solid media. The formulation is based on the scaled boundary-finite element method. The surrounding medium is approximately accounted for by a dashpot boundary condition derived from the acoustic impedances of the infinite medium. It is discussed under which circumstances this approximation leads to sufficiently accurate results. Computational costs are very low, since the surrounding medium does not require discretization and the number of degrees of freedom on the cross-section is significantly reduced by utilizing higher-order spectral elements. © 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.compstruc.2014.11.007

• 2015 • 190	Modelling and simulation of Internal Traverse Grinding: bridging meso- and macro-scale simulations Holtermann, R. and Menzel, A. and Schumann, S. and Biermann, D. and Siebrecht, T. and Kersting, P. Production Engineering 9 451-463 (2015) In this work, we focus on the computational bridging between the meso- and macro-scale in the context of the hybrid modelling of Internal Traverse Grinding with electro-plated cBN wheels. This grinding process satisfies the manufacturing industry demands for a high rate of material removal along with a high surface quality while minimising the number of manufacturing processes invoked. To overcome the major problem of the present machining process, namely a highly concentrated thermal load which can result in micro-structural damage and dimension errors of the workpiece, a hybrid simulation framework is currently under development. The latter consists of three components. First, a kinematic simulation that models the grinding wheel surface based on experimentally determined measurements is used to calculate the transient penetration history of every grain intersecting with the workpiece. Secondly, an h-adaptive, plane-strain finite element model incorporating elasto-plastic work hardening, thermal softening and ductile damage is used to simulate the proximity of one cBN grain during grinding and to capture the complex thermo-mechanical material response on a meso-scale. For the third component of the framework, the results from the preceding two simulation steps are combined into a macro-scale process model that shall in the future be used to improve manufacturing accuracy and to develop error compensation strategies accordingly. To achieve this objective, a regression analysis scheme is incorporated to approximate the influence of the several cutting mechanisms on the meso-scale and to transfer the homogenisation-based thermo-mechanical results to the macro-scale. © 2015, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-015-0613-z

• 2015 • 189	Modelling of non-linear switching effects in piezoceramics: A three-dimensional polygonal finite-element-based approach applied to oligo-crystals Kaliappan, J. and Menzel, A. Journal of Intelligent Material Systems and Structures 26 2322-2327 (2015) A polygonal finite-element formulation is applied to solve electromechanically coupled inhomogeneous boundary value problems for polycrystalline materials. Each grain is discretised by one single polygonal finite element, which allows the efficient simulation of general boundary value problems which still resolves individual grains in space. The constitutive model proposed for switching in piezoceramics makes use of a volume-fraction-based framework, where the respective volume fractions refer to the respective crystallographic variants and take the interpretation as internal variables. Their evolution is combined with non-linear hardening-type functions which additionally account for grain-size dependencies. The computational model is shown to reproduce typical hysteresis and butterfly curves on the polycrystalline level under complex electromechanical loading conditions. The results are obtained by direct volume-averaging with respect to the discretised domain and are in good qualitative agreement with experimental data. Moreover, grain-size effects, such as an increase in the coercive electric field value with decreasing grain size, are also captured. © The Author(s) 2014.
  	view abstract	doi: 10.1177/1045389X14554135

• 2015 • 188	Nano- And microlenses as concepts for enhanced performance of solar cells Schmid, M. and Manley, P. Journal of Photonics for Energy 5 (2015) Both metallic nanoparticles exhibiting plasmonic effects and dielectric nanoparticles coupling the light into resonant modes have shown successful applications to photovoltaics. On a larger scale, microconcentrator optics promise to enhance solar cell efficiency and to reduce material consumption. Here, we want to create a link between the concentrators on the nano- and on the microscale. From metallic nanospheres, we turn to dielectric ones and then look at increasing radii to approach the microscale. The lenses are investigated with respect to their interaction with light using three-dimensional simulations with the finite-element method. Resulting maps of local electric field distributions reveal the focusing behavior of the dielectric spheres. For larger lens sizes, ray tracing calculations, which give ray distributions in agreement with electric field intensities, can be applied. Calculations of back focal lengths in geometrical optics coincide with ray tracing results and allow insight into how the focal length can be tuned as a function of particle size, substrate refractive index, and the shape of the microlens. Despite the similarities we find for the nano- and the microlenses, integration into solar cells needs to be carefully adjusted, depending on the goals of material saving, concentration level, focal distance, and lens size. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE).
  	view abstract	doi: 10.1117/1.JPE.5.057003

• 2015 • 187	Nano-optical concept design for light management Schmid, M. and Tsakanikas, S. and Mangalgiri, G. and Andrae, P. and Song, M. and Yin, G. and Riedel, W. and Manley, P. Proceedings of SPIE - The International Society for Optical Engineering 9626 (2015) Efficient light management in optoelectronic devices requires nanosystems where high optical qualities coincide with suitable device integration. The requirement of chemical and electrical passivation for integrating nanostrutures in e.g.Thin film solar cells points towards the use of insulating and stable dielectric material, which however has to provide high scattering and near-fields as well. We investigate metal@dielectric core-shell nanoparticles and dielectric nanorods. Whereas core-shell nanoparticles can be simulated using Mie theory, nanorods of finite length are studied with the finite element method. We reveal that a metallic core within a thin dielectric shell can help to enhance scattering and near-field cross sections compared to a bare dielectric nanoparticle of the same radius. A dielectric nanorod has the benefit over a dielectric nanosphere in that it can generate much higher scattering cross sections and also give rise to a high near-field enhancement along its whole length. Electrical benefits of e.g. Ag@oxide nanoparticles in thin-film solar cells and ZnO nanorods in hybrid devices lie in reduction of recombination centers or close contact of the nanorod material with the surrounding organics, respectively. The optical benefit of dielectric shell material and elongated dielectric nanostructures is highlighted in this paper. © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.
  	view abstract	doi: 10.1117/12.2191081

• 2015 • 186	Newton-multigrid least-squares fem for s-v-p formulation of the navier-stokes equations Ouazzi, A. and Nickaeen, M. and Turek, S. and Waseem, M. Lecture Notes in Computational Science and Engineering 103 651-659 (2015) Least-squares finite element methods are motivated, beside others, by the fact that in contrast to standard mixed finite element methods, the choice of the finite element spaces is not subject to the LBB stability condition and the corresponding discrete linear system is symmetric and positive definite. We intend to benefit from these two positive attractive features, on one hand, to use different types of elements representing the physics as for instance the jump in the pressure for multiphase flow and mass conservation and, on the other hand, to show the flexibility of the geometric multigrid methods to handle efficiently the resulting linear systems. With the aim to develop a solver for non-Newtonian problems, we introduce the stress as a new variable to recast the Navier-Stokes equations into first order systems of equations. We numerically solve S-V-P, Stress-Velocity-Pressure, formulation of the incompressible Navier-Stokes equations based on the least-squares principles using different types of finite elements of low as well as higher order. For the discrete systems, we use a conjugate gradient (CG) solver accelerated with a geometric multigrid preconditioner. In addition, we employ a Krylov space smoother which allows a parameter-free smoothing. Combining this linear solver with the Newton linearization results in a robust and efficient solver. We analyze the application of this general approach, of using different types of finite elements, and the efficiency of the solver, geometric multigrid, throughout the solution of the prototypical benchmark configuration ‘flow around cylinder’. © Springer International Publishing Switzerland 2015.
  	view abstract	doi: 10.1007/978-3-319-10705-9_64

• 2015 • 185	Numerical analysis and experimental validation of the thermomechanical flow behaviour of the hot stamping steel MBW® 1500 Potdar, B. and Graff, S. and Kiefer, B. Key Engineering Materials 639 213-220 (2015) In virtual design of the hot stamping process, a reliable description of the material flow behaviour is an important input to ensure accurate estimations of the part's feasibility. Currently, to characterise the hot stamping material's flow behaviour at elevated temperatures, tensile and upsetting tests are available. The measurement of the flow behaviour out of such tests, which is generally temperature and strain rate dependent, still remains a complex task. Therefore traditional methods to measure flow curves out of such measurements are not necessarily precise enough. In this contribution the authors focus on non-isothermal conductive tensile tests of the manganeseboron steel MBW® 1500 in order to understand its flow behaviour at elevated temperature. Numerical calculations using Finite Element Method (FEM) of the tests itself with correct boundary conditions as well as for all necessary phenomena are used to identify accurately the material's flow curves by using inverse optimisation. Finally, for validation purpose the identified flow curves out of the optimisation method were used to simulate the hot stamping of two different parts. Both geometries were chosen such that various strain paths are covered i.e. uniaxial tension to plane strain. © 2015 Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.639.213

• 2015 • 184	Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices Balzani, D. and Gandhi, A. and Tanaka, M. and Schröder, J. Computational Mechanics 55 861-871 (2015) In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403–413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454–470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed. © 2015, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00466-015-1139-0

• 2015 • 183	Numerical investigation on the vibration of steam turbine inlet valves and the feedback to the dynamic flow field Domnick, C.B. and Benra, F.-K. and Brillert, D. and Dohmen, H.J. and Musch, C. Proceedings of the ASME Turbo Expo 8 (2015) The power output of steam turbines is controlled by steam turbine inlet valves. These valves have a large flow capacity and dissipate in throttled operation a huge amount of energy. Due to that, high dynamic forces occur in the valve which can cause undesired valve vibrations. In this paper, the structural dynamics of a valve are analysed. The dynamic steam forces obtained by previous computational fluid dynamic (CFD) calculations at different operating points are impressed on the structural dynamic finite element model (FEM) of the valve. Due to frictional forces at the piston rings and contact effects at the bushings of the valve plug and the valve stem the structural dynamic FEM is highly nonlinear and has to be solved in the time domain. Prior to the actual investigation grid and time step studies are carried out. Also the effect of the temperature distribution within the valve stem is discussed and the influence of the valve actuator on the vibrations is analysed. In the first step, the vibrations generated by the fluid forces are investigated. The effects of the piston rings on the structural dynamics are discussed. It is found, that the piston rings are able to reduce the vibration significantly by frictional damping. In the second step, the effect of the moving valve plug on the dynamic flow in the valve is analysed. The time dependent displacement of the valve is transferred to CFD calculations using deformable meshes. With this one way coupling method the response of the flow to the vibrations is analysed. Copyright © 2015 by Siemens Energy Inc.
  	view abstract	doi: 10.1115/GT2015-42182

• 2015 • 182	Numerical modeling of damage detection in concrete beams using piezoelectric patches Markovic, N. and Nestorovic, T. and Stojic, D. Mechanics Research Communications 64 15-22 (2015) Research and development of active monitoring systems for reinforced concrete structures should lead to improved structural safety and reliability. Numerical models of active monitoring and damage detection systems can help in the development and implementation of these systems. Modeling of damage detection process in a concrete beam with piezoelectric sensors/actuators based on wave propagation is investigated in this paper. Numerical modeling process is divided into two parts: (1) piezoelectric smart aggregates (SA), and (2) wave propagation models. Displacement obtained in the SA model is used as an input parameter for the modeling of wave propagation. Wavelet analysis is used as a signal processing tool and the damage index is calculated based on the wave energy. In this paper root-mean-square deviation (RMSD) damage index is used. Damage indices obtained by this numerical analysis are compared with experimental results. Very good fit between the finite element (FE) results and experimental results confirm a good FE approach of this problem. © 2015 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.mechrescom.2014.12.007

• 2015 • 181	Optimization of Porthole Die for Non-symmetric Composite Profiles Citrea, T. and Dahnke, C. and Gagliardi, F. and Haase, M. and Ambrogio, G. and Tekkaya, A.E. Materials Today: Proceedings 2 4778-4785 (2015) Composite extrusion aims at the improvement of mechanical properties of extrudates by embedding continuous reinforcing elements into a profile using a modified porthole die. The extrusion of non-symmetric reinforced profiles is a challenge, as the material flow has to be homogeneous. Die shape optimization for the production of non-symmetric reinforced profiles was investigated. The optimization phase took into account the process conditions aiming at a localized homogenization of the material flow to avoid profile distortion. The reinforcement effect on the material flow was analyzed by numerical investigations. The numerical results were verified by experiments. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.matpr.2015.10.012

• 2015 • 180	Orientation dependent deformation by slip and twinning in magnesium during single crystal indentation Zambaldi, C. and Zehnder, C. and Raabe, D. Acta Materialia 91 267-288 (2015) We present the orientation dependent indentation response of pure magnesium during single grain indentation. A conical indenter and maximum loads between 50 mN and 900 mN were employed. Indent topographies were acquired by confocal microscopy. The indents were also characterized by electron backscatter orientation microscopy for their microstructures. Pronounced activation of specific twinning systems was observed around the impressions. The resulting data were compiled into the inverse pole figure presentation of indent microstructures and topographies after Zambaldi and Raabe, Acta Mater. (2010). Three-dimensional crystal plasticity finite element simulation of the indentation deformation supports the interpretation of the orientation dependent slip and twinning patterns around the indents. The match between the activation of observed and simulated twinning variants is discussed with respect to the conditions for nucleation and growth of extension twins. Furthermore, the compatibility of the twinning strains with the imposed deformation is discussed based on the expanding cavity model of indentation. The orientation dependent response of magnesium during indentation is compared to the literature data for indentation of alpha-titanium and beryllium. Recommendations are given on how to exploit the characteristic nature of the observed indentation patterns to rapidly assess the relative activity of deformation mechanisms and their critical shear stresses during alloy development. © 2015 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2015.01.046

• 2015 • 179	Planar bias-tee circuit using single coupled-line approach for 71-76 GHz photonic transmitters Khani, B. and Rymanov, V. and Flammia, I. and Miech, M. and Stöhr, A. 2015 German Microwave Conference, GeMiC 2015 276-279 (2015) This paper presents a novel planar bias-tee (BT) circuit comprising a quarter-wave single coupled-line (SCL) section designed on 127 μm thick ROGERS RT/duroid 5880 laminate for E-band (71-76 GHz) wireless photonic transmitters. The BT circuit enables proper biasing for millimeter wave photodiodes (mm-wave PDs) through the RF-choke, and in addition, protects the hybrid integrated RF amplifier from being damaged by the DC voltage using the SCL DC-block. The planar RF-chock design is based upon two slotted split-ring resonators (SRRs) and is integrated in the DC bias line in order to prevent the leak of the RF signal into the voltage circuitry. Numerical results of the DC-block section show that in the entire 71-76 GHz band, the return loss (RL) is higher than 36 dB while the insertion loss (IL) is lower than 0.4 dB. The overall performance of the complete BT circuit (DC-block and RF-choke) has been calculated by the 3D full-wave electromagnetic field simulator based on the finite element method (RL > 20 dB, IL < 0.6 dB and RF signal suppression in the DC bias line (IS) > 30 dB). A via hole fencing surrounds the BT circuit to reduce the RF propagation losses into the laminate and to ensure that the grounded coplanar waveguide (GCPW) supports only a quasi-static TEM mode. © 2015 IMA: IMATech e.V.
  	view abstract	doi: 10.1109/GEMIC.2015.7107807

• 2015 • 178	Predicting thermal loading in NC milling processes Schweinoch, M. and Joliet, R. and Kersting, P. Production Engineering 9 179-186 (2015) In dry NC milling, a significant amount of heat is introduced into the workpiece due to friction and material deformation in the shear zone. Time-varying contact conditions, relative tool–workpiece movement and continuous geometric change of the workpiece due to material removal lead to a perpetually changing inhomogeneous temperature distribution within the workpiece. This in turn subjects the workpiece to ongoing complex thermomechanical deformations. Machining such a thermally loaded and deformed workpiece to exact specifications may result in unacceptable shape deviations and thermal errors, which become evident only after dissipation of the introduced heat. This paper presents a hybrid simulation system consisting of a geometric multiscale milling simulation and a finite element method kernel for solving problems of linear thermoelasticity. By combination and back-coupling, the described system is capable of accurately modeling heat input, thermal dispersion, transient thermomechanical deformation and resulting thermal errors as they occur in NC milling processes. A prerequisite to accurately predicting thermomechanical errors is the correct simulation of the temperature field within the workpiece during the milling process. Therefore, this paper is subjected to the precise prediction of the transient temperature distribution inside the workpiece. © 2014, German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-014-0598-z

• 2015 • 177	Reliability of microbolometer thermal imager sensors using chip-scale packaging Elßner, M. and Vogt, H. Procedia Engineering 120 1191-1196 (2015) This paper analyses relevant failure mechanisms for microbolometer thermal imager sensors that are assembled with a small size and low cost chip scale package. The analyses focus at device specific elements like the bolometer sensor structures, the longtime stability of the sensor and its performance, and the stability of the hermetic chip scale package. Executed reliability tests showed a high reliability of the sensor and the package without hard failures. The package survived harsh environmental accelerated stress tests and showed only a slight reduction of the shear strength through void formation and small cracks within the lead frame that could be verified through FEM simulations. The stress on the bolometers is investigated by thermomechanical FEM simulations. Executed reliability tests showed no enlargement in the number of defect pixel. The sensor performance showed a longtime drift and temperature dependence through outgassing processes inside the package leading to a significant performance reduction. Thus this effect is investigated closer and possible countermeasures are proposed. © 2015 The Authors. Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.proeng.2015.08.784

• 2015 • 176	Simulation of MQL deep hole drilling for predicting thermally induced workpiece deformations Biermann, D. and Blum, H. and Frohne, J. and Iovkov, I. and Rademacher, A. and Rosin, K. Procedia CIRP 31 148-153 (2015) The resulting thermomechanical load on the workpiece in deep hole drilling operations using minimum quantity lubrication (MQL) induces a strong in-process deflection of the machined component and can cause an insufficient accuracy of the produced hole. Also subsequent machining operations can be affected by the thermoelastic component of this deformation, which remains within the workpiece after the drilling process. Due to the comparatively long main time of typical deep hole drilling operations the thermomechanical simulation of commonly complex machined parts is challenging. In this paper, a fast finite-element approach using massive parallel solution methods is presented and validated for different wall thickness situations. © 2015 The Authors. Published by Elsevier B.V.
  	view abstract	doi: 10.1016/j.procir.2015.03.038

• 2015 • 175	Suppression of twinning and phase transformation in an ultrafine grained 2 GPa strong metastable austenitic steel: Experiment and simulation Shen, Y.F. and Jia, N. and Wang, Y.D. and Sun, X. and Zuo, L. and Raabe, D. Acta Materialia 97 305-315 (2015) Abstract An ultrafine-grained 304 austenitic 18 wt.% Cr-8 wt.% Ni stainless steel with a grain size of ∼270 nm was synthesized by accumulative rolling (67% total reduction) and annealing (550°C, 150 s). Uniaxial tensile testing at room temperature reveals an extremely high yield strength of 1890 ± 50 MPa and a tensile strength of 2050 ± 30 MPa, while the elongation reaches 6 ± 1%. Experimental characterization on samples with different grain sizes between 270 nm and 35 μm indicates that both, deformation twinning and martensitic phase transformation are significantly retarded with increasing grain refinement. A crystal plasticity finite element model incorporating a constitutive law reflecting the grain size-controlled dislocation slip and deformation twinning captures the micromechanical behavior of the steels with different grain sizes. Comparison of simulation and experiment shows that the deformation of ultrafine-grained 304 steels is dominated by the slip of partial dislocations, whereas for coarse-grained steels dislocation slip, twinning and martensite formation jointly contribute to the shape change. © 2015 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2015.06.053

• 2015 • 174	The approximate component mode synthesis special finite element method in two dimensions: Parallel implementation and numerical results Heinlein, A. and Hetmaniuk, U. and Klawonn, A. and Rheinbach, O. Journal of Computational and Applied Mathematics 289 116-133 (2015) Abstract A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is presented and parallel scalability issues are discussed for representative examples. Additionally, a parallel domain decomposition preconditioner (FETI-DP) is applied to solve the ACMS finite element system. Weak parallel scalability results for ACMS are presented for up to 1024 cores. Our numerical results also suggest a quadratic-logarithmic condition number bound for the preconditioned FETI-DP method applied to ACMS discretizations. © 2015 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cam.2015.02.053

• 2015 • 173	The influence of a brittle Cr interlayer on the deformation behavior of thin Cu films on flexible substrates: Experiment and model Marx, V.M. and Toth, F. and Wiesinger, A. and Berger, J. and Kirchlechner, C. and Cordill, M.J. and Fischer, F.D. and Rammerstorfer, F.G. and Dehm, G. Acta Materialia 89 278-289 (2015) Thin metal films deposited on polymer substrates are used in flexible electronic devices such as flexible displays or printed memories. They are often fabricated as complicated multilayer structures. Understanding the mechanical behavior of the interface between the metal film and the substrate as well as the process of crack formation under global tension is important for producing reliable devices. In the present work, the deformation behavior of copper films (50-200 nm thick), bonded to polyimide directly or via a 10 nm chromium interlayer, is investigated by experimental analysis and computational simulations. The influence of the various copper film thicknesses and the usage of a brittle interlayer on the crack density as well as on the stress magnitude in the copper after saturation of the cracking process are studied with in situ tensile tests in a synchrotron and under an atomic force microscope. From the computational point of view, the evolution of the crack pattern is modeled as a stochastic process via finite element based cohesive zone simulations. Both, experiments and simulations show that the chromium interlayer dominates the deformation behavior. The interlayer forms cracks that induce a stress concentration in the overlying copper film. This behavior is more pronounced in the 50 nm than in the 200 nm copper films. © Acta Materialia Inc. Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.actamat.2015.01.047

• 2015 • 172	Time-domain analysis of wave propagation in 3-D unbounded domains by the scaled boundary finite element method Chen, X. and Birk, C. and Song, C. Soil Dynamics and Earthquake Engineering 75 171-182 (2015) Transient wave propagation in three-dimensional unbounded domains is studied. An efficient numerical approach is proposed, which is based on using the displacement unit-impulse response matrix representing the interaction force-displacement relationship on the near field/far field interface. Spatially, an approximation is used to reduce the computational effort associated with the large size of three-dimensional problems. It is based on subdividing the fully coupled unbounded domain into multiple subdomains. The displacement unit-impulse response matrices of all subdomains are calculated separately. The error associated with this spatial decoupling can be reduced by placing the near field/far field interface further away from the domain of interest. Detailed parameter studies have been conducted using numerical examples, in order to provide guidelines for the proposed spatially local schemes, and to demonstrate the accuracy and high efficiency of the proposed method for three-dimensional soil-structure interaction problems. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.soildyn.2015.04.009

• 2015 • 171	Transient analysis of wave propagation in layered soil by using the scaled boundary finite element method Chen, X. J. and Birk, C. and Song, C. M. Computers and Geotechnics 63 1--12 (2015) An efficient method for modelling the propagation of elastic waves in layered media is developed. It is applicable to scalar and vector wave soil-structure interaction problems involving semi-infinite layers. The scaled boundary finite element method is employed to derive an equation for the displacement unit-impulse response matrix on the near field/far field interface. An accurate and efficient time discretization method is proposed for that equation. As the displacement unit-impulse response approaches zero, the convolution integral representing the force-displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. In addition, a reasonable viscous damping model is proposed for this problem. The existence of damping will cause the displacement unit-impulse response matrix to decay faster. Therefore, an earlier truncation time can be adopted, thus further reducing the computational effort. Numerical examples demonstrate the accuracy and high efficiency of the new method. (C) 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.compgeo.2014.08.008

• 2015 • 170	Variational prediction of the mechanical behavior of shape memory alloys based on thermal experiments Junker, P. and Jaeger, S. and Kastner, O. and Eggeler, G. and Hackl, K. Journal of the Mechanics and Physics of Solids 80 86-102 (2015) In this work, we present simulations of shape memory alloys which serve as first examples demonstrating the predicting character of energy-based material models. We begin with a theoretical approach for the derivation of the caloric parts of the Helmholtz free energy. Afterwards, experimental results for DSC measurements are presented. Then, we recall a micromechanical model based on the principle of the minimum of the dissipation potential for the simulation of polycrystalline shape memory alloys. The previously determined caloric parts of the Helmholtz free energy close the set of model parameters without the need of parameter fitting. All quantities are derived directly from experiments. Finally, we compare finite element results for tension tests to experimental data and show that the model identified by thermal measurements can predict mechanically induced phase transformations and thus rationalize global material behavior without any further assumptions. © 2015 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.jmps.2015.04.015

• 2014 • 169	A first-order system least squares method for hyperelasticity Müller, B. and Starke, G. and Schwarz, A. and Schröder, J. SIAM Journal on Scientific Computing 36 B795-B816 (2014) A least squares mixed finite element method for deformations of hyperelastic materials using stress and displacement as process variables is presented and studied. The method is investigated in detail for the specific case of a neo-Hookean material law and is based on the representation of the strain-stress relation. A formulation is derived for compressible materials and shown to remain valid in the incompressible limit, automatically enforcing the incompressibility constraint. The mapping properties of the first-order system operator are studied in appropriate Sobolev spaces. Under the assumption of a locally unique solution with sufficient regularity, it is proved that the firstorder least squares residual constitutes an upper bound for the error measured in a suitable norm, provided that the finite element approximation is sufficiently close. The method is tested numerically in a plane strain situation using next-to-lowest-order Raviart-Thomas elements for the stress tensor and conforming quadratic elements for the displacement components. The improvement of the stress representation is demonstrated by the evaluation of the boundary traction approximation. © 2014 Society for Industrial and Applied Mathematics.
  	view abstract	doi: 10.1137/130937573

• 2014 • 168	A gradient-enhanced continuum damage model for residually stressed fibre-reinforced materials at finite strains Waffenschmidt, T. and Polindara, C. and Menzel, A. Lecture Notes in Applied and Computational Mechanics 74 19-40 (2014) Themodelling of damage effects inmaterials constitutes a major challenge in various engineering-related disciplines. However, the assumption of purely local continuum damage formulations may lead to ill-posed boundary value problems and—with regard to numerical methods such as the finite element method—to meshdependent solutions, a vanishing localised damage zone upon mesh refinement, and hence physically questionable results. In order to circumvent these deficiencies, we present a non-local gradient-enhanced damage model at finite strains. We additively compose the hyperelastic constitutive response at local material point level of an isotropic matrix and of an anisotropic fibre-reinforced material. The inelastic constitutive response is characterised by a scalar [1– d]-damage model, where we assume only the anisotropic elastic part to damage. Furthermore, we enhance the local free energy by a gradient-term. This term essentially contains the gradient of the non-local damage variable which we introduce as an additional global field variable. In order to guarantee the equivalence between the local and non-local damage variable, we incorporate a penalisation term within the free energy. Based on the principle of minimum total potential energy, we obtain a coupled system of variational equations. The associated non-linear system of equations is symmetric and can conveniently be solved by standard incremental-iterative Newton-Raphson schemes or arc-length-based solution methods. As a further key aspect, we incorporate residual stresses by means of a multiplicative composition of the deformation gradient. As a three-dimensional finite element example, we study the material degradation of a fibre-reinforced tube subjected to internal pressure. This highlights the meshobjective and constitutive properties of the model and illustratively underlines the capabilities of the formulation with regard to biomechanical application such as the simulation of arteries. © Springer International Publishing Switzerland 2014.
  	view abstract	doi: 10.1007/978-3-319-10981-7_2

• 2014 • 167	A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials Waffenschmidt, T. and Polindara, C. and Menzel, A. and Blanco, S. Computer Methods in Applied Mechanics and Engineering 268 801-842 (2014) A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler-Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton-Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems-partially motivated by biomechanical application-highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed. © 2013 Elsevier B.V.
  	view abstract	doi: 10.1016/j.cma.2013.10.013

• 2014 • 166	A high-order doubly asymptotic open boundary for scalar waves in semi-infinite layered systems Prempramote, S. and Birk, C. and Song, Ch. IOP Conference Series: Materials Science and Engineering 10 (2014) Wave propagation in semi-infinite layered systems is of interest in earthquake engineering, acoustics, electromagnetism, etc. The numerical modelling of this problem is particularly challenging as evanescent waves exist below the cut-off frequency. Most of the high-order transmitting boundaries are unable to model the evanescent waves. As a result, spurious reflection occurs at late time. In this paper, a high-order doubly asymptotic open boundary is developed for scalar waves propagating in semi-infinite layered systems. It is derived from the equation of dynamic stiffness matrix obtained in the scaled boundary finite-element method in the frequency domain. A continued-fraction solution of the dynamic stiffness matrix is determined recursively by satisfying the scaled boundary finite-element equation at both high- and low-frequency limits. In the time domain, the continued-fraction solution permits the force-displacement relationship to be formulated as a system of first-order ordinary differential equations. Standard time-step schemes in structural dynamics can be directly applied to evaluate the response history. Examples of a semi-infinite homogeneous layer and a semi-infinite two-layered system are investigated herein. The displacement results obtained from the open boundary converge rapidly as the order of continued fractions increases. Accurate results are obtained at early time and late time. © 2010 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/1757-899X/10/1/012215

• 2014 • 165	A method to quantitatively upscale the damage initiation of dual-phase steels under various stress states from microscale to macroscale Lian, J. and Yang, H. and Vajragupta, N. and Münstermann, S. and Bleck, W. Computational Materials Science 94 245-257 (2014) The aim of this paper is to develop a micromechanical model to quantitatively upscale the damage initiation of dual-phase steels under various stress states from micro to macro and reveal the underlying mechanisms of the damage initiation dependency on stress states from a microstructural level. Finite element (FE) model based on the real microstructure of a DP600 steel sheet is employed by representative volume element (RVE) method. Several numerical aspects are also discussed, such as mesh size and discretisation feature of the phase boundary. The plastic strain localisation theory is applied to the RVE modelling without any other damage models or imperfections. Three typical stress states, uniaxial tension, plane-strain tension and equibiaxial tension, are considered to investigate the influence of the stress state on damage initiation. The quantitative evaluation of the damage initiation for three stress states obtained from the RVE simulation shows the dependency on both stress triaxiality and Lode angle. The results are further compared to the experimentally calibrated damage initiation locus (DIL) and a fairly good agreement is achieved. From this study, the general physical understanding of the effect of stress states on damage initiation is explored and the method for quantitative analysis of the damage initiation in a microstructural level is also established. The microstructure heterogeneity is considered as the key factor that contributes to the damage initiation behaviour of the dual-phase steel. © 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.commatsci.2014.05.051

• 2014 • 164	A model for high temperature creep of single crystal superalloys based on nonlocal damage and viscoplastic material behavior Trinh, B.T. and Hackl, K. Continuum Mechanics and Thermodynamics 26 551-562 (2014) A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown. © 2013 Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00161-013-0317-6

• 2014 • 163	A physically and geometrically nonlinear scaled-boundary-based finite element formulation for fracture in elastomers Behnke, R. and Mundil, M. and Birk, C. and Kaliske, M. International Journal for Numerical Methods in Engineering 99 966-999 (2014) This paper is devoted to the formulation of a plane scaled boundary finite element with initially constant thickness for physically and geometrically nonlinear material behavior. Special two-dimensional element shape functions are derived by using the analytical displacement solution of the standard scaled boundary finite element method, which is originally based on linear material behavior and small strains. These 2D shape functions can be constructed for an arbitrary number of element nodes and allow to capture singularities (e.g.,at a plane crack tip) analytically, without extensive mesh refinement. Mapping these proposed 2D shape functions to the 3D case, a formulation that is compatible with standard finite elements is obtained. The resulting physically and geometrically nonlinear scaled boundary finite element formulation is implemented into the framework of the finite element method for bounded plane domains with and without geometrical singularities. The numerical realization is shown in detail. To represent the physically and geometrically nonlinear material and structural behavior of elastomer specimens, the extended tube model and the Yeoh model are used. Numerical studies on the convergence behavior and comparisons with standard Q1P0 finite elements demonstrate the correct implementation and the advantages of the developed scaled boundary finite element. © 2014 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.4714

• 2014 • 162	A thermo-mechanically coupled field model for shape memory alloys Junker, P. and Hackl, K. Continuum Mechanics and Thermodynamics 26 859-877 (2014) The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations. © 2014, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00161-014-0345-x

• 2014 • 161	An accurate, fast and stable material model for shape memory alloys Junker, P. Smart Materials and Structures 23 (2014) Shape memory alloys possess several features that make them interesting for industrial applications. However, due to their complex and thermo-mechanically coupled behavior, direct use of shape memory alloys in engineering construction is problematic. There is thus a demand for tools to achieve realistic, predictive simulations that are numerically robust when computing complex, coupled load states, are fast enough to calculate geometries of industrial interest, and yield realistic and reliable results without the use of fitting curves. In this paper a new and numerically fast material model for shape memory alloys is presented. It is based solely on energetic quantities, which thus creates a quite universal approach. In the beginning, a short derivation is given before it is demonstrated how this model can be easily calibrated by means of tension tests. Then, several examples of engineering applications under mechanical and thermal loads are presented to demonstrate the numerical stability and high computation speed of the model. © 2014 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/0964-1726/23/11/115010

• 2014 • 160	An enhanced 1-way coupling method to predict elastic global hull girder loads Ley, J. and El Moctar, O. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE 4B (2014) This paper introduces a numerical method to predict global hull girder loads of sea-going vessels, taking into account the structural elasticity. A field method based on a Finite Volume discretisation is applied to simulate the nonlinear rigid ship motions and provides the external loads at the hull surface. The structural response is computed in a full transient 3D-Finite-Element Analysis. The lowest global structural mode shapes and eigenfrequen-cies are covered by the 3D-FE model. The mapping between the Finite Volume mesh and Finite Element grid, is performed by the Mesh-Based Code Coupling Interface (MpCCI). As long as only global vertical bending modes are considered, simplified beam models may sufficiently cover the structural response. However, the use of the 3D-FE model is motivated by the prediction of the global torsional and local loads that are influenced by hydroe-lastic effects. A 1-way coupling method is applied. To account for hydromass effects, the Finite-Element model is enhanced by acoustic elements. Acoustic wave equations are solved to simulate the sound wave propagation in water and to obtain realistic eigenfrequencies of the wetted hull. Structural and hydrody-namic damping is controlled by the Rayleigh-Damping method. Simulations are performed for an ultra large container vessel sailing in regular head waves. The computed time histories of the vertical bending moment are compared with experimental data and with numerical simulations using a strong 2-way coupling simulation that employs a Finite-Element Timoshenko-Beam. Copyright © 2014 by ASME.
  	view abstract	doi: 10.1115/OMAE2014-24199

• 2014 • 159	An experimental and numerical investigation of different shear test configurations for sheet metal characterization Yin, Q. and Zillmann, B. and Suttner, S. and Gerstein, G. and Biasutti, M. and Tekkaya, A.E. and Wagner, M.F.-X. and Merklein, M. and Schaper, M. and Halle, T. and Brosius, A. International Journal of Solids and Structures 51 1066-1074 (2014) Simple shear tests are widely used for material characterization especially for sheet metals to achieve large deformations without plastic instability. This work describes three different shear tests for sheet metals in order to enhance the knowledge of the material behavior under shear conditions. The test setups are different in terms of the specimen geometry and the fixtures. A shear test setup as proposed by Miyauchi, according to the ASTM standard sample, as well as an in-plane torsion test are compared in this study. A detailed analysis of the experimental strain distribution measured by digital image correlation is discussed for each test. Finite element simulations are carried out to evaluate the effect of specimen geometries on the stress distributions in the shear zones. The experimental macroscopic flow stress vs. strain behavior shows no significant influence of the specimen geometry when similar strain measurements and evaluation schemes are used. Minor differences in terms of the stress distribution in the shear zone can be detected in the numerical results. This work attempts to give a unique overview and a detailed study of the most commonly used shear tests for sheet metal characterization. It also provides information on the applicability of each test for the observation of the material behavior under shear stress with a view to material modeling for finite element simulations. © 2013 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijsolstr.2013.12.006

• 2014 • 158	An invariant formulation for phase field models in ferroelectrics Schrade, D. and Müller, R. and Gross, D. and Keip, M.-A. and Thai, H. and Schröder, J. International Journal of Solids and Structures 51 2144-2156 (2014) This paper introduces an electro-mechanically coupled phase field model for ferroelectric domain evolution based on an invariant formulation for transversely isotropic piezoelectric material behavior. The thermodynamic framework rests upon Gurtin's notion of a micro-force system in conjunction with an associated micro-force balance. This leads to a formulation of the second law, from which a generalized Ginzburg-Landau evolution equation is derived. The invariant formulation of the thermodynamic potential provides a consistent way to obtain the order parameter dependent elastic stiffness, piezoelectric, and dielectric tensor. The model is reduced to 2d and implemented into a finite element framework. The material constants used in the simulations are adapted to meet the thermodynamic condition of a vanishing micro-force. It is found that the thermodynamic potential taken from the literature has to be extended in order to avoid a loss of positive definiteness of the stiffness and the dielectric tensor. The small-signal response is investigated in the presence and in the absence of the additional regularizing terms in the potential. The simulations show the pathological behavior of the model in case these terms are not taken into account. The paper closes with microstructure simulations concerning a ferroelectric nanodot subjected to an electric field, a cracked single crystal, and a ferroelectric bi-crystal. © 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijsolstr.2014.02.021

• 2014 • 157	An optimization-based approach to enforcing mass conservation in level set methods Kuzmin, D. Journal of Computational and Applied Mathematics 258 78-86 (2014) This paper presents a new conservative level set method for numerical simulation of evolving interfaces. A PDE-constrained optimization problem is formulated and solved in an iterative fashion. The proposed optimal control procedure constrains the level set function to satisfy a conservation law for the corresponding Heaviside function. The target value of the state variable is defined as the solution to the standard level set transport equation. The gradient of the control variable corrects the convective flux in the nonlinear state equation so as to enforce mass conservation while minimizing deviations from the target state. A relaxation term is added when it comes to the design of an iterative solver for the nonlinear system. The potential of the optimization-based approach is illustrated by two numerical examples. © 2013 Published by Elsevier B.V.
  	view abstract	doi: 10.1016/j.cam.2013.09.009

• 2014 • 156	Beam-solid contact formulation for finite element analysis of pile-soil interaction with arbitrary discretization Ninić, J. and Stascheit, J. and Meschke, G. International Journal for Numerical and Analytical Methods in Geomechanics 38 1453-1476 (2014) This paper presents an embedded beam formulation for discretization independent finite element (FE) analyses of interactions between pile foundations or rock anchors and the surrounding soil in geotechnical and tunneling engineering. Piles are represented by means of finite beam elements embedded within FEs for the soil represented by 3D solid elements. The proposed formulation allows consideration of piles and pile groups with arbitrary orientation independently from the FE discretization of the surrounding soil. The interface behavior between piles and the surrounding soil is represented numerically by means of a contact formulation considering skin friction as well as pile tip resistance. The pile-soil interaction along the pile skin is considered by means of a 3D frictional point-to-point contact formulation using the integration points of the beam elements and reference points arbitrarily located within the solid elements as control points. The ability of the proposed embedded pile model to represent groups of piles objected to combined axial and shear loading and their interactions with the surrounding soil is demonstrated by selected benchmark examples. The pile model is applied to the numerical simulation of shield driven tunnel construction in the vicinity of an existing building resting upon pile foundation to demonstrate the performance of the proposed model in complex simulation environments. © 2014 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nag.2262

• 2014 • 155	Bionic optimization of concrete structures by evolutionary algorithms Schnellenbach-Held, M. and Habersaat, J.-E. Structural Engineering International: Journal of the International Association for Bridge and Structural Engineering (IABSE) 24 229-235 (2014) Floor slabs represent a large volume of concrete in buildings. The goal of this research is to achieve a structure that has an optimized bearing capacity. The optimization implies economic efficiency and sustainability. This paper describes a bionic optimization process that is applied in a project of the German Research Foundation (DFG) Priority Programme called "Concrete light. Future concrete structures using bionic, mathematical and engineering formfinding principles". The project involves adaption of three different natural structures that lead to a natural flow of forces. These natural structures are (a) spider webs, (b) hollow parts of bones and (c) geometries of structures such as the bottom side of water lilies or seashells. This scientific paper deals with the implementation of an optimization process for a configuration of reinforcement inspired by a spider web. Evolutionary Algorithms (EAs) are used for the development and optimization of an innovative and useful configuration of reinforcement. The EAs use reproduction, mutation and selection as mechanisms, inspired by biological evolution, to solve technical problems gradient-free. In this project the EA is combined with physical nonlinear finite element analyses. The EA is embedded into a C# application, in which the slab structure is generated and the finite element programme is started. The quality of the results is characterized by the fitness of each individual (reinforcement configuration), which is, for this example, the midspan displacement of the generated slab multiplied by the steel volume per slab. Accordingly, the midspan displacement is to be minimized during the process, with the minimum possible amount of reinforcement. The optimization variables are the angles and the number of rebars per slab. Several constrains need to be included to get comparable results between the developed slabs and the conventional slabs with orthogonally configured reinforcement. This paper presents the results of an optimized reinforcement configuration thus found by EA and comparisons with the behaviour of conventional slabs with a similar reinforcement ratio.
  	view abstract	doi: 10.2749/101686614X13830790993564

• 2014 • 154	Bridge design influences on the pressure conditions in the welding chamber for porthole die extrusion Gagliardi, F. and Schwane, M. and Citrea, T. and Haase, M. and Khalifa, N.B. and Tekkaya, A.E. Key Engineering Materials 622-623 87-94 (2014) Porthole die extrusion of lightweight alloys is used for the production of profiles, which may have complex cross section geometries. The mechanical properties of these profiles are deeply affected by the seam welds, which are generated in hollow profiles along the whole length. The seam welds result from the rejoining of the material streams in the welding chamber of the porthole die. The joining phase and hence the seam weld quality are strongly influenced by the temperature and the pressure conditions in the welding chamber. Those process conditions can be adjusted by a proper die design. In this work, the focus lies on the feeder section of the extrusion die, which consists of a set of bridges, whose shapes influence the material entry in the welding chamber. A numerical study was carried out to investigate different bridge shapes with regard to the pressure inside the welding chamber and the punch load. Subsequently, the volume of the bridge was fixed to isolate and better investigate the influence of the shape. It was observed that bridge designs leading to higher flow distortion cause higher pressure decrement along the welding plane and, consequently, degradation of the welding conditions. © (2014) Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.622-623.87

• 2014 • 153	Concentration driven phase transitions in multiphase porous media with application to methane oxidation in landfill cover layers Ricken, T. and Sindern, A. and Bluhm, J. and Widmann, R. and Denecke, M. and Gehrke, T. and Schmidt, T.C. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 94 609-622 (2014) This study focuses on a formulation within the theory of porus media for continuum multicomponent modeling of bacterial driven methane oxidation in a porous landfill cover layer which consists of a porous solid matrix (soil and bacteria) saturated by a liquid (water) and gas phase. The solid, liquid, and gas phases are considered as immiscible constituents occupying spatially their individual volume fraction. However, the gas phase is composed of three components, namely methane (CH4), oxygen (O2), and carbon dioxide (CO2). A thermodynamically consistent constitutive framework is derived by evaluating the entropy inequality on the basis of Coleman and Noll [8], which results in constitutive relations for the constituent stress and pressure states, interaction forces, and mass exchanges. For the final set of process variables of the derived finite element calculation concept we consider the displacement of the solid matrix, the partial hydrostatic gas pressure and osmotic concentration pressures. For simplicity, we assume a constant water pressure and isothermal conditions. The theoretical formulations are implemented in the finite element code FEAP by Taylor [29]. A new set of experimental batch tests has been created that considers the model parameter dependencies on the process variables; these tests are used to evaluate the nonlinear model parameter set. After presenting the framework developed for the finite element calculation concept, including the representation of the governing weak formulations, we examine representative numerical examples. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/zamm.201200198

• 2014 • 152	Construction of two- and three-dimensional statistically similar RVEs for coupled micro-macro simulations Balzani, D. and Scheunemann, L. and Brands, D. and Schröder, J. Computational Mechanics 54 1269-1284 (2014) In this paper a method is presented for the construction of two- and three-dimensional statistically similar representative volume elements (SSRVEs) that may be used in computational two-scale calculations. These SSRVEs are obtained by minimizing a least-square functional defined in terms of deviations of statistical measures describing the microstructure morphology and mechanical macroscopic quantities computed for a random target microstructure and for the SSRVE. It is shown that such SSRVEs serve as lower bounds in a statistical sense with respect to the difference of microstructure morphology. Moreover, an upper bound is defined by the maximum of the least-square functional. A staggered optimization procedure is proposed enabling a more efficient construction of SSRVEs. In an inner optimization problem we ensure that the statistical similarity of the microstructure morphology in the SSRVE compared with a target microstructure is as high as possible. Then, in an outer optimization problem we analyze mechanical stress–strain curves. As an example for the proposed method two- and three-dimensional SSRVEs are constructed for real microstructure data of a dual-phase steel. By comparing their mechanical response with the one of the real microstructure the performance of the method is documented. It turns out that the quality of the SSRVEs improves and converges to some limit value as the microstructure complexity of the SSRVE increases. This converging behavior gives reason to expect an optimal SSRVE at the limit for a chosen type of microstructure parameterization and set of statistical measures. © 2014, Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00466-014-1057-6

• 2014 • 151	Crack deflection in multi-layered four-point bending samples Brinckmann, S. and Völker, B. and Dehm, G. International Journal of Fracture 190 167-176 (2014) Four-point bending experiments are conceptually the method of choice when investigating the delamination strength of multi-layered components, which are of particular interest for semiconductor applications. However, experimental studies have shown that the crack continues as mode-I crack in most cases while delamination is rarely observed, thus making the four-point bending method useless. This study uses the finite element method with cohesive zones to study crack propagation and the likelihood of turning the initial mode-I crack into a delamination crack in a multi-layered structure. We close with a conclusion which can help to increase the delamination probability and thereby help to determine the delamination strengths of layered structures. © 2014, Springer Science+Business Media Dordrecht.
  	view abstract	doi: 10.1007/s10704-014-9981-1

• 2014 • 150	Dynamic response of foundations on three-dimensional layered soil using the scaled boundary finite element method Birk, C. and Behnke, R. IOP Conference Series: Materials Science and Engineering 10 (2014) This paper is devoted to the dynamic analysis of arbitrarily shaped three-dimensional foundations on layered ground using a coupled FEM-SBFEM approach. A novel scaled boundary finite element method for the analysis of three-dimensional layered continua over rigid bedrock is derived. The accuracy of the new method is demonstrated using rigid circular foundations resting on or embedded in nonhomogeneous soil layers as examples. © 2010 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/1757-899X/10/1/012228

• 2014 • 149	Effects of thermal cycling parameters on residual stresses in alumina scales of CoNiCrAlY and NiCoCrAlY bond coats Nordhorn, C. and Mücke, R. and Unocic, K.A. and Lance, M.J. and Pint, B.A. and Vaßen, R. Surface and Coatings Technology 258 608-614 (2014) Furnace cycling experiments were performed on free-standing high-velocity oxygen-fuel bond coat samples to investigate the effect of material composition, surface texture, and cycling conditions on the average stresses in the formed oxide scales after cooling. The oxide scale thicknesses were determined by SEM image analyses and information about the stresses were acquired by photo-stimulated luminescence-spectroscopy. Additionally, the scale thickness dependent stress fields were calculated in finite-element analyses including approximation functions for the surface roughness derived on the basis of profilometry data. The evolution of the average residual stress as a function of oxide scale thickness was subject to stochastic fluctuations predominantly caused by local scale spallations. In comparison to the supplemental modeling results, thermal stresses due to mismatch of thermal expansion coefficients are identified as the main contribution to the residual stresses. The theoretical results emphasize that analyses of spectroscopic data acquired for average stress investigations of alumina scales rely on detailed information about microstructural features. © 2014 Elsevier B.V.
  	view abstract	doi: 10.1016/j.surfcoat.2014.08.028

• 2014 • 148	Efficient Newton-multigrid solution techniques for higher order space-time Galerkin discretizations of incompressible flow Hussain, S. and Schieweck, F. and Turek, S. Applied Numerical Mathematics 83 51-71 (2014) In this paper, we discuss solution techniques of Newton-multigrid type for the resulting nonlinear saddle-point block-systems if higher order continuous Galerkin-Petrov (cGP(k)) and discontinuous Galerkin (dG(k)) time discretizations are applied to the nonstationary incompressible Navier-Stokes equations. In particular for the cGP(2) method with quadratic ansatz functions in time, which lead to 3rd order accuracy in the L2-norm and even to 4th order superconvergence in the endpoints of the time intervals, together with the finite element pair Q2/P1disc for the spatial approximation of velocity and pressure leading to a globally 3rd order scheme, we explain the algorithmic details as well as implementation aspects. All presented solvers are analyzed with respect to their numerical costs for two prototypical flow configurations. © 2014 IMACS.
  	view abstract	doi: 10.1016/j.apnum.2014.04.011

• 2014 • 147	Enhancing solar cell efficiency by lenses on the nano- And microscale Schmid, M. and Manley, P. Proceedings of SPIE - The International Society for Optical Engineering 9178 (2014) Metallic nanoparticles exhibiting plasmonic effects as well as dielectric nanoparticles coupling the light into resonant modes have both shown successful application to photovoltaics. On the larger scale, microconcentrator optics promise to enhance solar cell efficiency and reduce material consumption. Here we want to make the link between concentrators on the nano- And on the microscale. From metallic nanospheres we turn to dielectric ones and then look at increasing radii to approach concentrator optics on the mircoscale. The nano- And microlenses are investigated with respect to their interaction with light using 3D simulations with the finite element method. Resulting maps of local electric field distributions reveal the focusing behavior of the dielectric spheres. For larger lens sizes, ray tracing calculations can be applied which give ray distributions in agreement with areas of high electric field intensities. Calculations of back focal lengths using ray tracing coincide with results from geometrical optics simulations. They give us insight into how the focal length can be tuned as a function of particle size, but also depending on the substrate refractive index and the shape of the microlens. Turning from spherical to segment-shaped lenses allows us to approach the realistic case of microconcentrator optics and to draw conclusions about focus tuning and system design. Despite the similarities of focusing behavior we find for the nano- And the microlenses, the integration into solar cells needs to be carefully adjusted, depending on the ambition of material saving, concentration level, focal distance and lens size, all being closely related. © 2014 SPIE.
  	view abstract	doi: 10.1117/12.2061132

• 2014 • 146	Experimental and computational studies on the femoral fracture risk for advanced core decompression Tran, T.N. and Warwas, S. and Haversath, M. and Classen, T. and Hohn, H.P. and Jäger, M. and Kowalczyk, W. and Landgraeber, S. Clinical Biomechanics 29 412-417 (2014) Background Two questions are often addressed by orthopedists relating to core decompression procedure: 1) Is the core decompression procedure associated with a considerable lack of structural support of the bone? and 2) Is there an optimal region for the surgical entrance point for which the fracture risk would be lowest? As bioresorbable bone substitutes become more and more common and core decompression has been described in combination with them, the current study takes this into account. Methods Finite element model of a femur treated by core decompression with bone substitute was simulated and analyzed. In-vitro compression testing of femora was used to confirm finite element results. Findings The results showed that for core decompression with standard drilling in combination with artificial bone substitute refilling, daily activities (normal walking and walking downstairs) are not risky for femoral fracture. The femoral fracture risk increased successively when the entrance point is located further distal. The critical value of the deviation of the entrance point to a more distal part is about 20 mm. Interpretation The study findings demonstrate that optimal entrance point should locate on the proximal subtrochanteric region in order to reduce the subtrochanteric fracture risk. Furthermore the consistent results of finite element and in-vitro testing imply that the simulations are sufficient. © 2014 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.clinbiomech.2014.02.001

• 2014 • 145	Experimental investigation and numerical simulation of the mechanical and thermal behavior of a superelastic shape memory alloy beam during bending Ullrich, J. and Schmidt, M. and Schütze, A. and Wieczorek, A. and Frenzel, J. and Eggeler, G. and Seelecke, S. ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2014 2 (2014) Superelastic Shape Memory Alloys (SMA) are typically used in applications where the martensitic phase transformation is exploited for its reversible, large deformation such as medical applications (e.g. stents). In this work, we focus on the mechanical and thermal behavior of a Nickel-Titanium SMA strip in bending mode. One possible application of this mode is to provide a restoring force when used in joints of SMA wire actuator systems making the need for an antagonistic SMA actuator redundant. In these applications mentioned above, typically only the mechanical properties are of interest while the temperature is considered constant, even though the martensitic phase transformation in SMA is a thermomechanically coupled process. As a part of the DFG (German Research Association) Priority Programme SPP1599 "Ferroic Cooling" which aims at advancing the development of solid state cooling devices, we have an equally large interest for the thermal evolution of Nickel-Titanium SMA during deformation and its induced phase transformation. In this paper we investigate the thermal and the mechanical response of a SMA beam during bending experiments in which the deformation is induced by holding one end of a SMA strip fixed while the other end is subject to a prescribed deflection. Sensors and high speed thermal cameras are used to capture reaction forces, deformations and temperature changes. We compare these experimental results with numerical simulation results obtained from Finite Element simulations where a thermo-mechanically coupled SMA model is implemented into a finite deformation framework. © 2014 by ASME.
  	view abstract	doi: 10.1115/SMASIS20147619

• 2014 • 144	FE-simulation and validation of liquid-bi-orientation- Zimmer, J. and Chauvin, G. and Stommel, M. AIP Conference Proceedings 1593 90-95 (2014) An established method to produce thin walled bottles is Stretch Blow Molding (SBM). Polyethylene terephthalate (PET)-preforms are first heated above their glass transition temperature and subsequently transferred into a closed cavity. In a second step the hot preforms are axially elongated by a stretch rod and simultaneously inflated by pressurized air until a contact with the cavity wall is reached (blowing stage). After a cooling phase, the resulting bottle is ejected and further transferred to a filling station, where the desired liquid content is poured in (filling stage). Alternatively to this sequential procedure, a new process combines the blowing and filling phases. This is done by using the desired liquid content as a pressure medium to inflate the hot preforms. Hence, no separated filling station is required. Moreover the filling time is drastically reduced and the cooling is increased through the heat transfer between hot preform and cold liquid. In the following this process is denoted as liquid-bi-orientation (LBO). Despite of its obvious advantages, LBO is not yet used for industrial series production because SBM is well controlled and established. In this paper the LBO process is investigated by experiments and FE-simulations to obtain a deeper insight and to increase process knowledge. The experiments are conducted at a prototype machine. Hereby, a high speed camera in combination with a transparent cavity enables a recording of the preform deformation. Furthermore, FE-simulations with coupled fluid-structure interactions are conducted to predict the process. In comparison to the high speed video the capabilities of the process model are evaluated. © 2014 American Institute of Physics.
  	view abstract	doi: 10.1063/1.4873741

• 2014 • 143	Finite element based determination and optimization of seam weld positions in porthole die extrusion of double hollow profile with asymmetric cross section Schwane, M. and Kloppenborg, T. and Ben Khalifa, N. and Jäger, A. and Tekkaya, A.E. Key Engineering Materials 585 95-102 (2014) Finite elemente analysis (FEA) allows to reduce development time during the die design stage as well as costly extrusion trials with prototypes. Therefore, it is essential that FEA computation provides reliable results. Among other output quantities such as temperature, load, or die stress, the prediction of material flow is one of the most essential ones. Especially in porthole dies, the material flow can be very complex and thus the position of the seam welds in the profile may be uncertain. In this study the particle tracing method was utilized to determine and finally adjust the seam weld positions in a double hollow profile with varying wall thicknesses over the cross section. The seam weld positions resulting from the original die design were determined by Eulerian FEA computation in the first step. Subsequently, the seam weld positions were adjusted by changing the die geometry. The simulation results were verified by means of extrusion tests, which were conducted under industrial conditions. In addition, Lagrangian and Eulerian FEA was utilized to analyze the evolution of the seam weld positions by evaluation of material flow as well as pressure distribution during the transient initial stage and the steady-state stage of the extrusion process. It was demonstrated that steady state process simulation and the particle tracing method can be used for the prediction of seam weld positions in complex hollow cross sections. © (2014) Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.585.95

• 2014 • 142	Finite element simulation of three-dimensional particulate flows using mixture models Gorb, Y. and Mierka, O. and Rivkind, L. and Kuzmin, D. Journal of Computational and Applied Mathematics 270 443-450 (2014) In this paper, we discuss the numerical treatment of three-dimensional mixture models for (semi-)dilute and concentrated suspensions of particles in incompressible fluids. The generalized Navier-Stokes system and the continuity equation for the volume fraction of the disperse phase are discretized using an implicit high-resolution finite element scheme, and maximum principles are enforced using algebraic flux correction. To prevent the volume fractions from exceeding the maximum packing limit, a conservative overshoot limiter is applied to the converged convective fluxes at the end of each time step. A numerical study of the proposed approach is performed for 3D particulate flows over a backward-facing step and in a lid-driven cavity. © 2013 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.cam.2013.12.020

• 2014 • 141	Fitting of constitutive material parameters for FE-based machining simulations for functionally graded steel components Tiffe, M. and Biermann, D. and Zabel, A. Key Engineering Materials 611-612 1202-1209 (2014) The composition of different materials and their specific properties like tensile strength and toughness is one way to achieve workpiece characteristics which are tailored to the later application. Another approach is the subsequent local heat treatment of workpieces made of homogeneous materials. However, both ways are costly and go along with several subsequent process steps. Therefore, mono-material workpieces which were manufactured by thermo-mechanical forming processes may provide such tailored properties in the form of functional gradations. Furthermore, the process chain is shortened by the combination of forming and heat treatment, but nevertheless machining processes are still needed for proper workpiece finish. This puts the challenge of varying process conditions due to hardness alterations within a single process step, e.g. turning. In addition to experimental investigations simulative analysis techniques are desired to evaluate mechanical as well as thermal loads on tool and workpiece. In the case of FE-based microscopic chip formation simulations proper material behaviour needs to be determined with respect to material hardness. This paper describes the approach of fitting Johnson-Cook material parameters as a function of workpiece material hardness. In order to achieve realistic stress states within the process zone, this approach considers the yield strength as a linear function of the hardness. It is shown how the hardness influences the cutting conditions and how the Johnson-Cook parameters are identified. Then these parameters are validated in three-dimensional simulations of exterior dry turning by comparison of simulated process forces and chip formation to experimentally achieved ones. © 2014 Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.611-612.1202

• 2014 • 140	Identification of parameters in nonlinear geotechnical models using extenden Kalman filter Nestorović, T. and Nguyen, L.T. and Trajkov, M. MATEC Web of Conferences 16 (2014) Direct measurement of relevant system parameters often represents a problem due to different limitations. In geomechanics, measurement of geotechnical material constants which constitute a material model is usually a very diffcult task even with modern test equipment. Back-analysis has proved to be a more effcient and more economic method for identifying material constants because it needs measurement data such as settlements, pore pressures, etc., which are directly measurable, as inputs. Among many model parameter identification methods, the Kalman filter method has been applied very effectively in recent years. In this paper, the extended Kalman filter-local iteration procedure incorporated with finite element analysis (FEA) software has been implemented. In order to prove the effciency of the method, parameter identification has been performed for a nonlinear geotechnical model. © 2014 published by EDP Sciences.
  	view abstract	doi: 10.1051/matecconf/20141605010

• 2014 • 139	In-situ measurement of loading stresses with X-ray diffraction for yield locus determination Güner, A. and Zillmann, B. and Lampke, T. and Tekkaya, A.E. International Journal of Automotive Technology 15 303-316 (2014) The application of the X-ray diffraction method is introduced to solve the problem of inhomogeneous deformation fields in the specimens used for sheet metal characterization. In this method, strains are measured on one side of a specimen with optical measurement systems. On the other side, loading stresses on a specimen are captured with an X-ray diffractometer mounted on a universal testing machine. By this way, the whole stress-strain history of a material point is tracked during testing. The method was first applied to uniaxial tension tests, whereby the applicability of the theory of stress factors and effective X-ray elastic constants were tested. The relaxation behavior of a sheet material which shows itself as stress drops during in-situ experimentation was characterized and compensated by a visco-plastic material model for different stress states. The proposed method was applied to characterize aluminum alloy AA5182 under plane strain tension and shear conditions and the results were compared with the conventionally obtained yield locus. Numerical analyses of a workpiece with the Vegter and Yld2000-2D material models show that the enriched yield locus definition with accurate plane strain tension and shear stresses captures the experimentally obtained surface strains more precisely. © 2014 The Korean Society of Automotive Engineers and Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s12239-014-0031-9

• 2014 • 138	Indentation of self-similar indenters: An FEM-assisted energy-based analysis Pöhl, F. and Huth, S. and Theisen, W. Journal of the Mechanics and Physics of Solids 66 32-41 (2014) In this study, an energy-based approach is used to derive general relationships between two independent parameters of the load-displacement curve (C and Wel/Wtot) and the mechanical properties of Ludwik-power law materials (E, K, and n). The approach uses conventional continuum mechanics to describe the elastic and plastic zone including their mean strains and volumes induced by indentation. It does not account for the indentation size effect which is owed to the nucleation of dislocations within the plastic zone, as it is described by the model developed by Nix and Gao (1998). The energy-based approach in combination with FEM simulations give an insight into the complex deformation processes during indentation and the relationships between the material parameters and the indentation results. The results are discussed and interpreted in the context of solving the forward and inverse indentation problem for self-similar indenters. © 2014 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.jmps.2014.02.002

• 2014 • 137	Mixed FEM of higher-order for time-dependent contact problems Rademacher, A. and Schröder, A. and Blum, H. and Kleemann, H. Applied Mathematics and Computation 233 165-186 (2014) In this paper mixed finite element methods of higher-order for time-dependent contact problems are discussed. The mixed methods are based on resolving the contact conditions by the introduction of Lagrange multipliers. Dynamic Signorini problems with and without friction are considered involving thermomechanical and rolling contact. Rothe's method is used to provide a suitable time and space discretization. To discretize in time, a stabilized Newmark method is applied as an adequate time stepping scheme. The space discretization relies on finite elements of higher-order. In each time step the resulting problems are solved by Uzawa's method or, alternatively, by methods of quadratic programming via a suitable formulation in terms of the Lagrange multipliers. Numerical results are presented towards an application in production engineering. The results illustrate the performance of the presented techniques for a variety of problem formulations. © 2014 Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.amc.2014.01.063

• 2014 • 136	Modeling and finite element simulation of loading-path-dependent hardening in sheet metals during forming Clausmeyer, T. and Güner, A. and Tekkaya, A.E. and Levkovitch, V. and Svendsen, B. International Journal of Plasticity 63 64-93 (2014) A recent material model considering the evolution of plastic anisotropy in interstitial free steels is validated for the forming process of the channel die, a complex part. In the model the evolution of the intra-granular microstructure is represented by tensor-valued internal variables. The model accounts for the cross hardening behavior observed in rheological tests of interstitial free steels. A novel cross hardening indicator which is directly derived from the constitutive model is proposed. This cross hardening indicator is a quantitative measure for the occurrence of cross hardening in the forming process of complex parts. A correlation between the occurrence of cross hardening and larger values of the stored (elastic) energy is observed. The influence of cross hardening on the forming process is investigated, in particular, the drawing forces and the geometric deviations due to springback. The influence of cross hardening on the forming process of the channel die geometry is small. The influence of cross hardening on the more complex S-Rail geometry is larger due to larger plastic deformation and more severe loading path changes. The concept of the proposed transient hardening indicator should be applicable to other models for the evolution of plastic anisotropy. A possible use of the cross hardening indicator would be the efficient choice of the material model in the context of sheet metal forming simulations. © 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijplas.2014.01.011

• 2014 • 135	Modelling of tool engagement and FEM-simulation of chip formation for drilling processes Tiffe, M. and Biermann, D. Advanced Materials Research 1018 183-188 (2014) Drilling is the most used machining operation in modern manufacturing. Consequently, a high efficiency is desired which can be achieved by proper tool geometries and process conditions. The claim for a high degree of process understanding is met by the attempt to visualize the chip formation on a micro scale, e.g. by the use of the finite element method. While two-dimensional FE-simulations of cutting processes are established 3D is the next step to take for further analysis of the drilling processes. Nevertheless, this puts high challenges to the simulative approach in order to achieve valid results. This paper deals with the modelling and the simulation of drilling operations with respect to tool and workpiece geometry. In order to create an acceptable starting condition it is useful to consider the engagement situation of the tool and the workpiece as an ideal state with a defined uncut chip thickness in front of the cutting edge. This provides shorter calculation times due to earlier steady-state chip formation compared to simulations with workpieces which are modeled with uniform surfaces like planes or cones in the initial state. Therefore, the engagement situation is created by the utilization of a geometric-kinematical modelling technique in which an array of rays and their intersections with a triangular mesh constitute a discrete description of a surface. The obtained set of points is further used for triangulation to generate the workpiece geometry mesh. Finally, finite element simulations of the drilling processes are carried out and are analyzed with respect to drilling torque and feed force. © (2014) Trans Tech Publications, Switzerland.
  	view abstract	doi: 10.4028/www.scientific.net/AMR.1018.183

• 2014 • 134	Numerical modeling of elastic waveguides coupled to infinite fluid media using exact boundary conditions Gravenkamp, H. and Birk, C. and Song, C. Computers and Structures 141 36-45 (2014) The simulation of guided waves in plate structures and cylinders coupled to infinite fluids is addressed. The approach is based on the Scaled Boundary Finite Element Method. Only a straight line is discretized that represents the through-thickness direction or the radial direction. The surrounding fluid is accounted for by employing a damping boundary condition that is based on the analytical description of the radiation impedance. Since the radiation impedance is a function of the wavenumber in the waveguide, an iterative solution procedure is applied. The algorithm is highly efficient while the results are in agreement with the Global Matrix Method. © 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.compstruc.2014.05.010

• 2014 • 133	Numerical modelling of wave propagation in anisotropic soil using a displacement unit-impulse-response-based formulation of the scaled boundary finite element method Chen, X. and Birk, C. and Song, C. Soil Dynamics and Earthquake Engineering 65 243-255 (2014) An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to soil-structure interaction problems involving scalar and vector waves, unbounded domains of arbitrary geometry and anisotropic soil. The scaled boundary finite element method is employed to derive a novel equation for the displacement unit-impulse response matrix on the soil-structure interface. The proposed method is based on a piecewise linear approximation of the first derivative of the displacement unit-impulse response matrix and on the introduction of an extrapolation parameter in order to improve the numerical stability. In combination, these two ideas allow for the choice of significantly larger time steps compared to conventional methods, and thus lead to increased efficiency. As the displacement unit-impulse response approaches zero, the convolution integral representing the force-displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. Numerical examples demonstrate the accuracy and high efficiency of the new method for two-dimensional soil-structure interaction problems. © 2014 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.soildyn.2014.06.019

• 2014 • 132	On the modelling of electro-viscoelastic response of electrostrictive polyurethane elastomers Ask, A. and Menzel, A. and Ristinmaa, M. IOP Conference Series: Materials Science and Engineering 10 (2014) Electroactive polymers (EAP) deform under electric fields. This effect in fact generates various new fields of engineering applications of high technological interest. As an advantage, EAP may undergo deformations much larger than those capable by electroactive ceramics - however, to the price of acting at comparatively low forces. As common for polymers, EAP exhibit time-dependent material behaviour. The model proposed in this contribution, on the one hand, captures these electro-viscoelastic effects and, on the other hand, also nicely fits into iterative finite element formulations in order to simulate general boundary value problems. While the deformation itself as well as the electric potential are introduced as global degrees of freedom, the internal variables accounting for the viscous response are incorporated at the so-called local integration point level. Apart form calibrating the model against experimental data, a simple coupled finite element example is studied to show the applicability of the finite deformation electro-viscoelastic formulation proposed. © 2010 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/1757-899X/10/1/012101

• 2014 • 131	Optimal control for mass conservative level set methods Basting, C. and Kuzmin, D. Journal of Computational and Applied Mathematics 270 343-352 (2014) This paper presents two different versions of an optimal control method for enforcing mass conservation in level set algorithms. The proposed PDE-constrained optimization procedure corrects a numerical solution to the level set transport equation so as to satisfy a conservation law for the corresponding Heaviside function. In the original version of this method, conservation errors are corrected by adding the gradient of a scalar control variable to the convective flux in the state equation. In the present paper, we investigate the use of vector controls. The alternative formulation offers additional flexibility and requires less regularity than the original method. The nonlinear system of first-order optimality conditions is solved using a standard fixed-point iteration. The new methodology is evaluated numerically and compared to the scalar control approach. © 2013 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.cam.2013.12.040

• 2014 • 130	Residual stresses in continuously reinforced composite profiles with symmetric cross sections Schwane, M. and Kloppenborg, T. and Haase, M. and Khalifa, N.B. and Tekkaya, A.E. Procedia CIRP 18 126-131 (2014) Composite profiles composed of aluminum base material and steel reinforcing elements manufactured by bar extrusion exhibit residual stresses. These stresses occur due to the different thermal shrinkage of the materials during cooling of the profile. In this paper, the residual stresses are investigated by means of analytical and numerical analyses. The influence of the reinforcing volume and the material behavior, i.e. the plastification of the base material, is discussed. Furthermore, the residual stresses in symmetric profile cross sections with multiple reinforcings are examined and compared to the stresses in a simple composite rod with a centric reinforcing. © 2014 Elsevier B.V.
  	view abstract	doi: 10.1016/j.procir.2014.06.119

• 2014 • 129	Simulation of composite hot extrusion with high reinforcing Volumes Schwane, M. and Citrea, T. and Dahnke, C. and Haase, M. and Khalifa, N.B. and Tekkaya, A.E. Procedia Engineering 81 1265-1270 (2014) Experimental results, which indicate a significant influence of the reinforcing elements on the material flow during composite extrusion with high reinforcing volumes, are presented. In order to analyze the process numerically, finite element simulations with models taking into account the reinforcing elements were carried out. The results are discussed with regard to the material flow and the load of the reinforcing elements. © 2014 The Authors. Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.proeng.2014.10.108

• 2014 • 128	Simulation of grinding processes using finite element analysis and geometric simulation of individual grains Siebrecht, T. and Biermann, D. and Ludwig, H. and Rausch, S. and Kersting, P. and Blum, H. and Rademacher, A. Production Engineering 8 345-353 (2014) The wear-resistance of sheet metal forming tools can be increased by thermally sprayed coatings. However, without further treatment, the high roughness of the coatings leads to poor qualities of the deep drawn sheet surfaces. In order to increase the surface quality of deep drawing tools, grinding on machining centers is a suitable solution. Due to the varying engagement situations of the grinding tools on free-formed surfaces, the process forces vary as well, resulting in inaccuracies of the ground surface shape. The grinding process can be optimized by means of a simulative prediction of the occurring forces. In this paper, a geometric-kinematic simulation coupled with a finite element analysis is presented. Considering the influence of individual grains, an additional approximation to the resulting topography of the ground surface is possible. By using constructive solid geometry and dexel modeling techniques, multiple grains can be simulated with the geometric-kinematic approach simultaneously. The process forces are predicted with the finite element method based on an elasto-plastic material model. Single grain engagement experiments were conducted to validate the simulation results. © 2014 German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-013-0524-9

• 2014 • 127	Simulation of the effect of realistic surface textures on thermally induced topcoat stress fields by two-dimensional interface functions Nordhorn, C. and Mücke, R. and Vaßen, R. Surface and Coatings Technology 258 181-188 (2014) The simulation of thermally induced three-dimensional stress fields in multilayer systems with rough interfaces according to the distribution of stress levels by two-dimensional modeling approaches is investigated here by performing a case study on atmospherically plasma-sprayed thermal barrier coating systems. In order to analyze the microstructure effect, the pronounced interface roughness of these systems is simulated with different approximation functions, whose parameters are derived on the basis of measured surface roughness parameters. Finite element analyses of realistic three-dimensional and multiple two-dimensional models were performed ensuring that consistent boundary conditions were established in both cases. These analyses yielded stress distributions as a function of the thickness of a thermally grown oxide layer. In comparison to the reference histogram for the stress distribution in the three-dimensional model, the analyses of the two-dimensional approximation models result in histograms which correctly reflect essential oxide-growth-related features such as stress field inversion and reduction of maximum stress levels. However, these simplifying two-dimensional models do not reflect all the details of the stress distributions. The three-dimensional reference is found to be too complex with respect to the geometric interface features to be replaced by a single two-dimensional approximating function. © 2014 Elsevier B.V.
  	view abstract	doi: 10.1016/j.surfcoat.2014.09.032

• 2014 • 126	Statistical process modelling for machining of inhomogeneous mineral subsoil Weihs, C. and Raabe, N. and Ferreira, M. and Rautert, C. Studies in Classification, Data Analysis, and Knowledge Organization 46 253-263 (2014) Because in the machining process of concrete, tool wear and production time are very cost sensitive factors, the adaption of the tools to the particular machining processes is of major importance. We show how statistical methods can be used to model the influences of the process parameters on the forces affecting the workpiece as well as on the chip removal rate and the wear rate of the used diamond. Based on these models a geometrical simulation model can be derived which will help to determine optimal parameter settings for specific situations. As the machined materials are in general abrasive, usual discretized simulation methods like finite elements models can not be applied. Hence our approach is another type of discretization subdividing both material and diamond grain into Delaunay tessellations and interpreting the resulting micropart connections as predetermined breaking points. Then, the process is iteratively simulated and in each iteration the interesting entities are computed. © Springer International Publishing Switzerland 2014.
  	view abstract	doi: 10.1007/978-3-319-01264-3_22

• 2014 • 125	Synthesis, characterization, and nanoindentation response of single crystal Fe-Cr-Ni alloys with FCC and BCC structures Xia, Y.Z. and Bei, H. and Gao, Y.F. and Catoor, D. and George, E.P. Materials Science and Engineering A 611 177-187 (2014) Fe-based alloys are used extensively in many structural applications including under irradiation conditions in the nuclear industry. In this study, model Fe-Cr, Fe-Ni and Fe-Cr-Ni alloys that are the basis of many structural steels were synthesized as single crystals and characterized. The compositions investigated were Fe-15Cr, Fe-30Cr, Fe-30Ni and Fe-15Cr-15Ni (at%). Several key mechanical properties were determined which will be useful in further studies of irradiation/deformation-induced defects. Incipient plasticity and slip characteristics were investigated by nanoindentation on (001) and (1-10) surfaces, and hardness, modulus, pop-in behavior and theoretical strength were determined. The slip trace patterns after microindentation were imaged in a microscope. A novel slip trace analysis was developed and the underlying deformation mechanisms identified. The analysis shows that under both (001) and (1-10) indentations, the activated slip system for the BCC alloys is {112} for the FCC alloys the activated slip plane is {111}. These results were confirmed with finite element simulations using a slip-based crystal-plasticity model. Finally, the effects of heterogeneous pop-in mechanisms are discussed in the context of incipient plasticity in the four different alloys. © 2014 Elsevier B.V.
  	view abstract	doi: 10.1016/j.msea.2014.05.079

• 2014 • 124	Texture and microstructure evolution during non-crystallographic shear banding in a plane strain compressed Cu-Ag metal matrix composite Jia, N. and Raabe, D. and Zhao, X. Acta Materialia 76 238-251 (2014) We studied the texture and microstructure evolution in a plane strain compressed Cu-Ag metal matrix composite (MMC) with a heterophase microstructure using crystal plasticity finite element simulations. Lattice reorientations induced by both crystallographic (dislocation slip and twinning) and non-crystallographic (shear banding) mechanisms are addressed. First, simulations on a polycrystalline composite are made. Quite similar texture trends are observed for the composites and for the individual single-phase materials, namely, copper-type texture components in the Cu phase and brass-type texture components in the Ag phase. This result differs from experimental data that show less copper-type and more brass-type textures in both phases for the composite materials. To explore co-deformation mechanisms that lead to the specific crystallographic textures in the MMC, bicrystal simulations for the composite with specific initial orientation combinations are performed. The bicrystal simulations reproduce the experimentally observed trends of texture evolution in the respective phases of the composite, indicating that the localized stress and strain fields as well as the co-deformation mechanisms within the actual heterophase microstructure are well captured. The modeling shows that to accommodate plastic deformation between adjacent phases in the bicrystals, pronounced shear bands are triggered by stress concentration at the hetero-interfaces. With further deformation the bands penetrate through the phase boundaries and lead to larger lattice rotations. The simulations confirm that the shear banding behavior in heterophase composites is different from that in single-phase metals and the texture evolution in composite materials is strongly influenced by the starting texture, the local constraints exerted from the phase boundaries and the constitutive properties of the abutting phases. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.actamat.2014.05.036

• 2014 • 123	The CG1-DG2 method for convection-diffusion equations in 2D Bittl, M. and Kuzmin, D. and Becker, R. Journal of Computational and Applied Mathematics 270 21-31 (2014) In this paper, we present the CG1-DG2 method for convection-diffusion equations. The space of continuous piecewise-linear functions is enriched with discontinuous quadratics so that the resultant finite element approximation is continuous at the vertices of the mesh but may have jumps across the edges. Three different approaches to the discretization of the diffusive part are considered: the symmetric interior penalty Galerkin method, the non-symmetric interior penalty Galerkin method and the Baumann-Oden method. In the context of elliptic problems we summarize well-known a priori error estimates for the discontinuous Galerkin approximation which carry over to the CG1-DG2 approach. Both methods have the same convergence rate which is also confirmed by numerical studies for diffusion and convection-diffusion problems. © 2014 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.cam.2014.03.008

• 2014 • 122	The computation of dispersion relations for axisymmetric waveguides using the Scaled Boundary Finite Element Method Gravenkamp, H. and Birk, C. and Song, C. Ultrasonics 54 1373-1385 (2014) This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior. © 2014 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.ultras.2014.02.004

• 2014 • 121	The generalized Hill model: A kinematic approach towards active muscle contraction Göktepe, S. and Menzel, A. and Kuhl, E. Journal of the Mechanics and Physics of Solids 72 20-39 (2014) Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion. © 2014 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.jmps.2014.07.015

• 2014 • 120	The modeling scheme to evaluate the influence of microstructure features on microcrack formation of DP-steel: The artificial microstructure model and its application to predict the strain hardening behavior Vajragupta, N. and Wechsuwanmanee, P. and Lian, J. and Sharaf, M. and Münstermann, S. and Ma, A. and Hartmaier, A. and Bleck, W. Computational Materials Science 94 198-213 (2014) Due to the existence of constituents with strong distinction in mechanical properties, dual phase steels exhibit remarkably high-energy absorption along with excellent combination of strength and ductility. Furthermore, these constituents also affect deformation and microcrack formation in which various mechanisms can be observed. Thus, a reliable microstructure-based simulation approach for describing these deformations and microcrack initiation is needed. Under this framework of modeling scheme development, several work packages have been carried out. These work packages includes algorithm to generate the artificial microstructure model, a procedure to derive plasticity parameters for each constituent, and characterization of the microcrack formation and initiation criteria determination. However, due to the complexity of topic and in order to describe each work package in detail, this paper focused only on the approach to generate the artificial microstructure model and its application to predict the strain hardening behavior. The approach was based on the quantitative results of metallographic microstructure analysis and their statistical representation. The dual phase steel was first characterized by EBSD analysis to identify individual phase grain size distribution functions. The results were then input into a multiplicatively weighted Voronoi tessellation based algorithm to generate artificial microstructure geometry models. Afterwards, nanoindentation was performed to calibrate crystal plasticity parameters of ferrite and empirical approach based on local chemical composition was used to approximate flow curve of martensite. By assigning the artificial microstructure model with plasticity description of each constituent, strain-hardening behavior of DP-steel was then predicted. © 2014 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.commatsci.2014.04.011

• 2014 • 119	The reference solution approach to hp-adaptivity in finite element flux-corrected transport algorithms Bittl, M. and Kuzmin, D. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 8353 LNCS 197-204 (2014) This paper presents an hp-adaptive flux-corrected transport algorithm based on the reference solution approach. It features a finite element approximation with unconstrained high-order elements in smooth regions and constrained Q1 elements in the neighborhood of steep fronts. The difference between the reference solution and its projection into the current (coarse) space is used as an error indicator to determine the local mesh size h and polynomial degree p. The reference space is created by increasing the polynomial degree p in smooth elements and h-refining the mesh in nonsmooth elements. The smoothness is determined by a hierarchical regularity estimator based on discontinuous higher-order reconstructions of the solution and its derivatives. The discrete maximum principle for linear/bilinear finite elements is enforced using a linearized flux-corrected transport (FCT) scheme. p-refinement is performed by enriching a continuous bilinear approximation with continuous or discontinuous basis functions of polynomial degree p ≥ 2. The algorithm is implemented in the open-source software package HERMES. The use of hierarchical data structures that support arbitrary level hanging nodes makes the extension of FCT to hp-FEM relatively straightforward. The accuracy of the proposed methodology is illustrated by a numerical example for a two-dimensional benchmark problem with a known exact solution. © 2014 Springer-Verlag.
  	view abstract	doi: 10.1007/978-3-662-43880-0_21

• 2014 • 118	Towards the multi-scale simulation of martensitic phase-transformations: An efficient post-processing approach applied to turning processes Ostwald, R. and Tiffe, M. and Bartel, T. and Zabel, A. and Menzel, A. and Biermann, D. Journal of Materials Processing Technology 214 1516-1523 (2014) This work presents an efficient finite element based scheme for the prediction of process properties and especially the material condition of workpiece surfaces after turning. This is achieved by using a database generated with the help of a micromechanically motivated material model - capable of simulating interactions of phase transitions and plasticity - for the efficient post-processing of a macroscopic thermo-mechanically coupled finite element simulation of the turning process. This modelling technique is applied to the martensitic part of a functionally graded workpiece which is produced by thermo-mechanically controlled forging processes. Those workpieces provide locally varying material conditions, which are tailored to the later application. The resulting pre-products have to be turned in order to achieve the desired final workpiece geometry and surfaces. Such processes strongly affect material properties such as hardness and ductility. A deterioration of the functionality of the gradation, i.e. the martensitic surface properties, may occur by generation of residual tensile principal stresses which can occur accompanied by white layer formation. These deteriorations can be avoided by adjusting the process parameters appropriately. Especially the cutting speed is supposed to be on a low level (vc < 80 m/min) to avoid thermally driven formation of a white layer and the generation of tensile residual stresses. It is shown how finite element simulations can give insight into the material interactions and thereby facilitate the support of the process parameter adjustment in order to support efficient and reliable part production in industrial applications. © 2014 Elsevier B.V.
  	view abstract	doi: 10.1016/j.jmatprotec.2014.02.022

• 2014 • 117	User defined finite element for modeling and analysis of active piezoelectric shell structures Nestorović, T. and Marinković, D. and Shabadi, S. and Trajkov, M. Meccanica 49 1763-1774 (2014) This paper presents the user defined nine-node piezoelectric shell element and its implementation within a user element subroutine for modeling and analysis of thin-walled active composite structures. The element has been implemented within commercial finite element software ABAQUS. Application of the element covers modeling of arbitrary thin-walled structures also with complex geometries, whereby the automated mesh generation has been accomplished by developing a Python based interface for meshing procedure. In order to be able to perform the post-processing, a special adaptation of the user element had to be performed for visualization purposes. The implemented element regards the piezoelectric thin layers polarized in the thickness direction and it is based on the e31 piezoelectric effect. It has been also shown that this biquadratic nine-node element based on degenerated shell approach is less prone to locking effects and more suitable for implementation with curved structures. Through several examples the accuracy of the implemented user defined shell element as well as of the Python-based mesh extension has been demonstrated, along with the possibilities for post-processing. Meshing the structures with the nine-node user element is not third party software dependent. © 2014 The Author(s).
  	view abstract	doi: 10.1007/s11012-014-9925-x

• 2013 • 116	A minimization-based finite element formulation for interface-preserving level set reinitialization Basting, C. and Kuzmin, D. Computing 95 S13-S25 (2013) This paper presents a new approach to reinitialization in finite element methods for the level set transport equation. The proposed variational formulation is derived by solving a minimization problem. A penalty term is introduced to preserve the shape of the free interface in the process of redistancing. In contrast to hyperbolic PDE reinitialization, the resulting boundary value problem is elliptic and can be solved using a simple fixed-point iteration method. The minimization-based approach makes it possible to define the desired geometric properties in terms of a suitable potential function. In particular, truncated distance functions can be generated using a doublewell potential. The results of a numerical study indicate that the new methodology is a promising alternative to conventional reinitialization techniques. © 2013 Springer-Verlag Wien.
  	view abstract	doi: 10.1007/s00607-012-0259-z

• 2013 • 115	A positivity-preserving finite element method for chemotaxis problems in 3D Strehl, R. and Sokolov, A. and Kuzmin, D. and Horstmann, D. and Turek, S. Journal of Computational and Applied Mathematics 239 290-303 (2013) We present an implicit finite element method for a class of chemotaxis models in three spatial dimensions. The proposed algorithm is designed to maintain mass conservation and to guarantee positivity of the cell density. To enforce the discrete maximum principle, the standard Galerkin discretization is constrained using a local extremum diminishing flux limiter. To demonstrate the efficiency and robustness of this approach, we solve blow-up problems in a 3D chemostat domain. To give a flavor of more complex and realistic chemotactic applications, we investigate the pattern dynamics and aggregating behavior of the bacteria Escherichia coli and Salmonella typhimurium. The obtained numerical results are in good qualitative agreement with theoretical studies and experimental data reported in the literature. © 2012 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.cam.2012.09.041

• 2013 • 114	A Simultaneous Augmented Lagrange Approach for the Simulation of Soft Biological Tissue Böse, D. and Brinkhues, S. and Erbel, R. and Klawonn, A. and Rheinbach, O. and Schröder, J. Lecture Notes in Computational Science and Engineering 91 369-376 (2013) In this paper, we consider the elastic deformation of arterial walls as occurring, e.g., in the process of a balloon angioplasty, a common treatment in the case of atherosclerosis. Soft biological tissue is an almost incompressible material. To account for this property in finite element simulations commonly used free energy functions contain terms penalizing volumetric changes. The incorporation of such penalty terms can, unfortunately, spoil the convergence of the nonlinear iteration scheme, i.e., of Newton's method, as well as of iterative solvers applied for the solution of the linearized systems of equations. We show that the augmented Lagrange method can improve the convergence of the linear and nonlinear iteration schemes while, at the same time, implementing a guaranteed bound for the volumetric change. Our finite element model of an atherosclerotic arterial segment, see Fig. 1, is constructed from intravascular ultrasound images; for details see [4]. © Springer-Verlag Berlin Heidelberg 2013.
  	view abstract	doi: 10.1007/978-3-642-35275-1_43

• 2013 • 113	A three-phase thermo-hydro-mechanical finite element model for freezing soils Zhou, M.M. and Meschke, G. International Journal for Numerical and Analytical Methods in Geomechanics 37 3173-3193 (2013) Artificial ground freezing (AGF) is a commonly used technique in geotechnical engineering for ground improvement such as ground water control and temporary excavation support during tunnel construction in soft soils. The main potential problem connected with this technique is that it may produce heave and settlement at the ground surface, which may cause damage to the surface infrastructure. Additionally, the freezing process and the energy needed to obtain a stable frozen ground may be significantly influenced by seepage flow. Evidently, safe design and execution of AGF require a reliable prediction of the coupled thermo-hydro-mechanical behavior of freezing soils. With the theory of poromechanics, a three-phase finite element soil model is proposed, considering solid particles, liquid water, and crystal ice as separate phases and mixture temperature, liquid pressure, and solid displacement as the primary field variables. In addition to the volume expansion of water transforming into ice, the contribution of the micro-cryo-suction mechanism to the frost heave phenomenon is described in the model using the theory of premelting dynamics. Through fundamental physical laws and corresponding state relations, the model captures various couplings among the phase transition, the liquid transport within the pore space, and the accompanying mechanical deformation. The verification and validation of the model are accomplished by means of selected analyses. An application example is related to AGF during tunnel excavation, investigating the influence of seepage flow on the freezing process and the time required to establish a closed supporting frozen arch. © 2013 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nag.2184

• 2013 • 112	An edge-based smoothed finite element method for 3D analysis ofsolid mechanics problems Cazes, F. and Meschke, G. International Journal for Numerical Methods in Engineering 94 715-739 (2013) The edge-based smoothed finite element method (ES-FEM) was proposed recently in Liu, Nguyen-Thoi, and Lam to improve the accuracy of the FEM for 2D problems. This method belongs to the wider family of the smoothed FEM for which smoothing cells are defined to perform the numerical integration over the domain. Later, the face-based smoothed FEM (FS-FEM) was proposed to generalize the ES-FEM to 3D problems. According to this method, the smoothing cells are centered along the faces of the tetrahedrons of the mesh. In the present paper, an alternative method for the extension of the ES-FEM to 3D is investigated. This method is based on an underlying mesh composed of tetrahedrons, and the approximation of the field variables is associated with the tetrahedral elements; however, in contrast to the FS-FEM, the smoothing cells of the proposed ES-FEM are centered along the edges of the tetrahedrons of the mesh. From selected numerical benchmark problems, it is observed that the ES-FEM is characterized by a higher accuracy and improved computational efficiency as compared with linear tetrahedral elements and to the FS-FEM for a given number of degrees of freedom. © 2013 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.4472

• 2013 • 111	An hp-adaptive flux-corrected transport algorithm for continuous finite elements Bittl, M. and Kuzmin, D. Computing 95 S27-S48 (2013) This paper presents an hp-adaptive flux-corrected transport algorithm for continuous finite elements. The proposed approach is based on a continuous Galerkin approximation with unconstrained higher-order elements in smooth regions and constrained P1/Q1 elements in the neighborhood of steep fronts. Smooth elements are found using a hierarchical smoothness indicator based on discontinuous higher-order reconstructions. A gradient-based error indicator determines the local mesh size h and polynomial degree p. The discrete maximum principle for linear/bilinear finite elements is enforced using a linearized flux-corrected transport (FCT) algorithm. The same limiting strategy is employed when it comes to constraining the L2 projection of data from one finite-dimensional space into another. The new algorithm is implemented in the open-source software package Hermes. The use of hierarchical data structures that support arbitrary-level hanging nodes makes the extension of FCT to hp-FEM relatively straightforward. The accuracy of the proposed method is illustrated by a numerical study for a two-dimensional benchmark problem with a known exact solution. © 2013 Springer-Verlag Wien.
  	view abstract	doi: 10.1007/s00607-012-0223-y

• 2013 • 110	An imbricate finite element method (i-fem) using full, reduced, and smoothed integration Cazes, F. and Meschke, G. Computational Mechanics 52 993-1021 (2013) Abstract A method to design finite elements that imbricate with each other while being assembled, denoted as imbricate finite element method, is proposed to improve the smoothness and the accuracy of the approximation based upon low order elements. Although these imbricate elements rely on triangular meshes, the approximation stems from the shape functions of bilinear quadrilateral elements. These elements satisfy the standard requirements of the finite element method: continuity, delta function property, and partition of unity. The convergence of the proposed approximation is investigated by means of two numerical benchmark problems comparing three different schemes for the numerical integration including a cell-based smoothed FEM based on a quadratic shape of the elements edges. The method is compared to related existing methods. © Springer-Verlag Berlin Heidelberg 2013.
  	view abstract	doi: 10.1007/s00466-013-0860-9

• 2013 • 109	Computational model for the cell-mechanical response of the osteocyte cytoskeleton based on self-stabilizing tensegrity structures Kardas, D. and Nackenhorst, U. and Balzani, D. Biomechanics and Modeling in Mechanobiology 12 167-183 (2013) The mechanism by which mechanical stimulation on osteocytes results in biochemical signals that initiate the remodeling process inside living bone tissue is largely unknown. Even the type of stimulation acting on these cells is not yet clearly identified. However, the cytoskeleton of osteocytes is suggested to play a major role in the mechanosensory process due to the direct connection to the nucleus. In this paper, a computational approach to model and simulate the cell structure of osteocytes based on self-stabilizing tensegrity structures is suggested. The computational model of the cell consists of the major components with respect to mechanical aspects: the integrins that connect the cell with the extracellular bone matrix, and different types of protein fibers (microtubules and intermediate filaments) that form the cytoskeleton, the membrane-cytoskeleton (microfilaments), the nucleus and the centrosome. The proposed geometrical cell models represent the cell in its physiological environment which is necessary in order to give a statement on the cell behavior in vivo. Studies on the mechanical response of osteocytes after physiological loading and in particular the mechanical response of the nucleus show that the load acting on the nucleus is rising with increasing deformation applied to the integrins. © 2012 Springer-Verlag.
  	view abstract	doi: 10.1007/s10237-012-0390-y

• 2013 • 108	Design of next generation thermal barrier coatings - Experiments and modelling Gupta, M. and Curry, N. and Nylén, P. and Markocsan, N. and Vaßen, R. Surface and Coatings Technology 220 20-26 (2013) Thermal barrier coating (TBC) systems have been used in the gas turbine industry since the 1980s. The future needs both the air and land based turbine industry involve higher operating temperatures with longer lifetime on the component so as to increase power and efficiency of gas turbines. The aim of this study was to meet these future needs by further development of zirconia coatings. The intention was to design a coating system which could be implemented in industry within the next 3. years. Different morphologies of ceramic topcoat were evaluated; using dual layer systems and polymers to generate porosity. Dysprosia stabilised zirconia was also included in this study as a topcoat material along with the state-of-the-art yttria stabilised zirconia (YSZ). High purity powders were selected in this work. Microstructure was assessed with scanning electron microscope and an in-house developed image analysis routine was used to characterise porosity content. Evaluations were carried out using the laser flash technique to measure thermal conductivity. Lifetime was assessed using thermo-cyclic fatigue testing. Finite element analysis was utilised to evaluate thermal-mechanical material behaviour and to design the morphology of the coating with the help of an artificial coating morphology generator through establishment of relationships between microstructure, thermal conductivity and stiffness. It was shown that the combined empirical and numerical approach is an effective tool for developing high performance coatings. The results show that large globular pores and connected cracks inherited within the coating microstructure result in a coating with best performance. A low thermal conductivity coating with twice the lifetime compared to the industrial standard today was fabricated in this work. © 2012 Elsevier B.V.
  	view abstract	doi: 10.1016/j.surfcoat.2012.09.015

• 2013 • 107	Elastoplastic buckling as source of misinterpretation of micropillar tests Daum, B. and Dehm, G. and Clemens, H. and Rester, M. and Fischer, F.D. and Rammerstorfer, F.G. Acta Materialia 61 4996-5007 (2013) Microscopic compression tests (micropillar tests) are typically used to obtain stiffness and strength properties of materials at small length scales. In this work it is shown that structural effects, in particular instabilities, have implications on the resulting load-displacement diagram. Care has to be taken when the measured load-displacement path of a micropillar is interpreted as a stress-strain path of the material. Several structural effects are discussed by means of computational analysis. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.actamat.2013.04.046

• 2013 • 106	FEM modelling of a coaxial three-electrode test cell for electrochemical impedance spectroscopy in lithium ion batteries Klink, S. and Höche, D. and La Mantia, F. and Schuhmann, W. Journal of Power Sources 240 273-280 (2013) Electrochemical impedance spectroscopy for lithium ion batteries has recently gained increasing attention due to its ability of non-invasive evaluation of important electrochemical parameters. Commonly used three-electrode test cells, however, proved unreliable due to asymmetric current line distributions, causing severe distortions of impedance spectra. Finite element method (FEM) simulations can visualize these current lines at different frequencies and simulate impedance spectra at given geometries. By applying FEM simulations to a recently developed coaxial impedance test cell, limiting conditions for reliable impedance measurements could be identified. Using a reference electrode in coaxial position yields sufficiently reliable results as long as the electrode misalignment is small compared to the electrolyte thickness and edge effects are prevented. © 2013 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.jpowsour.2013.03.186

• 2013 • 105	Finite element method-assisted acquisition of the matrix influence on the indentation results of an embedded hard phase Pöhl, F. and Huth, S. and Theisen, W. Materials Science and Engineering A 559 822-828 (2013) FE-simulations were performed in order to quantify the matrix influence on the load-displacement curve and thus on the apparent hardness and Young's modulus of an embedded hard phase. The model system investigated in this study is the cold work tool steel X210Cr12 with an embedded spherical M 7C 3 carbide. In order to investigate the matrix influence on the indentation results, two different heat-treatment conditions were distinguished (soft-annealed and quenched+tempered). For each material combination, as well as several hard phase diameters, load-displacement curves and mechanical properties were calculated (via traditional Oliver and Pharr method) [1]. For low hard phase sizes or deep indentation depths, the surrounding matrix undergoes plastic deformation as the hard phase is pushed into it. This push-in event leads to significant errors in the calculated material parameters. A critical maximum indentation depth was determined depending on the hard phase diameter. It is shown that the ratio of indentation depth and hard phase diameter is the quantity of importance. © 2012 Elsevier B.V.
  	view abstract	doi: 10.1016/j.msea.2012.09.029

• 2013 • 104	Finite strain viscoelasticity: How to consistently couple discretizations in time and space on quadrature-point level for full order p ≥ 2 and a considerable speed-up Eidel, B. and Stumpf, F. and Schröder, J. Computational Mechanics 52 463-483 (2013) In computational viscoelasticity, the spatial finite element discretization for the global solution of the weak form of the balance of momentum is coupled to the temporal discretization for solving local initial value problems (IVP) of viscoelastic flow. In this contribution we show that this global-local or space-time coupling is consistent, if the total strain tensor as the coupling quantity exhibits the same approximation order p in time as the Runge-Kutta (RK) integration algorithm. To this end we construct interpolation polynomials, based on data at tn+1, tn, ⋯, tn+2-p, p ≥ 2, which provide consistent strain data at RK stages. This is a generalization of the idea proposed in (Eidel and Kuhn, Int J Numer Methods Eng 87(11):1046-1073, 2011). For lower-order strain interpolation, time integration exhibits order reduction and therefore low efficiency. For consistent strain interpolation, the adapted RK methods up to p=4 obtain full convergence order and thus approve the novel concept of consistency. High speed-up factors substantiate the improved efficiency compared with Backward-Euler. © 2013 Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s00466-012-0823-6

• 2013 • 103	Grain size evolution simulation in aluminium alloys AA 6082 and AA 7020 during hot forward extrusion process Foydl, A. and Segatori, A. and Ben Khalifa, N. and Donati, L. and Brosius, A. and Tomesani, L. and Tekkaya, A.E. Materials Science and Technology (United Kingdom) 29 100-110 (2013) The present paper investigates the grain size evolution in aluminium alloys AA 6082 and AA 7020 during hot forward extrusion process. The aim of the present work is the definition and implementation of a predictive algorithm that is able to compute the evolution of the grain shape during the process within the finite element method code Deform. Extrusion experiments were performed at two levels: at reduced scale for investigating and identifying the predictive equations and at industrial scale for validating the developed algorithm. At small scale extrusion, a complete factorial plan was performed for two alloys at three different temperatures, three extrusion ratios and two ram speeds: the discards and extrudates from the experiments were quenched immediately in order to avoid any potential recrystallisation, hence allowing measurements of transitional processing steps. At the industrial scale, instead, the 7020 alloy was extruded with two different die designs, thus producing a 20 mm diameter round bar under different extrusion ratios and strain paths. Finite element simulations were initially validated over visioplastic investigations in order to establish an accurate computation of the material flow, then experimental and numerical results were coupled, thus allowing the definition of the grain evolution model that was successfully integrated and validated on industrial scale trials. © 2013 Institute of Materials, Minerals and Mining.
  	view abstract	doi: 10.1179/1743284712Y.0000000132

• 2013 • 102	Influence of different transition zones on the dynamic response of track-subgrade systems Shan, Y. and Albers, B. and Savidis, S.A. Computers and Geotechnics 48 21-28 (2013) A railway track-subgrade system is modeled using the finite element method (FEM). Two different transition zones between a bridge and an ordinary subgrade, usually used for high speed passenger lines in China, are investigated. Both the calculated vertical displacement and acceleration of the rail and the slab and the calculated vertical displacement and the stress of the subgrade surface of the two transition zones are compared. The dynamic response of the two-part transition section is better than that of the inverted trapezoid transition section, and a 30-m length of both transition sections is recommended. The dynamic response of the track-subgrade system changes abruptly after the first 3. m of the transition section, measured from the bridge abutment. Special attention should be given to this critical zone during construction. © 2012 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compgeo.2012.09.006

• 2013 • 101	Method for the evaluation of stretch blow molding simulations with free blow trials Zimmer, J. and Stommel, M. IOP Conference Series: Materials Science and Engineering 48 (2013) Finite-Element (FE) simulations are a valuable tool to support the analysis and optimization of production processes. In order to achieve realistic simulation results, a consistent simulation set-up followed by an evaluation through experiments is crucial. Stretch Blow Molding (SBM) is a commonly applied forming method to produce thin walled bottles. Polyethylene terephthalate (PET) preforms are biaxially stretched into a closed cavity to form a bottle. In this process the thermo-mechanical material behavior during forming greatly influences the performance of the end product and consequently plays a key role for a reliable process simulation. To ensure a realistic material representation in the simulation model, an adequate material model is calibrated with stress-strain curves from biaxial tests. Thin PET-sheets are stretched under defined temperatures and strain rates. These representative experiments include process simplifications regarding geometry, heating and deformation parameters. Therefore, an evaluation step subsequent to the simulation set-up is inevitable. This paper presents a method for extracting temperature dependent stress-strain-curves from experiments close to the production process which enables the crucial evaluation of a process simulation. In the SBM process, the wall thickness distribution of the bottle refers to the preform deformation over time but does not fully define the thermo-mechanical material behavior. In the presented method, PET-preforms receive thermal treatment with Infrared (IR)-heaters from an SBM-machine and are subsequently inflated into free air (free-blow-trial). An IR-camera is used to obtain the temperature distribution on the preform immediately before blowing. Two high speed cameras are synchronized with a pressure sensor to consequently calculate reliable stress-strain curves at any point on the preform surface. These data is finally compared to results from FE-simulations of the free blow trials.
  	view abstract	doi: 10.1088/1757-899X/48/1/012004

• 2013 • 100	Micromechanical modelling of damage and failure in dual phase steels Lian, J. and Vajragupta, N. and Münstermann, S. Key Engineering Materials 554-557 2369-2374 (2013) Dual phase (DP) steels consisting of two phases, ferrite and dispersed martensite, offer an attractive combination of strength and stretchability, which is a result of the strong distinctions of these constituents in mechanical properties. However, the damage behaviour in DP steels exhibits a rather complex scenario: voids are generated by the debonding of the hard phase from the matrix and the inner cracking of the hard phase in addition to by inclusions. The target of this study is to describe the initiation and evolution of damage in DP steel and develop a microstructure-based model which is capable of reflecting the underlying damage mechanisms. Both uniaxial and biaxial tensile tests are performed and the subsequent metallographic investigations are executed to reveal the mechanisms of damage initiation and evolution under different stress state condition and attention will be paid on the influence of various microstructural features on the initiation of damage. In finite element (FE) simulations, the microstructural features are taken into account by the representative volume elements (RVE). Different treatments of the constitutive behaviour of each constituent including isotropic hardening rule and crystallographically dependent configuration with crystal plasticity finite element method are investigated. Several numerical aspects are also discussed, such as RVE size, mesh size, element type, and boundary connections. In the end, the study is attempting to achieve a quantitative assessment of the cold formability of the investigated steel in a microscopic level based on microstructure information of material as well as to understand the damage mechanisms under different stress states condition which cause the macroscopic failure during plastic deformation. Copyright © 2013 Trans Tech Publications Ltd.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.554-557.2369

• 2013 • 99	Modeling and simulation of heat input in deep-hole drilling with twist drills and MQL Biermann, D. and Iovkov, I. Procedia CIRP 8 88-93 (2013) Former investigations on deep-hole drilling using twist drills and MQL indicated that the heat input into the workpiece results not only from the primary thermal load within the machining zone but also from the secondary heating at the borehole wall. In order to determine the primary heat flow into the machined part an experimental setup for drilling devoid of the influence of the borehole wall has been developed. The results show that the machining time is the major factor: the lower the machining time the lower the measured temperature within the workpiece. A finite-element-(FE)-based simulation in consideration of the material removal has been implemented and studied, regarding the process, the FE-mesh and the time discretisation. Based on the reliable parameter, obtained by the discretisation study, a simulation control loop is presented which allows the calculation of the rate of heat flow into the machined part. It is remarkable that due to the material removal the heat flow into the workpiece increases when machining with higher cutting speed and feed values, while the measured and simulated temperature decreases. Copyright © 2013 Elsevier B.V.
  	view abstract	doi: 10.1016/j.procir.2013.06.070

• 2013 • 98	Modeling approach for the determination of material flow and welding conditions in porthole die extrusion with gas pocket formation Schwane, M. and Gagliardi, F. and Jäger, A. and Ben Khalifa, N. and Tekkaya, A.E. Key Engineering Materials 554-557 787-793 (2013) The material flow in porthole dies is of crucial importance with regard to the seam weld quality in aluminum extrusion. Thus, experimental as well as numerical investigations on the effect of die geometry on the material flow were conducted. The experimental tests were performed on a 10 MN laboratory extrusion press. During the experimental trials, the extrusion ratio was varied by means of exchangeable die plates. Since the modular die allows removal of the aluminum in the welding chamber as well as in the feeders after the process, the material flow could be inspected in detail. The experimental results were used to improve the accuracy of FEA simulations, which were also conducted by commercial software. An attempt was made to improve the result quality of Eulerian FEA model regarding the simulation of an extrusion process with a gas pocket in the welding chamber. The influence of the modeling approach on the predicted material flow and on the contact pressure was analyzed and finally linked to the seam weld quality. Copyright © 2013 Trans Tech Publications Ltd.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.554-557.787

• 2013 • 97	Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI Pierce, D.M. and Ricken, T. and Holzapfel, G.A. International Journal for Numerical Methods in Biomedical Engineering 29 807-821 (2013) We propose a new 3D biphasic constitutive model designed to incorporate structural data on the sample/patient-specific collagen fiber network. The finite strain model focuses on the load-bearing morphology, that is, an incompressible, poroelastic solid matrix, reinforced by an inhomogeneous, dispersed fiber fabric, saturated with an incompressible fluid at constant electrolytic conditions residing in strain-dependent pores of the collagen-proteoglycan solid matrix. In addition, the fiber network of the solid influences the fluid permeability and an intrafibrillar portion that cannot be 'squeezed out' from the tissue. We implement the model into a finite element code. To demonstrate the utility of our proposed modeling approach, we test two hypotheses by simulating an indentation experiment for a human tissue sample. The simulations use ultra-high field diffusion tensor magnetic resonance imaging that was performed on the tissue sample. We test the following hypotheses: (i) the through-thickness structural arrangement of the collagen fiber network adjusts fluid permeation to maintain fluid pressure (Biomech. Model. Mechanobiol. 7:367-378, 2008); and (ii) the inhomogeneity of mechanical properties through the cartilage thickness acts to maintain fluid pressure at the articular surface (J. Biomech. Eng. 125:569-577, 2003). For the tissue sample investigated, both through-thickness inhomogeneities of the collagen fiber distribution and of the material properties serve to influence the interstitial fluid pressure distribution and maintain fluid pressure underneath the indenter at the cartilage surface. Tissue inhomogeneity appears to have a larger effect on fluid pressure retention in this tissue sample and on the advantageous pressure distribution. © 2012 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/cnm.2524

• 2013 • 96	Modelling, simulation and experimental investigation of chip formation in internal traverse grinding Holtermann, R. and Schumann, S. and Menzel, A. and Biermann, D. Production Engineering 7 251-263 (2013) We present recent developments in modelling and simulation of internal traverse grinding, a high speed machining process which enables both a large material removal rate and high surface quality. We invoke a hybrid modelling framework, including a process scale model, simulations on a mesoscale capturing the proximity of a single cBN grain and an analysis framework to investigate the grinding wheel topography. Moreover, we perform experiments to verify our simulations. Focus in this context is the influence of the cutting speed variation on the grain specific heat generation. © 2013 German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-013-0449-3

• 2013 • 95	Monolithic Newton-multigrid solution techniques for incompressible nonlinear flow models Damanik, H. and Hron, J. and Ouazzi, A. and Turek, S. International Journal for Numerical Methods in Fluids 71 208-222 (2013) We present special Newton-multigrid techniques for stationary incompressible nonlinear flow models discretized by the high order LBB-stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviors and also regarding different problem sizes and types of nonlinearity. Here, local pressure Schur complement techniques are presented as a generalization of the classical Vanka smoother. The discussed methodology is implemented for the well-known flow around cylinder benchmark configuration for generalized Newtonian as well as non-Newtonian flows including non-isothermal, shear/pressure dependent and viscoelastic effects. © 2012 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/fld.3656

• 2013 • 94	Numerical investigation of the incremental tube forming process Becker, C. and Isik, K. and Bayraktar, A. and Chatti, S. and Hermes, M. and Soyarslan, C. and Tekkaya, A. E. Key Engineering Materials 554-557 664-670 (2013) As a response to the recent years' growing demand for innovation in manufacturing processes towards lightweight design in several industrial sectors, a new process, called Incremental Tube Forming (ITF), and a corresponding machine layout have been developed. ITF is a process to manufacture bent tubes with varying cross-sections. During ITF a tube is clamped in a feeding device, which transports the tube through a spinning tool, where the diameter reduction takes place. This stage is followed by a superposed bending process without suppressing continuous feeding. This combination leads to various advantages such as improved tool life with reduced tool forces and improved product accuracy (e.g. springback behavior), as it is shown in various experimental works. This paper presents a complementary numerical treatment of the process using FEA. For this purpose, a 3D model is constructed using ABAQUS/Explicit, where the tube is modeled with conventional shell elements with uniformly reduced integration to avoid shear and membrane locking (S4R), whereas the spinning rolls are modeled as discrete rigid. With this model, the influences of process parameters, such as diameter reduction ratio and tool geometry, are investigated. This helps not only to gain a deeper understanding of the process but also to interpret already gathered experimental data with better precision and, thus establishing a basis for further improvement and optimization of this fairly new process. Copyright © 2013 Trans Tech Publications Ltd.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.554-557.664

• 2013 • 93	Numerical modelling of powder metallurgical coatings on ring-shaped parts integrated with ring rolling Kebriaei, R. and Frischkorn, J. and Reese, S. and Husmann, T. and Meier, H. and Moll, H. and Theisen, W. Journal of Materials Processing Technology 213 2015-2032 (2013) Today's demands for flexible and economic production of ring-shaped work pieces coated by functional layers can only be met by new manufacturing techniques. These are suitably based on precise process modelling and high-performance control systems. The process-integrated powder coating by radial axial rolling of rings introduces a new hybrid production technique. It takes advantage of the high temperatures and high forces of the ring rolling process. This is not only to increase the ring's diameter, but also to integrate powder metallurgical multi-functional coatings within the same process. To improve the feasibility assessment of the proposed geometries and material combinations as well as to investigate important quantities such as the stress state in the rolling gaps and the residual porosity of the powder metallurgically produced layer, the versatile application of the finite element method (FEM) is crucial. Therefore, parameterized two-dimensional and three-dimensional finite element (FE) models are created. It will be shown that the implementation of a new control mechanism based on Apollonian mutually orthogonal circles and bipolar coordinates allows an efficient stabilization of the proposed systems. The paper is concluded by a detailed description of the process simulation and a comparison of its results with experimental data. © 2013 Elsevier B.V.
  	view abstract	doi: 10.1016/j.jmatprotec.2013.05.023

• 2013 • 92	Parallelized computational modeling of pile-soil interactions in mechanized tunneling Meschke, G. and Ninić, J. and Stascheit, J. and Alsahly, A. Engineering Structures 47 35-44 (2013) The construction of tunnels in soft ground causes short and long term ground deformations resulting from the disturbance of the virgin stress state of the soil and the changing pore water conditions. In particular in urban tunneling, in each stage of the construction process, interactions between the construction process, the soil and existing building infrastructure need to be evaluated to limit the risk of damage on existing buildings and to decide on appropriate mitigation measures. Besides conventional tunneling, mechanized tunneling is a well established and flexible technology in particular in urban areas, which allows for tunnel advances in a wide range of soils and difficult conditions. The paper presents a finite element model for the simulation of interactions between mechanized tunnel construction, the surrounding soil and existing buildings resting on pile foundations in the framework of a process-oriented simulation model for mechanized tunneling. The performance of the model is demonstrated by means of selected prototype analyses. As a consequence of the high computational demand connected with this type of spatio-temporal simulations, problem specific parallelization techniques are investigated to increase the numerical efficiency of the numerical analyses. © 2012 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.engstruct.2012.07.001

• 2013 • 91	Preliminary study for flaw detection in nodular cast iron by cyclic loading and thermography Tillmann, W. and Feng, X. and Fischer, G. and Nellesen, J. NDT and E International 56 28-37 (2013) The objective of this paper is to deduce thermographic parameters from infrared (IR) picture series which indicate the presence of bulk defects in nodular cast iron. For this task, specimens manufactured with and without artificial defects are sinusoidally loaded in the range of the fatigue limit for a short period. During this time, the IR picture series were recorded with a high-speed IR camera. After a picture alignment, the time-dependency of the average gray values in picture subsets was analyzed by discrete Fourier transform (DFT) to get the magnitude and phase shift of the fundamental frequency of the local IR radiation power. The results of the experiments and FE simulations indicate consistently that the volume defects can be detected on the basis of the average and standard deviation of the phase shift distributions on the surface of the specimens. © 2013 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.ndteint.2013.01.017

• 2013 • 90	Simulation of electromagnetic forming of a cross-shaped cup by means of a viscoplasticity model coupled with damage at finite strains Kiliclar, Y. and Demir, O.K. and Vladimirov, I.N. and Kwiatkowski, L. and Reese, S. and Tekkaya, A.E. Key Engineering Materials 554-557 2363-2368 (2013) In the field of sheet metal forming conventional forming processes are well established. However, a quasi-static forming process combined with a high speed forming process can enhance the forming limits of a single one. In this paper, the investigation of the process chain quasi-static deep drawing - electromagnetic forming by means of a new coupled damage-viscoplasticity model for large deformations is performed. The finite strain constitutive model, used in the finite element simulation combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The coupling of damage and plasticity is carried out in a constitutive manner according to the effective stress concept. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasistatic deep drawing processes with high speed electromagnetic forming. Copyright © 2013 Trans Tech Publications Ltd.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.554-557.2363

• 2013 • 89	Simulation of shear banding in heterophase co-deformation: Example of plane strain compressed Cu-Ag and Cu-Nb metal matrix composites Jia, N. and Roters, F. and Eisenlohr, P. and Raabe, D. and Zhao, X. Acta Materialia 61 4591-4606 (2013) The co-deformation and shear localization in heterophase alloys is studied using two-dimensional crystal plasticity finite element simulations on plane strain compressed Cu-Ag and Cu-Nb metal matrix composites. The aim is to study the fundamentals of micromechanics, co-deformation and shear banding in materials with heterophase interfaces. It is observed that, depending on the initial orientations of the crystals, co-deformation of the constituent heterophases often proceeds via collective mechanisms, i.e. by pronounced shear banding triggered by stress concentration at the interfaces. This phenomenon leads to highly localized strains within the bands, exceeding the average strain in part by two orders of magnitude. Shear band development is related to the inherent mechanical properties of each crystal and also to the properties of the abutting crystals. The predicted topology and nature of the cross-phase shear bands, i.e. the extreme local strains, significant bending of the interface regions, and sharp strain localization that propagates across the interfaces, agree well with experimental observations in cold-rolled composites. The simulations reveal that cross-phase shear banding leads to large and highly localized values of stress and strain at heterophase interfaces. Such information is essential for a better understanding of the micromechanical boundary conditions inside co-deformed composites and the associated shear-induced chemical mixing. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.actamat.2013.04.029

• 2013 • 88	Stabilization techniques and a posteriori error estimates for the obstacle problem Biermann, D. and Iovkov, I. and Blum, H. and Rademacher, A. and Klein, N. and Suttmeier, F.-T. Applied Mathematical Sciences 7 6329-6346 (2013) This work deals with a posteriori error estimates for the obstacle problem. Deriving an estimator on the basis of the variational inequal- ity with respect to the primal variable, an inconsistent one is obtained. To achieve consistency, this problem is treated by a Lagrange formalism, which transfers the variational inequality into a saddle point problem. Different techniques to ensure the stability of the discretization and to solve the discrete problems by iterative solvers are studied and com- pared. Numerical tests confirm our results of consistent a posteriori error estimation. © 2013 Dirk Biermann et al.
  	view abstract	doi: 10.12988/ams.2013.39504

• 2013 • 87	Towards a complete FEM-based simulation toolkit on GPUs: Unstructured grid finite element geometric multigrid solvers with strong smoothers based on sparse approximate inverses Geveler, M. and Ribbrock, D. and Göddeke, D. and Zajac, P. and Turek, S. Computers and Fluids 80 327-332 (2013) We describe our FE-gMG solver, a finite element geometric multigrid approach for problems relying on unstructured grids. We augment our GPU- and multicore-oriented implementation technique based on cascades of sparse matrix-vector multiplication by applying strong smoothers. In particular, we employ Sparse Approximate Inverse (SPAI) and Stabilised Approximate Inverse (SAINV) techniques. We focus on presenting the numerical efficiency of our smoothers in combination with low- and high-order finite element spaces as well as the hardware efficiency of the FE-gMG. For a representative problem and computational grids in 2D and 3D, we achieve a speedup of an average of 5 on a single GPU over a multithreaded CPU code in our benchmarks. In addition, our strong smoothers can deliver a speedup of 3.5 depending on the element space, compared to simple Jacobi smoothing. This can even be enhanced to a factor of 7 when combining the usage of approximate inverse-based smoothers with clever sorting of the degrees of freedom. In total the FE-gMG solver can outperform a simple (multicore-) CPU-based multigrid by a total factor of over 40. © 2012 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compfluid.2012.01.025

• 2013 • 86	Validation of a heat input model for the prediction of thermomechanical deformations during NC milling Joliet, R. and Byfut, A. and Kersting, P. and Schröder, A. and Zabel, A. Procedia CIRP 8 403-408 (2013) During roughing in NC milling, heat is introduced into the workpiece. For the manufacturing of large structural components, a constantly changing temperature field is created due to the rapid movement and the varying contact conditions between tool and workpiece. Therefore, significant deformations can cause form errors that lead to rejects in the production process. In this paper, a simulation system for the prediction of transient workpiece temperatures is presented. In order to calibrate the system, simple experiments have been conducted, and a model for the introduction of energy into the workpiece via cutting has been developed. The newly developed cutting-energy input model makes it possible to perform fast simulations. Therefore, it can be used to perform simulations of the thermoelastic workpiece deformations during milling of complex shaped parts. Copyright © 2013 Elsevier B.V.
  	view abstract	doi: 10.1016/j.procir.2013.06.124

• 2012 • 85	A micromechanical damage simulation of dual phase steels using XFEM Vajragupta, N. and Uthaisangsuk, V. and Schmaling, B. and Münstermann, S. and Hartmaier, A. and Bleck, W. Computational Materials Science 54 271-279 (2012) As a result of their microstructures being made up by constituents with strong distinctions in mechanical properties, multiphase steels exhibit high energy absorption as well as an excellent combination of strength and ductility. Furthermore, the microstructural composition influences the failure behaviour of such kind of steels because of the occurrence of different fracture mechanisms in parallel. When the failure behaviour of dual phase (DP) steels is investigated, several types of failures are typically observed, such as the ductile failure of ferrite, the brittle failure of martensite and the interface debonding between phases. Hence, a reliable microstructure-based simulation approach must be developed that describes material deformation and failure under any given loading condition. In this work, two different damage mechanics methods were employed to study the interaction between failure modes in DP steels by means of a representative volume element (RVE). In order to consider the characteristics of a real microstructure, all involved phases were modelled with a precise volume fraction. Firstly, the extended finite element method (XFEM) was used to study the damage onset and progression in martensitic regions without prescribing the crack path. Secondly, a damage curve was derived and employed for the ductile ferritic phase. By combining these two damage models in the RVE model on microscopic scale, development of different failures modes in DP steels could be investigated. © 2011 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.commatsci.2011.10.035

• 2012 • 84	A modified scaled boundary finite element method for three-dimensional dynamic soil-structure interaction in layered soil Birk, C. and Behnke, R. International Journal for Numerical Methods in Engineering 89 371-402 (2012) This paper is devoted to the analysis of elastodynamic problems in 3D-layered systems which are unbounded in the horizontal direction. For this purpose, a finite element model of the near field is coupled to a scaled boundary finite element model (SBFEM) of the far field. The SBFEM is originally based on describing the geometry of a half-space or full-space domain by scaling the geometry of the near field/far field interface using a radial coordinate. A modified form of the SBFEM for waves in a 2D layer is also available. None of these existing formulations can be used to describe a 3D-layered medium. In this paper, a modified SBFEM for the analysis of 3D-layered continua is derived. Based on the use of a scaling line instead of a scaling centre, a suitable scaled boundary transformation is proposed. The derivation of the corresponding scaled boundary finite element (SBFE) equations in displacement and stiffness is presented in detail. The latter is a nonlinear differential equation with respect to the radial coordinate, which has to be solved numerically for each excitation frequency considered in the analysis. Various numerical examples demonstrate the accuracy of the new method and its correct implementation. These include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3D soil deposits over rigid bedrock. Hysteretic damping is assumed in some cases. The dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results. © 2011 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.3251

• 2012 • 83	An alternative strategy for the solution of heat and incompressible fluid flow problems via the finite volume method Nickaeen, M. and Ashrafizadeh, A. and Turek, S. Numerical Heat Transfer; Part A: Applications 62 393-411 (2012) The characteristic-based split (CBS) method has been widely used in the finite element community to facilitate the numerical solution of Navier-Stokes (NS) equations. However, this computational algorithm has rarely been employed in the finite volume context and the stabilization of the numerical solution procedure has traditionally been addressed differently in volume-based numerical schemes. In this article, the CBS-based finite volume algorithm is employed to formulate and solve a number of laminar incompressible flow and convective heat transfer problems. Both explicit and implicit versions of the algorithm are first explained and validated in the context of the solution of a lid-driven cavity problem and a backward facing step (BFS) flow problem. The modified algorithm, capable of modelling the coupling between the momentum and energy balance equations, is then introduced and used to solve a buoyancy-driven cavity flow problem. Computational results show that the CBS finite volume algorithm can be reliably used in the solution of laminar incompressible heat and fluid flow problems. © 2012 Copyright Taylor and Francis Group, LLC.
  	view abstract	doi: 10.1080/10407782.2012.703465

• 2012 • 82	An edge-based imbricate finite element method (EI-FEM) with full and reduced integration Cazes, F. and Meschke, G. Computers and Structures 106-107 154-175 (2012) An Edge-based Imbricate Finite Element Method (EI-FEM), aiming at combining the ease of mesh generation using triangular elements and the improved accuracy of quadrilateral elements, is proposed. Two finite elements for 2D analyses that imbricate each other while being assembled are designed based upon the triangulation of the domain. By means of two numerical benchmark analyses, we show that similar improvements with respect to numerical accuracy as obtained by the recently proposed Edge-based Smoothed Finite Element Method (ES-FEM) can be obtained, without sacrificing the standard concepts of the Finite Element Method. © 2012 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.compstruc.2012.04.011

• 2012 • 81	An electromechanically coupled micro-sphere framework: Application to the finite element analysis of electrostrictive polymers Thylander, S. and Menzel, A. and Ristinmaa, M. Smart Materials and Structures 21 (2012) The number of industrial applications of electroactive polymers (EAPs) is increasing and, consequently, the need for reliable modelling frameworks for such materials as well as related robust simulation techniques continuously increases. In this context, we combine the modelling of non-linear electroelasticity with a computational micro-sphere formulation in order to simulate the behaviour of EAPs. The micro-sphere approach in general enables the use of physics-based constitutive models like, for instance, the so-called worm-like chain model. By means of the micro-sphere formulation, scalar-valued micromechanical constitutive relations can conveniently be extended to a three-dimensional continuum setting. We discuss several electromechanically coupled numerical examples and make use of the finite element method to solve inhomogeneous boundary value problems. The incorporated material parameters are referred to experimental data for an electrostrictive polymer. The numerical examples show that the coupled micro-sphere formulation combined with the finite element method results in physically sound simulations that mimic the behaviour of an electrostrictive polymer. © 2012 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/0964-1726/21/9/094008

• 2012 • 80	An improved continued-fraction-based high-order transmitting boundary for time-domain analyses in unbounded domains Birk, C. and Prempramote, S. and Song, C. International Journal for Numerical Methods in Engineering 89 269-298 (2012) A high-order local transmitting boundary to model the propagation of acoustic or elastic, scalar or vector-valued waves in unbounded domains of arbitrary geometry is proposed. It is based on an improved continued-fraction solution of the dynamic stiffness matrix of an unbounded medium. The coefficient matrices of the continued-fraction expansion are determined recursively from the scaled boundary finite element equation in dynamic stiffness. They are normalised using a matrix-valued scaling factor, which is chosen such that the robustness of the numerical procedure is improved. The resulting continued-fraction solution is suitable for systems with many DOFs. It converges over the whole frequency range with increasing order of expansion and leads to numerically more robust formulations in the frequency domain and time domain for arbitrarily high orders of approximation and large-scale systems. Introducing auxiliary variables, the continued-fraction solution is expressed as a system of linear equations in iω in the frequency domain. In the time domain, this corresponds to an equation of motion with symmetric, banded and frequency-independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable in the frequency and time domains. Analytical and numerical examples demonstrate the superiority of the proposed method to an existing approach and its suitability for time-domain simulations of large-scale systems. © 2011 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.3238

• 2012 • 79	Anisotropic density growth of bone - A computational micro-sphere approach Waffenschmidt, T. and Menzel, A. and Kuhl, E. International Journal of Solids and Structures 49 1928-1946 (2012) Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties. The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots. © 2012 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijsolstr.2012.03.035

• 2012 • 78	Application of an anisotropic growth and remodelling formulation to computational structural design Waffenschmidt, T. and Menzel, A. Mechanics Research Communications 42 77-86 (2012) A classical structural optimisation problem consists of a problem-specific objective function which has to be minimised in consideration of particular constraints with respect to design and state variables. In this contribution we adopt a conceptually different approach for the design of a structure which is not based on a classical optimisation technique. Instead, we establish a constitutive micro-sphere-framework in combination with an energy-driven anisotropic microstructural growth formulation, which was originally proposed for the simulation of adaptation and remodelling phenomena in hard biological tissues such as bones. The goal of this contribution is to investigate this anisotropic growth formulation with a special emphasis on its application to structural design problems. To this end, four illustrative three-dimensional benchmark-type boundary value problems are discussed and compared qualitatively with the results obtained by classical structural optimisation strategies. The simulation results capture the densification effects and clearly identify the main load bearing regions. It turns out, that even though making use of this conceptually different growth formulation as compared to the procedures used in a classical structural optimisation context, we identify qualitatively very similar structures or rather regions of densification. Moreover, in contrast to common structural optimisation strategies, which mostly aim to optimise merely the size, shape or topology, our formulation also contains the improvement of the material itself, which - apart from the structural improvement - results in the generation of problem-specific local material anisotropy and textured evolution. © 2012 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.mechrescom.2011.12.004

• 2012 • 77	Application of the multiscale fem to the modeling of nonlinear composites with a random microstructure Klinge, S. and Hackl, K. International Journal for Multiscale Computational Engineering 10 213-227 (2012) In this contribution the properties and application of the multiscale finite element program MSFEAP are presented. This code is developed on basis of coupling the homogenization theory with the finite element method. According to this concept, the investigation of an appropriately chosen representative volume element yields the material parameters needed for the simulation of a macroscopic body. The connection of scales is based on the principle of volume averaging and the Hill-Mandel macrohomogeneity condition. The latter leads to the determination of different types of boundary conditions for the representative volume element and in this way to the postulation of a well-posed problem at this level. The numerical examples presented in the contribution investigate the effective material behavior of microporous media. An isotropic and a transversally anisotropic microstructure are simulated by choosing an appropriate orientation and geometry of the representative volume element in each Gauss point. The results are verified by comparing them with Hashin-Shtrikman's analytic bounds. However, the chosen examples should be understood as simply an illustration of the program application, while its main feature is a modular structure suitable for further development. © 2012 by Begell House, Inc.
  	view abstract	doi: 10.1615/IntJMultCompEng.2012002059

• 2012 • 76	Bem and fem results of displacements in a poroelastic column Albers, B. and Savidis, S.A. and Tasan, H.E. and Von Estorff, O. and Gehlken, M. International Journal of Applied Mathematics and Computer Science 22 883-896 (2012) The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the simple example of a poroelastic column but also the impact of different values of the permeability coefficient is investigated.
  	view abstract	doi: 10.2478/v10006-012-0065-y

• 2012 • 75	Benchmark computations of 3D laminar flow around a cylinder with CFX, OpenFOAM and FeatFlow Bayraktar, E. and Mierka, O. and Turek, S. International Journal of Computational Science and Engineering 7 253-266 (2012) Numerically challenging, comprehensive benchmark cases are of great importance for researchers in the field of CFD. Numerical benchmark cases offer researchers frameworks to quantitatively explore limits of the computational tools and to validate them. Therefore, we focus on simulations of challenging benchmark tests, laminar and transient 3D flows around a cylinder, and aim to establish a new comprehensive benchmark case by doing direct numerical simulations with three distinct CFD software packages, OpenFOAM, Ansys-CFX and FeatFlow which employ different numerical approaches to the discretisation of the incompressible Navier-Stokes equations. All the software tools successfully pass the benchmark tests and show a good agreement such that the benchmark result was precisely determined. As a main result, the CFD software package with high order finite element approximation has been found to be computationally more efficient and accurate than the ones adopting low order space discretisation methods. Copyright © 2012 Inderscience Enterprises Ltd.
  	view abstract	doi: 10.1504/IJCSE.2012.048245

• 2012 • 74	Computational simulation of mechanized tunneling as part of an integrated decision support platform Meschke, G. and Nagel, F. and Stascheit, J. International Journal of Geomechanics 11 519-528 (2012) Mechanized tunneling is characterized by a staged procedure of excavation and lining erection and continuous support of the soil by means of supporting fluids (or compressed air) at the tunnel face and pressurized grouting of the tail gap. The interactions between the tunnel boring machine (TBM), the support measures, and the soil, including the groundwater, determine the efficiency, safety, and effects on the existing infrastructure. In this paper, a process-oriented numerical simulation model for mechanized tunneling and its integration in the context of an integrated optimization platform for tunneling (IOPT) is addressed. The simulation model is based upon the finite-element method and considers the transient excavation process and all relevant components, support measures, and processes, along with their interactions during tunnel advance. In particular, the model allows the investigation of the effects of drilling and stand-still periods upon the generation of a filter cake at the tunnel face. This is demonstrated by the numerical analysis of a straight tunnel advance by means of a hydroshield machine in water-saturated soft soil. © 2011 American Society of Civil Engineers.
  	view abstract	doi: 10.1061/(ASCE)GM.1943-5622.0000044

• 2012 • 73	Effect of welding parameters on the heat-affected zone of AISI409 ferritic stainless steel Ranjbarnodeh, E. and Hanke, S. and Weiss, S. and Fischer, A. International Journal of Minerals, Metallurgy and Materials 19 923-929 (2012) One of the main problems during the welding of ferritic stainless steels is severe grain growth within the heat-affected zone (HAZ). In the present study, the microstructural characteristics of tungsten inert gas (TIG) welded AISI409 ferritic stainless steel were investigated by electron backscattered diffraction (EBSD), and the effects of welding parameters on the grain size, local misorientation, and low-angle grain boundaries were studied. A 3-D finite element model (FEM) was developed to predict the effects of welding parameters on the holding time of the HAZ above the critical temperature of grain growth. It is found that the base metal is not fully recrystallized. During the welding, complete recrystallization is followed by severe grain growth. A decrease in the number of low-angle grain boundaries is observed within the HAZ. FEM results show that the final state of residual strains is caused by competition between welding plastic strains and their release by recrystallization. Still, the decisive factor for grain growth is heat input. © 2012 University of Science and Technology Beijing and Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/s12613-012-0648-5

• 2012 • 72	FEM multigrid techniques for fluid-structure interaction with application to hemodynamics Razzaq, M. and Damanik, H. and Hron, J. and Ouazzi, A. and Turek, S. Applied Numerical Mathematics 62 1156-1170 (2012) We present special finite element and multigrid techniques for solving prototypical cerebral aneurysm hemodynamics problems numerically. An arbitrary Lagrangian-Eulerian (ALE) formulation is employed for this fluid-structure interaction (FSI) application. We utilize the well-known high order finite element pair Q2P1 for discretization in space to gain high accuracy and robustness and perform as time-stepping a fully implicit second order accurate time integrator. The resulting nonlinear discretized algebraic system is solved by an iterative Newton solver which approximates the Jacobian matrix by the divided difference approach, and the resulting linear system is solved by means of Krylov type and geometrical multigrid solvers with a Vanka-like smoother. The aim of this paper is to study the interaction of the elastic walls of an aneurysm with the geometrical shape of an implanted stent structure for prototypical 2D configurations. Preliminary results for the stent-assisted occlusion of a cerebral aneurysm and a qualitative analysis of the behavior of the elasticity of the walls vs. the geometrical details of the stent for prototypical flow situation are presented. Additionally, our approach is designed in such a way that complicated realistic constitutive relations for biomechanics applications for blood vessel simulations can be easily integrated. © 2011 IMACS.
  	view abstract	doi: 10.1016/j.apnum.2010.12.010

• 2012 • 71	Finite element-fictitious boundary methods (FEM-FBM) for 3D particulate flow Münster, R. and Mierka, O. and Turek, S. International Journal for Numerical Methods in Fluids 69 294-313 (2012) In this paper we discuss numerical simulation techniques using a finite element approach in combination with the fictitious boundary method (FBM) for rigid particulate flow configurations in 3D. The flow is computed with a multigrid finite element solver (FEATFLOW), the solid particles are allowed to move freely through the computational mesh which can be static or adaptively aligned by a grid deformation method allowing structured as well as unstructured meshes. We explain the details of how we can use the FBM to simulate flows with complex geometries that are hard to describe analytically. Stationary and time-dependent numerical examples, demonstrating the use of such geometries are provided. Our numerical results include well-known benchmark configurations showing that the method can accurately and efficiently handle prototypical particulate flow situations in 3D with particles of different shape and size. © 2011 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/fld.2558

• 2012 • 70	Goal oriented error control for frictional contact problems in metal forming Blum, H. and Rademacher, A. and Schröder, A. Key Engineering Materials 504-506 987-992 (2012) In this note, techniques for goal oriented error control of finite element discretizations are proposed for frictional contact problems. The finite element discretization is based on a mixed method, where Lagrange multipliers are introduced to capture the geometrical and frictional contact conditions. A posteriori error estimates for user-defined, probably non-linear quantities of interest are derived using the dual weighted residual method (DWR). Numerical results substantiate the applicability of the presented techniques to the simulation of metal forming processes.© (2012) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.504-506.987

• 2012 • 69	Influences of deformation strain, strain rate and cooling rate on the Burgers orientation relationship and variants morphology during β→α phase transformation in a near α titanium alloy He, D. and Zhu, J.C. and Zaefferer, S. and Raabe, D. and Liu, Y. and Lai, Z.L. and Yang, X.W. Materials Science and Engineering A 549 20-29 (2012) High temperature compression deformation studies of Ti-6Al-2Zr-1Mo-1V titanium alloy in full β phase region with different strains/strain rates and then with subsequent varied cooling rates were performed to understand the microstructure evolution. Crystal orientation information and microstructure morphology of all tested samples were investigated by electron backscatter diffraction (EBSD) measurements. The crystal orientations of prior high temperature β grains were estimated by reconstructing the retained β phase at room temperature. The theoretical crystal orientations of all possible α variants within an investigated prior β grain were calculated according to the Burgers orientation relationship (OR) between parent and product phase. The calculated and experimental results were then compared and analyzed. The influences of deformation strain, strain rate and cooling rate on the Burgers OR between prior β matrix and precipitated α phase were investigated. Full discussions have been conducted by combination of crystal plasticity finite element method (CP-FEM) grain-scale simulation results. The results indicate that external factors (such as deformation strain, strain rate and cooling rate) have a slight influence on the obeying of Burgers OR rule during β → α phase transformation. However, strain rate and cooling rate have a significant effect on the morphology of precipitated α phase. © 2012 Elsevier B.V.
  	view abstract	doi: 10.1016/j.msea.2012.03.110

• 2012 • 68	Inverse analysis for multiphase nonlinear composites with random microstructure Klinge, S. International Journal for Multiscale Computational Engineering 10 361-373 (2012) The contribution considers the application of inverse analysis to the identification of the material parameters of nonlinear composites. For this purpose a combination of the Levenberg-Marquardt method with the multiscale finite element method is used. The first one belongs to the group of gradient-based optimization methods, and the latter is a numerical procedure for modeling heterogeneous materials which is applicable in the case when the ratio of characteristic sizes of the scales tends to zero. Emphasis is placed on the investigation of problems with an increasing number of unknown materials parameters, as well as on the manifestation of the ill-posedness of inverse problems. These effects first occurred in the case of three-phase materials. The illustrative examples are concerned with cases where such a combination of experimental data is used that effects of ill-posedness are alleviated and a unique solution is achieved. © 2012 by Begell House, Inc.
  	view abstract	doi: 10.1615/IntJMultCompEng.2012002946

• 2012 • 67	Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach Grytz, R. and Sigal, I.A. and Ruberti, J.W. and Meschke, G. and Crawford Downs, J. Mechanics of Materials 44 99-109 (2012) Glaucoma is among the leading causes of blindness worldwide. The ocular disease is characterized by irreversible damage of the retinal ganglion cell axons at the level of the lamina cribrosa (LC). The LC is a porous, connective tissue structure whose function is believed to provide mechanical support to the axons as they exit the eye on their path from the retina to the brain. Early experimental glaucoma studies have shown that the LC remodels into a thicker, more posterior structure which incorporates more connective tissue after intraocular pressure (IOP) elevation. The process by which this occurs is unknown. Here we present a microstructure motivated growth and remodeling (G&R) formulation to explore a potential mechanism of these structural changes. We hypothesize that the mechanical strain experienced by the collagen fibrils in the LC stimulates the G&R response at the micro-scale. The proposed G&R algorithm controls collagen fibril synthesis/degradation and adapts the residual strains between collagen fibrils and the surrounding tissue to achieve biomechanical homeostasis. The G&R algorithm was applied to a generic finite element model of the human eye subjected to normal and elevated IOP. The G&R simulation underscores the biomechanical need for a LC at normal IOP. The numerical results suggest that IOP elevation leads to LC thickening due to an increase in collagen fibril mass, which is in good agreement with experimental observations in early glaucoma monkey eyes. This is the first study to demonstrate that a biomechanically-driven G&R mechanism can lead to the LC thickening observed in early experimental glaucoma. © 2011 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.mechmat.2011.07.004

• 2012 • 66	Modeling of curing processes based on a multi-field potential. Single- and multiscale aspects Klinge, S. and Bartels, A. and Steinmann, P. International Journal of Solids and Structures 49 2320-2333 (2012) This paper provides a continuum mechanical model for the curing of polymers, including the incompressibility effects arising at the late stages of the process. For this purpose, the free energy density functional is split into a deviatoric and a volumetric part, and a multifield formulation is inserted. An integral formulation of the functional is used to depict the time-dependent material behavior. The model is also coupled with the multiscale finite element method, a numerical approach serving for the modeling of heterogeneous materials with a highly oscillatory microstructure. The effects of the proposed extensions are illustrated on the basis of several numerical examples concerned with the study of the influence of Poisson's ratio on the curing process and the behavior of the microheterogeneous polymers. © 2012 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijsolstr.2012.04.034

• 2012 • 65	Modeling techniques for the prediction of workpiece deflections in NC milling Kersting, P. and Biermann, D. Procedia CIRP 2 83-86 (2012) Due to the characteristics of the milling process, modeling workpiece dynamics during the machining of freeform surfaces is a challenge: The relative movement between the milling tool and the workpiece leads to a variation of the excitation position, and the material removal process results in changing modal parameters of the workpiece. In this paper, an ongoing work is discussed dealing with different modeling techniques for the prediction of workpiece deflections: a finite element model, a particle-based approach, and an oscillator-based technique. These three methods and their integration into a simulation system for the modeling of NC milling are presented and discussed by simulating the machining of a turbine blade. c- 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Dr. Ir. Wessel W. Wits. © 2012 Published.
  	view abstract	doi: 10.1016/j.procir.2012.05.045

• 2012 • 64	Modelling and validation of dielectric properties of human skin in the MHz region focusing on skin layer morphology and material composition Huclova, S. and Erni, D. and Fröhlich, J. Journal of Physics D: Applied Physics 45 (2012) Human skin consists of several layers with distinct dielectric properties. Physiological processes leading to changes in dielectric properties of the specific layers can potentially be non-invasively monitored employing dielectric spectroscopy. So far no comprehensive skin and underlying tissue model is available for this purpose in the frequency range between 1 and 100MHz. Focusing on this dispersion-dominated frequency region, different multilayer skin models are investigated. First, with sublayers obtained from two-phase mixtures, second, three-phase mixtures of shelled cell-like ellipsoids and finally, multiphase mixtures obtained from numerical models of single cells generated using a flexible surface parametrization method. All models are numerically evaluated using the finite-element method and a fringing field sensor on the top of the multilayer system serving as a probe. Furthermore, measurements with the sensor probing skin in vivo were performed. The validity of the models was tested by removing the uppermost skin layer, the stratum corneum (SC). It was found that only a three-phase mixture (extracellular medium, cell membrane and cytoplasm) at least can qualitatively reproduce the measured dispersion still occurring without the SC if the model is set up without a priori knowledge of the dispersive behaviour as e.g. a ColeCole fit to measured data. Consequently, microstructural features of tissue have to be part of any accurate skin model in the MHz region.
  	view abstract	doi: 10.1088/0022-3727/45/2/025301

• 2012 • 63	Non-crystallographic shear banding in crystal plasticity FEM simulations: Example of texture evolution in α-brass Jia, N. and Roters, F. and Eisenlohr, P. and Kords, C. and Raabe, D. Acta Materialia 60 1099-1115 (2012) We present crystal plasticity finite element simulations of the texture evolution in α-brass polycrystals under plane strain compression. The novelty is a non-crystallographic shear band mechanism [Anand L, Su C. J Mech Phys Solids 2005;53:1362] that is incorporated into the constitutive model in addition to dislocation and twinning. Non-crystallographic deformation associated with shear banding leads to weaker copper and S texture components and to a stronger brass texture compared to simulations enabling slip and twinning only. The lattice rotation rates are reduced when shear banding occurs. This effect leads to a weaker copper component. Also, the initiation of shear banding promotes brass-type components. In summary the occurrence of non-crystallographic deformation through shear bands shifts face-centered-cubic deformation textures from the copper type to the brass type. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.actamat.2011.10.047

• 2012 • 62	Numerical and experimental investigation on lap shear fracture of Al/CFRP laminates Naghipour, P. and Schulze, K. and Hausmann, J. and Bartsch, M. Composites Science and Technology 72 1718-1724 (2012) This paper presents a new approach to numerically investigate the lap shear fracture of a hybrid laminate made of Carbon Fibre Reinforced Plastic (CFRP) and metal foil plies (e.g. aluminium), validated by corresponding experiments. The numerical Finite Element (FE) model of the hybrid laminate, subjected to lap shear fracture, is composed of five laminas with alternating metal/CFRP layers with cohesive elements lying within Al/CFRP interface. In the FE model, individual CFRP laminas are assumed as an orthotropic homogenized continuum under plane stress, and aluminium facesheets are modelled as an elastic-plastic continuum. The Al/CFRP interface is represented via quadratic cohesive elements, the constitutive law of which is an exponentially decaying law representing the degrading behaviour of the interface (implemented as user element in ABAQUS). The numerical model captures the experimentally obtained results with minimal error, and predicts the failure modes successfully. The influence of specimen geometry (e.g. overlap length, total length, and total width) on lap shear fracture response is analyzed in detail in this study, too, in order to confirm the specimen design for the test, as there is still no corresponding test standard for hybrid laminates. © 2012 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compscitech.2012.07.012

• 2012 • 61	Numerical approach for the evaluation of seam welding criteria in extrusion processes Schwane, M. and Kloppenborg, T. and Reeb, A. and Ben Khalifa, N. and Brosius, A. and Weidenmann, K.A. and Tekkaya, A.E. Key Engineering Materials 504-506 517-522 (2012) The accurate simulation and the optimization of extrusion processes can be a helpful technique to ensure producibility of complex aluminum profiles, for example for the automobile industry. Currently, the die designing is based on expert's knowledge and cost-intensive prototyping. The paper deals with numerical investigations based on finite element simulations as well as experimental investigations of an industrial extrusion process. A newly developed method for longitudinal seam weld prediction is applied to analyze the position of the longitudinal welding line and the welding quality. © (2012) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.504-506.517

• 2012 • 60	Numerical simulation of interactions between the shield-supported tunnel construction process and the response of soft water-saturated soils Nagel, F. and Stascheit, J. and Meschke, G. International Journal of Geomechanics 12 689-696 (2012) During the design and construction of shield-driven tunnels, a reliable analysis of the construction process is required for the prognosis of the process-induced surface settlements, changes in soil stresses, and changes in groundwater conditions, as well as for the determination of the loads acting on the tunnel tube and on the tunnel-boring machine. In this context, numerical simulation methods like the finite-element method allow for a realistic description of the construction process and its impact on the surrounding underground. The investigated problem is governed by the interactions between the tunneling process and the surrounding underground and its constituents-soil grains, groundwater, and pore air. The tunnel-construction process interacts with the surrounding underground via the heading face support, by frictional contact between shield skin and soil, and because of grouting of the annular gap. Considering these interactions, a holistic simulation model is presented for the process-oriented simulation of shield-supported tunnel advance and its interactions with fully saturated, partially saturated, or nonsaturated soft soil. Its applicability is demonstrated by selected simulations of real-scale examples. Parametric studies are performed to investigate the influence of soil conditions and of process parameters on the time-variant settlements and groundwater conditions, showing its capabilities with respect to the simulation of the soil-process interactions in front, above, and behind the tunnel-boring machine. © 2012 American Society of Civil Engineers.
  	view abstract	doi: 10.1061/(ASCE)GM.1943-5622.0000174

• 2012 • 59	Orientation dependence of shear banding in face-centered-cubic single crystals Jia, N. and Eisenlohr, P. and Roters, F. and Raabe, D. and Zhao, X. Acta Materialia 60 3415-3434 (2012) We present crystal plasticity finite element simulations of plane strain compression of α-Brass single crystals with different initial orientations. The aim is to study the fundamentals of mesoscale structure and texture development in face-centered-cubic (fcc) metals with low stacking fault energy (SFE). Shear banding depends on the initial orientation of the crystals. In Copper and Brass-R-oriented crystals which show the largest tendency to form shear bands, an inhomogeneous texture distribution induced by shear banding is observed. To also understand the influence of the micromechanical boundary conditions on shear band formation, simulations on Copper-oriented single crystals with varying sample geometry and loading conditions are performed. We find that shear banding can be understood in terms of a mesoscopic softening mechanism. The predicted local textures and the shear banding patterns agree well with experimental observations in low SFE fcc crystals. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.actamat.2012.03.005

• 2012 • 58	Parameter identification for two-phase nonlinear composites Klinge, S. Computers and Structures 108-109 118-124 (2012) In many cases, the microstructure of composite materials is not known and cannot directly be accessed such that an inverse analysis is necessary for its investigation. This approach requires the implementation of two tools: an optimization method for the minimization of the error problem and a mechanical approach for the solution of the direct problem, i.e. the simulation of composite materials. Our particular choice deals with the combination of the Levenberg-Marquardt method with the multiscale finite element method. The numerical examples are concerned with the investigation of the elastic parameters for two-phase materials. Emphasis is placed on the discussion of convergence and sensitivity with respect to the initial guess. © 2012 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.compstruc.2012.02.008

• 2012 • 57	Partially relaxed energy potentials for the modelling of microstructures - Application to shape memory alloys Bartel, T. and Menzel, A. GAMM Mitteilungen 35 59-74 (2012) Energy relaxation is well-established by several researchers - especially in the field of the modelling of solid-solid phase transformations. Nevertheless, critics still counter this concept by considering it as a purely mathematical tool with poor physical significance. In this contribution we aim at emphasising the significance of energy relaxation methods for the modelling of dissipative solids and especially microstructure formation and its further evolution. In particular, we shall point out aspects and advantages of this concept which are not straight forward to achieve within alternative schemes. ©c 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/gamm.201210005

• 2012 • 56	Performance of mixed and enhanced finite elements for strain localization in hypoplasticity Trinh, B.T. and Hackl, K. International Journal for Numerical and Analytical Methods in Geomechanics 36 1125-1150 (2012) Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three-field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. © 2011 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nag.1042

• 2012 • 55	Phase-transformations interacting with plasticity - A micro-sphere model applied to TRIP steel Ostwald, R. and Bartel, T. and Menzel, A. Computational Materials Science 64 12-16 (2012) We present an efficient model for the simulation of polycrystalline materials, particularly accounting for the interactions of solid to solid phase-transformations and plasticity. The underlying one-dimensional model is embedded into a micro-sphere formulation in order to simulate three-dimensional boundary value problems. Representative numerical examples are provided for both the micro-level and the macro-level. Moreover, a finite element implementation of the model is presented and discussed. © 2012 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.commatsci.2012.05.015

• 2012 • 54	Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations Jayabal, K. and Menzel, A. European Journal of Computational Mechanics 21 92-102 (2012) Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples. © 2012 Taylor & Francis.
  	view abstract	doi: 10.1080/17797179.2012.702432

• 2012 • 53	Prediction of temperature distribution in dissimilar arc welding of stainless steel to carbon steel Ranjbarnodeh, E. and Serajzadeh, S. and Kokabi, A.H. and Fischer, A. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 226 117-125 (2012) In this work, a three-dimensional model has been proposed to predict temperature distribution and weld-pool shape during dissimilar arc welding of low-carbon steel (CK4) and ferritic stainless steel (AISI 409). The model has been developed using the finite-element software ANSYS, while in the analysis, the effects of process parameters, as well as dilution, in the weld pool have been considered. To verify the predictions, welding experiments were conducted under different welding conditions, and the model results were then compared with the measured weld-pool geometry; a reasonable consistency was observed. © 2011 Authors.
  	view abstract	doi: 10.1177/0954405411403551

• 2012 • 52	Simulation of the long term behaviour of plastics components Stommel, M. and Naumann, T. Macromolecular Symposia 311 92-97 (2012) This paper presents a method to model the mechanical behavior of polymers over a wide time- and load-range by means of finite element analyses. The method includes a material model as well as the determination of material parameters to calibrate the material model. As a special feature of this method the model is calibrated only by using creep data that are commonly available in material data bases. So the procedure improves the simulation of the long time behavior of plastic-components without an additional experimental effort. In combination with time-temperature-superposition principle, the temperature dependency of the long term behavior is represented, too. The simulation results are validated by creep experiments on an example part. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/masy.201000099

• 2012 • 51	The multiscale approach to the curing of polymers incorporating viscous and shrinkage effects Klinge, S. and Bartels, A. and Steinmann, P. International Journal of Solids and Structures 49 3883-3900 (2012) This contribution deals with the modeling of viscoelastic and shrinkage effects accompanying the curing of polymers at multiple length scales. For the modeling of viscous effects, the deformation at the microlevel is decomposed into an elastic and a viscoelastic part, and a corresponding energy density consisting of equilibrium and non-equilibrium parts is proposed. The former is related to the total deformation; it has the form of a convolution integral and depends on the time evolution of the material parameters. The non-equilibrium part depends on the elastic part of deformations only. The material parameters are constant in time, thus an integral form is not necessary. In contrast to the viscous effects, the modeling of shrinkage effects does not require any further extension of the expression for the energy density, but an additional decomposition of the deformation into a shrinkage and a mechanical part. Since the material compressibility is taken into consideration, a multifield formulation is applied for the equilibrium as well as for the non-equilibrium energy part. As a final aspect, the paper includes a study of macroheterogenous polymers for whose modeling the multiscale finite element method is applied. Within this numerical approach, a macroscopic body is treated as a homogeneous body whose effective properties are evaluated on the basis of the simulations which are carried out at the level of the representative volume element. The application of the model proposed is illustrated on the basis of examples studying the influence of individual parameters on the stress state as well as the influence of the volume fraction of different phases at the microscale on the effective material behavior. © 2012 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijsolstr.2012.08.016

• 2012 • 50	Theory-guided materials design of multi-phase Ti-Nb alloys with bone-matching elastic properties Friák, M. and Counts, W.A. and Ma, D. and Sander, B. and Holec, D. and Raabe, D. and Neugebauer, J. Materials 5 1853-1872 (2012) We present a scale-bridging approach for modeling the integral elastic response of polycrystalline composite that is based on a multi-disciplinary combination of (i) parameter-free first-principles calculations of thermodynamic phase stability and single-crystal elastic stiffness; and (ii) homogenization schemes developed for polycrystalline aggregates and composites. The modeling is used as a theory-guided bottom-up materials design strategy and applied to Ti-Nb alloys as promising candidates for biomedical implant applications. The theoretical results (i) show an excellent agreement with experimental data and (ii) reveal a decisive influence of the multi-phase character of the polycrystalline composites on their integral elastic properties. The study shows that the results based on the density functional theory calculations at the atomistic level can be directly used for predictions at the macroscopic scale, effectively scale-jumping several orders of magnitude without using any empirical parameters. © 2012 by the authors; licensee MDPI, Basel, Switzerland.
  	view abstract	doi: 10.3390/ma5101853

• 2011 • 49	3D self-assembled plasmonic superstructures of gold nanospheres: Synthesis and characterization at the single-particle level Gellner, M. and Steinigeweg, D. and Ichilmann, S. and Salehi, M. and Schütz, M. and Kömpe, K. and Haase, M. and Schlücker, S. Small 7 3445-3451 (2011) The synthesis of 3D self-assembled plasmonic superstructures of gold nanospheres as well as the characterization of their structural and optical properties at the single-particle level is presented. This experimental work is complemented by FEM (finite element method) simulations of elastic scattering spectra and the spatial |E| 4 distribution for establishing structure-activity correlations in these complex 3D nanoclusters. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  	view abstract	doi: 10.1002/smll.201102009

• 2011 • 48	A finite element simulation of biological conversion processes in landfills Robqeck, M. and Ricken, T. and Widmann, R. Waste Management 31 663-669 (2011) Landfills are the most common way of waste disposal worldwide. Biological processes convert the organic material into an environmentally harmful landfill gas, which has an impact on the greenhouse effect. After the depositing of waste has been stopped, current conversion processes continue and emissions last for several decades and even up to 100. years and longer. A good prediction of these processes is of high importance for landfill operators as well as for authorities, but suitable models for a realistic description of landfill processes are rather poor. In order to take the strong coupled conversion processes into account, a constitutive three-dimensional model based on the multiphase Theory of Porous Media (TPM) has been developed at the University of Duisburg-Essen. The theoretical formulations are implemented in the finite element code FEAP. With the presented calculation concept we are able to simulate the coupled processes that occur in an actual landfill. The model's theoretical background and the results of the simulations as well as the meantime successfully performed simulation of a real landfill body will be shown in the following. © 2010 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.wasman.2010.08.007

• 2011 • 47	A Newton-like finite element scheme for compressible gas flows Gurris, M. and Kuzmin, D. and Turek, S. Computers and Fluids 46 245-251 (2011) Semi-implicit and Newton-like finite element methods are developed for the stationary compressible Euler equations. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers, which is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. Special emphasis is laid on the numerical treatment of weakly imposed characteristic boundary conditions. Numerical evidence for unconditional stability is presented. It is shown that the proposed approach offers higher accuracy and better convergence behavior than algorithms in which the boundary conditions are implemented in a strong sense. © 2011 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.compfluid.2011.01.025

• 2011 • 46	A viscoelastic thin rod model for large deformations: Numerical examples Beyrouthy, J. and Neff, P. Mathematics and Mechanics of Solids 16 887-896 (2011) We present a Cosserat-based 3D-1D dimensional reduction for a viscoelastic finite strain model. The numerical resolution of the reduced coupled minimization/evolution problem is based on a splitting method. We start by approximating the minimization problem using the finite element method with P1 Lagrange elements. The solution of this problem is used in the time-incremental formulation of the evolution problem. © SAGE Publications 2011.
  	view abstract	doi: 10.1177/1081286511407113

• 2011 • 45	An efficient algorithm for the inverse problem in elasticity imaging by means of variational r-adaption Arnold, A. and Bruhns, O.T. and Mosler, J. Physics in Medicine and Biology 56 4239-4265 (2011) A novel finite element formulation suitable for computing efficiently the stiffness distribution in soft biological tissue is presented in this paper. For that purpose, the inverse problem of finite strain hyperelasticity is considered and solved iteratively. In line with Arnold et al (2010 Phys. Med. Biol. 55 2035), the computing time is effectively reduced by using adaptive finite element methods. In sharp contrast to previous approaches, the novel mesh adaption relies on an r-adaption (re-allocation of the nodes within the finite element triangulation). This method allows the detection of material interfaces between healthy and diseased tissue in a very effective manner. The evolution of the nodal positions is canonically driven by the same minimization principle characterizing the inverse problem of hyperelasticity. Consequently, the proposed mesh adaption is variationally consistent. Furthermore, it guarantees that the quality of the numerical solution is improved. Since the proposed r-adaption requires only a relatively coarse triangulation for detecting material interfaces, the underlying finite element spaces are usually not rich enough for predicting the deformation field sufficiently accurately (the forward problem). For this reason, the novel variational r-refinement is combined with the variational h-adaption (Arnold et al 2010) to obtain a variational hr-refinement algorithm. The resulting approach captures material interfaces well (by using r-adaption) and predicts a deformation field in good agreement with that observed experimentally (by using h-adaption). © 2011 Institute of Physics and Engineering in Medicine.
  	view abstract	doi: 10.1088/0031-9155/56/14/004

• 2011 • 44	Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method Krüger, T. and Varnik, F. and Raabe, D. Computers and Mathematics with Applications 61 3485-3505 (2011) The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barths-Biesel, J.M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech. 113 (1981) 251267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13 (1973) 245264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy. © 2011 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.camwa.2010.03.057

• 2011 • 43	Efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach Mosler, J. and Stanković, L. and Radulović, R. International Journal for Numerical Methods in Engineering 88 1008-1041 (2011) This paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains. Focus is on localized plastic deformation particularly relevant for slip bands. In contrast to already existing models, the proposed implementation allows to consider several interacting discontinuities in each finite element. Based on a proper re-formulation of the kinematics, an efficient parameterization of the deformation gradient is derived. It permits to compute the strains explicitly that improves the performance significantly. However, the most important novel contribution of the present paper is the advocated variational constitutive update. Within this framework, every aspect is naturally driven by energy minimization, i.e. all unknown variables are jointly computed by minimizing the stress power. The proposed update relies strongly on an extended principle of maximum dissipation. This framework provides enough flexibility for different failure types and for a broad class of non-associative evolution equations. By discretizing the aforementioned continuous variational principle, an efficient numerical implementation is obtained. It shows, in addition to its physical and mathematical elegance, several practical advantages. For instance, the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities. © 2011 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.3210

• 2011 • 42	Experimental and computational investigation of machining processes for functionally graded materials Biermann, D. and Menzel, A. and Bartel, T. and Höhne, F. and Holtermann, R. and Ostwald, R. and Sieben, B. and Tiffe, M. and Zabel, A. Procedia Engineering 19 22-27 (2011) Experiments on dry face turning of functionally graded heat treatable steel are conducted. The workpieces have a hardened zone of approx. 60 HRC and a non-hardened zone of approx. 30 HRC. PCBN tools are used with different feeds, cutting speeds and depths of cut. Measurements of residual stresses in the surface layer reveal compressive stresses in the hardened zone and tensile stresses in the non-hardened zone. These experimental observations are compared with the results of representative simulations of the cutting process. A large-deformation thermo-elastoviscoplastic material model is used and the geometry of the cutting tool is precisely reflected by the finite element discretisation. To predict the overall response, an adaptive remeshing scheme and full thermo-mechanical coupling is accounted for. Moreover, measured residual stresses are incorporated as initial conditions within the simulation. © 2012 Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.proeng.2011.11.074

• 2011 • 41	Finite element analysis of the demagnetization effect and stress inhomogeneities in magnetic shape memory alloy samples Haldar, K. and Kiefer, B. and Lagoudas, D.C. Philosophical Magazine 91 4126-4157 (2011) This paper is concerned with the finite element analysis of boundary value problems involving nonlinear magnetic shape memory behavior, as might be encountered in experimental testing or engineering applications of magnetic shape memory alloys (MSMAs). These investigations mainly focus on two aspects: first, nonlinear magnetostatic analysis, in which the nonlinear magnetic properties of the MSMA are predicted by the phenomenological internal variable model previously developed by Kiefer and Lagoudas, is utilized to investigate the influence of the demagnetization effect on the interpretation of experimental measurements. An iterative procedure is proposed to deduce the true constitutive behavior of MSMAs from experimental data that typically reflect the shape-dependent system response of a sample. Secondly, the common assumption of a homogeneous Cauchy stress distribution in the MSMA sample is tested. This is motivated by the expectation that the influence of magnetic body forces and body couples caused by field matter interactions may not be negligible in MSMAs that exhibit blocking stresses of well below 10 MPa. To this end, inhomogeneous Maxwell stress distributions are first computed in a post-processing step, based on the magnetic field and magnetization distributions obtained in the magnetostatic analysis. Since the computed Maxwell stress fields, though allowing a first estimation of the influence of the magnetic force and couple, do not satisfy equilibrium conditions, a finite element analysis of the coupled field equations is performed in a second step to complete the study. It is found that highly non-uniform Cauchy stress distributions result under the influence of magnetic body forces and couples, with magnitudes of the stress components comparable to externally applied bias stress levels. © 2011 Taylor & Francis.
  	view abstract	doi: 10.1080/14786435.2011.602031

• 2011 • 40	Finite element modeling of the effect of heat input on residual stresses in dissimilar joints Ranjbarnodeh, E. and Serajzadeh, S. and Hosein Kokabi, A. and Hanke, S. and Fischer, A. International Journal of Advanced Manufacturing Technology 55 649-656 (2011) In the present study, a thermo-elastic-plastic model was developed in order to evaluate the residual stresses in dissimilar automatic tungsten inert gas (TIG) welds between plain carbon steel CK4 and a ferritic stainless steel AISI409. The effect of welding heat input on the magnitude and the distribution of residual stresses was investigated and the results of simulation were validated by X-ray diffraction measurements. It is shown that the calculated residual stresses are in good agreement with the residual stresses determined experimentally. It was found that the magnitudes of stresses at the weld center line increases with increasing the welding speed. © 2010 Springer-Verlag London Limited.
  	view abstract	doi: 10.1007/s00170-010-3095-3

• 2011 • 39	Finite element modelling of process-integrated powder coating by radial axial rolling of rings Frischkorn, J. and Kebriaei, R. and Reese, S. and Moll, H. and Theisen, W. and Husmann, T. and Meier, H. AIP Conference Proceedings 1353 339-344 (2011) The process-integrated powder coating by radial axial rolling of rings represents a new hybrid production technique applied in the manufacturing of large ring-shaped work pieces with functional layers. It is thought to break some limitations that come along with the hot isostatic pressing (HIP) which is used nowadays to apply the powdery layer material onto the rolled substrate ring. Within the new process the compaction of the layer material is integrated into the ring rolling and HIP becomes dispensable. Following this approach the rolling of such compound rings brings up some new challenges. The volume of a solid ring stays nearly constant during the rolling. This behaviour can be exploited to determine the infeed of the rollers needed to reach the desired ring shape. Since volume consistency cannot be guaranteed for the rolling of a compound ring the choice of appropriate infeed of the rollers is still an open question. This paper deals with the finite element (FE) simulation of this new process. First, the material model that is used to describe the compaction of the layer material is shortly reviewed. The main focus of the paper is then put on a parameterized FE ring rolling model that incorporates a control system in order to stabilize the process. Also the differences in the behaviour during the rolling stage between a compound and a solid ring will be discussed by means of simulation results. © 2011 American Institute of Physics.
  	view abstract	doi: 10.1063/1.3589538

• 2011 • 38	Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model Junker, P. and Hackl, K. Computational Mechanics 47 505-517 (2011) We present a finite element implementation of a micromechanically motivated model for poly-crystalline shape memory alloys, based on energy minimization principles. The implementation allows simulation of anisotropic material behavior as well as the pseudo-elastic and pseudoplastic material response of whole samples. The evolving phase distribution over the entire specimen is calculated. The finite element model predicts the material properties for a relatively small number of grains. For different points of interest in the specimen the model can be consistently evaluated with a significantly higher number of grains in a post-processing step, which allows to predict the re-orientation of martensite at different loads. The influence of pre-texture on the material's properties, due to some previous treatment like rolling, is discussed. © Springer-Verlag 2010.
  	view abstract	doi: 10.1007/s00466-010-0555-4

• 2011 • 37	Finite-element simulation of the anti-buckling-effect of a shape memory alloy bar Richter, F. and Kastner, O. and Eggeler, G. Journal of Materials Engineering and Performance 20 719-730 (2011) Shape memory alloys (SMA) are characterized by an intricate stress-strain curve modified by temperature, posing thermomechanically coupled problems. A model able to address this feature is the Mü ller-Achenbach- Seelecke (MAS) model which had been ported into the user material interface in the finite-element (FEM) simulation software ABAQUS. The literature on this model mainly focuses on pseudo-elasticity of SMA at elevated temperature. We address a numerical investigation in the low-temperature pseudo-plastic regime. The present publication deals with the little-known anti-buckling effect which occurs in de-twinned and pre-bent martensitic bars under axial compression. It was experimentally demonstrated by Urushiyama et al. (JSME (The Japan Society of Mechanical Engineers) Int. J. Ser. A, Solid Mech. Mater. Eng., 2003, 46(1), p 60-67). This study reveals that the origin of this effect roots in an interplay of inhomogeneous stress states and mechanically induced twin-twin phase transformations. The proper explanation of the anti-buckling effect can be inferred from the explicit knowledge of the martensitic phase composition of the bar during the process.We show that the MAS model is capable to resolve this matter in detail, hence addressing the reliability of this particular model also in the pseudo-plastic regime of SMA. The study thereby implies that the MAS model is an excellent modeling tool for the analysis of complex, thermomechanically coupled processes. © ASM International.
  	view abstract	doi: 10.1007/s11665-010-9797-8

• 2011 • 36	Grout and bentonite flow around a TBM: Computational modeling and simulation-based assessment of influence on surface settlements Nagel, F. and Meschke, G. Tunnelling and Underground Space Technology 26 445-452 (2011) Adequate consideration of the various interactions between the Tunnel Boring Machine (TBM) and the surrounding underground is a pre-requisite for reliable prognoses in shield supported tunneling based upon numerical analysis. In addition to face support and the grouting of the annular gap the contact conditions along the shield skin between the moving TBM and the surrounding, deforming soil constitute the most relevant component of TBM-soil interactions in mechanized tunneling. This paper is concerned with the analysis of the interface conditions between the shield skin and the soil and its adequate numerical representation in the context of a process-oriented numerical simulation model for mechanized tunneling. The situation around the shield skin is influenced by the design of the Tunnel Boring Machine, the deformational behavior of the surrounding underground and by a possible inflow of process liquids into the steering gap. A novel simulation method is proposed which allows to model the viscous flow of the process liquids into the steering gap and its interactions with the face support, the tail void grouting, the deforming soil and the moving TBM. The proposed numerical model for the TBM-soil interaction is part of a recently developed three-dimensional, process-oriented finite element model for shield tunneling (Nagel et al., 2010). It allows to investigate the effects of the inflow of process liquids into the steering gap during TBM advance considering realistic machine-related and geological conditions. It is, in particular, capable to compute the pressure distribution within the developing liquid film in association with the face support and grouting conditions and to predict its influence on the surface settlements and the overall TBM-soil interaction affecting, e.g. the hydraulic jack forces or shield deformations. © 2010 Elsevier Ltd.
  	view abstract	doi: 10.1016/j.tust.2010.12.001

• 2011 • 35	Implicit finite element schemes for stationary compressible particle-laden gas flows Gurris, M. and Kuzmin, D. and Turek, S. Journal of Computational and Applied Mathematics 235 5056-5077 (2011) The derivation of macroscopic models for particle-laden gas flows is reviewed. Semi-implicit and Newton-like finite element methods are developed for the stationary two-fluid model governing compressible particle-laden gas flows. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers. This is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters and the additional strong nonlinearity caused by interfacial coupling terms. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. The original Jacobian is replaced by a low-order approximation. Special emphasis is laid on the numerical treatment of weakly imposed boundary conditions. It is shown that the proposed approach offers unconditional stability and faster convergence rates for increasing CFL numbers. The strongly coupled solver is compared to operator splitting techniques, which are shown to be less robust. © 2011 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.cam.2011.04.036

• 2011 • 34	Inverse method for identification of initial yield locus of sheet metals utilizing inhomogeneous deformation fields Güner, A. and Yin, Q. and Soyarslan, C. and Brosius, A. and Tekkaya, A.E. International Journal of Material Forming 4 121-128 (2011) Accurate finite element simulation of sheet metal forming processes requires among others accurate description of plastic behaviour of materials. This is achieved by utilization of sophisticated yield criteria having several material parameters. This work proposes a procedure which makes use of the distribution of strains to identify the initial yield locus of sheet metals by the help of inverse analysis. For this purpose a flat specimen having a varying cross-section is introduced, which is capable of revealing different deformation states in one test. Numerical simulations are performed with 2 representative materials for steel and aluminium, using the material model Yld2000-2d. The results of these simulations are treated as experimentally obtained results and with the inverse methods it is tried to obtain the given yield locus. The relation between the supplied input and the outcome of the inverse algorithm is studied by examining different objective function definitions. The numerical studies show that inclusion of the strain distribution in the definition of objective function is a key issue in identification of the yield locus. The orientation of the specimen with respect to the rolling direction also determines the amount and quality of the information used for parameter identification. Consequently the circumstances, under which the inverse method can predict the initial yield locus, are defined. © 2010 Springer-Verlag France.
  	view abstract	doi: 10.1007/s12289-010-1009-4

• 2011 • 33	Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: Application of a polygonal finite element approach Jayabal, K. and Menzel, A. and Arockiarajan, A. and Srinivasan, S.M. Computational Mechanics 48 421-435 (2011) A micromechanically motivated model is proposed to capture nonlinear effects and switching phenomena present in ferroelectric polycrystalline materials. The changing remnant state of the ferroelectric crystal is accounted for by means of so-called back fields-such as back stresses-to resist or assist further switching processes in the crystal depending on the local loading history. To model intergranular effects present in ferroelectric polycrystals, the computational model elaborated is embedded into a mixed polygonal finite element approach, whereby an individual ferroelectric grain is represented by one single irregular polygonal finite element. This computationally efficient coupled simulation framework is shown to reproduce the specific characteristics of the responses of ferroelectric polycrystals under complex electromechanical loading conditions in good agreement with experimental observations. © 2011 Springer-Verlag.
  	view abstract	doi: 10.1007/s00466-011-0595-4

• 2011 • 32	Modeling of dynamic microstructure evolution of en AW-6082 alloy during hot forward extrusion Parvizian, F. and Güzel, A. and Jäger, A. and Lambers, H.-G. and Svendsen, B. and Tekkaya, A.E. and Maier, H.J. Computational Materials Science 50 1520-1525 (2011) The aim of this work is to present briefly a model for predicting and simulating the evolution of microstructure, in particular the evolution of grains, during hot forming processes of aluminum alloy EN AW-6082 and give a comparison with the experimental results. The model is a physically motivated phenomenological model based on internal state dependent variables. The microstructure evolution is a temperature dependent process and is simulated in a fully coupled thermo-mechanical process by help of Finite Element software Abaqus. The results are compared and verified with experimental results obtained by EBSD measurement of a small-scale extrusion process established for scientific purposes. The simulation results are in reasonable agreement with experiment. © 2010 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.commatsci.2010.12.009

• 2011 • 31	Modeling the effective properties and thermomechanical behavior of SMA-SMP multifunctional composite laminates Jarali, C.S. and Raja, S. and Kiefer, B. Polymer Composites 32 910-927 (2011) The research work presents the modeling of effective properties and thermo-mechanical behavior of shape memory fiber (SMF) and shape memory polymer (SMP) composite laminates using micromechanical approaches based on the method of mixtures (MOM) and method of cells (MOC). The fiber is made of a nickel-titanium (Ni-Ti) shape memory alloy (SMA), while the matrix consists of a shape memory thermoset epoxy polymer (SMP). The use of an SMP matrix provides large strain compatibility with the SMA fiber, while being active at high temperatures without losing its elastic properties. Additionally, the SMP matrix is also able to produce similar pseudoelastic and shape memory effects, which are noticed in SMAs. In the analysis, a two step homogenization scheme is followed. In the first step the effective properties of each layer are determined via a micromechanics approach with iso-strain conditions. In the second step the effective properties of the SMF-SMP composite are computed making a thin plate theory assumption, which takes into account the transverse shear deformations. The possible elastic couplings for SMF-SMP laminates are discussed, and the laminate force and moment resultants are computed for various laminate configurations. The analysis takes into account the effects of phase transformations and the resulting change in the fiber-matrix modulus. The results have been compared by considering different fiber volume fractions, temperatures, fiber orientations, and lamina stacking sequences. The results show that adaptive SMA-SMP composites laminates can be developed that provide shape controllability via tunable laminate stiffnesses leading to optimal response. Furthermore, the work presents the necessary framework for a reliable and efficient analysis of SMA-SMP laminates for practical applications. The theory can be directly used in established plate and shell formulations of finite element analysis. Finally, the variations in force and moment resultants with respect to fiber orientations and stacking sequences are presented, which are useful to study the bending and buckling characteristics of active composites for shape control of adaptive structures. The work concludes that efficient adaptive laminate development for high performance composite applications, exhibiting large shape adaptivity, high stresses, and increased stiffness, are feasible as compared to SMA composites without active matrix. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers.
  	view abstract	doi: 10.1002/pc.21110

• 2011 • 30	Newest developments on the manufacture of helical profiles by hot extrusion Khalifa, N.B. and Tekkaya, A.E. ASME 2011 International Manufacturing Science and Engineering Conference, MSEC 2011 1 459-463 (2011) The paper presents a new innovative direct extrusion process, Helical Profile Extrusion (HPE), which increases the flexibility of aluminum profile manufacturing processes. The application fields of such profiles can be seen in screw rotors for compressors and pumps. The investigations concentrate on experimental and numerical analyses by 3D-FEM simulations to analyze the influence of friction on the material flow in the extrusion die in order to find out the optimal parameters with reference to the twisting angle and contour accuracy. By means of FEM, the profile shape could be optimized by modifying the die design. The numerical results were validated by experiments. For these investigations, a common aluminum alloy AA6060 was used. The accuracy of the profile contour could be improved significantly. However, increasing the twist angle is limited due to geometrical aspects. Copyright © 2010 by ASME.
  	view abstract	doi: 10.1115/MSEC2011-50126

• 2011 • 29	Novel approach for the treatment of cyclic loading using a potential-based cohesive zone model Scheider, I. and Mosler, J. Procedia Engineering 10 2164-2169 (2011) The development of cohesive zone models in the finite element framework dates back some 30 years, and cohesive interface elements are nowadays employed as a standard tool in scientific and engineering communities. They have been successfully applied to a broad variety of different materials and loading scenarios. However, many of such constitutive models are simply based on traction-separation relations without deducing them from energy potentials. By way of contrast, a thermodynamically consistent cohesive zone model suitable for the analysis of low cycle fatigue is elaborated in the present contribution. For that purpose, a plasticity-based cohesive law including isotropic hardening/softening is supplemented by a damage model. First results of this new approach to cyclic loading will be presented illustrating the applicability to low cycle fatigue. © 2011 Published by Elsevier Ltd.
  	view abstract	doi: 10.1016/j.proeng.2011.04.358

• 2011 • 28	On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization Homayonifar, M. and Mosler, J. International Journal of Plasticity 27 983-1003 (2011) The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e.; an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid-solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress-strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well. © 2010 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijplas.2010.10.009

• 2011 • 27	Strategies for springback compensation regarding process robustness Gösling, M. and Kracker, H. and Brosius, A. and Kuhnt, S. and Tekkaya, A.E. Production Engineering 5 49-57 (2011) In this article, strategies which compensate geometrical deviations caused by springback are discussed using finite element simulations and statistical modelling techniques. First of all the ability to predict springback using a finite element simulation model is analysed. For that purpose numerical predictions and experiments are compared with each other regarding the amount of springback. In a next step, different strategies for compensating springback such as a modification of stress condition, component stiffness and tool geometry are introduced. On the basis of finite element simulations these different compensation strategies are illustrated for a stretch bending process and experimentally checked for an example. Finally springback simulations are compared regarding their robustness against noise variables such as friction and material properties. Thereby a method based on statistical prediction models is introduced which allows for an accurate approximation of the springback distribution with less numerical effort in comparison to a classical Monte-Carlo method. © 2010 German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-010-0251-4

• 2011 • 26	Structural analysis of articular cartilage using multiphoton microscopy: Input for biomechanical modeling Lilledahl, M.B. and Pierce, D.M. and Ricken, T. and Holzapfel, G.A. and Davies, C.D.L. IEEE Transactions on Medical Imaging 30 1635-1648 (2011) The 3-D morphology of chicken articular cartilage was quantified using multiphoton microscopy (MPM) for use in continuum-mechanical modeling. To motivate this morphological study we propose aspects of a new, 3-D finite strain constitutive model for articular cartilage focusing on the essential load-bearing morphology: an inhomogeneous, poro-(visco)elastic solid matrix reinforced by an anisotropic, (visco)elastic dispersed fiber fabric which is saturated by an incompressible fluid residing in strain-dependent pores. Samples of fresh chicken cartilage were sectioned in three orthogonal planes and imaged using MPM, specifically imaging the collagen fibers using second harmonic generation. Employing image analysis techniques based on Fourier analysis, we derived the principal directionality and dispersion of the collagen fiber fabric in the superficial layer. In the middle layer, objective thresholding techniques were used to extract the volume fraction occupied by extracellular collagen matrix. In conjunction with information available in the literature, or additional experimental testing, we show how this data can be used to derive a 3-D map of the initial solid volume fraction and Darcy permeability. © 2011 IEEE.
  	view abstract	doi: 10.1109/TMI.2011.2139222

• 2011 • 25	Variational principles in dissipative electro-magneto-mechanics: A framework for the macro-modeling of functional materials Miehe, C. and Rosato, D. and Kiefer, B. International Journal for Numerical Methods in Engineering 86 1225-1276 (2011) This paper presents a general framework for the macroscopic, continuum-based formulation and numerical implementation of dissipative functional materials with electro-magneto-mechanical couplings based on incremental variational principles. We focus on quasi-static problems, where mechanical inertia effects and time-dependent electro-magnetic couplings are a priori neglected and a time-dependence enters the formulation only through a possible rate-dependent dissipative material response. The underlying variational structure of non-reversible coupled processes is related to a canonical constitutive modeling approach, often addressed to so-called standard dissipative materials. It is shown to have enormous consequences with respect to all aspects of the continuum-based modeling in macroscopic electro-magneto-mechanics. At first, the local constitutive modeling of the coupled dissipative response, i.e. stress, electric and magnetic fields versus strain, electric displacement and magnetic induction, is shown to be variational based, governed by incremental minimization and saddle-point principles. Next, the implications on the formulation of boundary-value problems are addressed, which appear in energy-based formulations as minimization principles and in enthalpy-based formulations in the form of saddle-point principles. Furthermore, the material stability of dissipative electro-magneto-mechanics on the macroscopic level is defined based on the convexity/concavity of incremental potentials. We provide a comprehensive outline of alternative variational structures and discuss details of their computational implementation, such as formulation of constitutive update algorithms and finite element solvers. From the viewpoint of constitutive modeling, including the understanding of the stability in coupled electro-magneto-mechanics, an energy-based formulation is shown to be the canonical setting. From the viewpoint of the computational convenience, an enthalpy-based formulation is the most convenient setting. A numerical investigation of a multiferroic composite demonstrates perspectives of the proposed framework with regard to the future design of new functional materials. Copyright © 2011 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.3127

• 2010 • 24	A computational remodeling approach to predict the physiological architecture of the collagen fibril network in corneo-scleral shells Grytz, R. and Meschke, G. Biomechanics and Modeling in Mechanobiology 9 225-235 (2010) Organized collagen fibrils form complex networks that introduce strong anisotropic and highly nonlinear attributes into the constitutive response of human eye tissues. Physiological adaptation of the collagen network and the mechanical condition within biological tissues are complex and mutually dependent phenomena. In this contribution, a computational model is presented to investigate the interaction between the collagen fibril architecture and mechanical loading conditions in the corneo-scleral shell. The biomechanical properties of eye tissues are derived from the single crimped fibril at the micro-scale via the collagen network of distributed fibrils at themeso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continuous re-orientation of preferred fibril orientations and a continuous adaptation of the fibril dispersion. The presented approach is applied to a numerical human eye model considering the cornea and sclera. The predicted fibril morphology correlates well with experimental observations from X-ray scattering data. © Springer-Verlag 2009.
  	view abstract	doi: 10.1007/s10237-009-0173-2

• 2010 • 23	A hybrid modeling concept for ultra low cycle fatigue of metallic structures based on micropore damage and unit cell models Hommel, J.-H. and Meschke, G. International Journal of Fatigue 32 1885-1894 (2010) The paper presents a concept for life-time predictions of metallic structures subjected to ultra low cycle fatigue. The proposed hybrid strategy is characterized by a combination of unit cell analyses on a microstructural level and a micropore damage model used for structural analyses on the macroscopic level. To account for the large plastic deformations evolving during cyclic loading, an advanced elasto-plastic model using a Bari-Hassan-type kinematic hardening rule based on a superposition of several kinematic hardening laws according to Armstrong-Frederick is employed. Micromechanically oriented unit cell analyses are used for a calibration of the model parameters of a macroscopic Gurson-type model. Numerical results include the validation of the macroscopic Gurson model based on laboratory test results on steel specimens as well as a prototype application to a life-time prediction of a metallic spherical pressure vessel subjected to earthquake loading. © 2010 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.ijfatigue.2010.06.006

• 2010 • 22	A modified least-squares mixed finite element with improved momentum balance Schwarz, A. and Schröder, J. and Starke, G. International Journal for Numerical Methods in Engineering 81 286-306 (2010) The main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible linear elasticity. Based on a classical least-squares formulation, a modified weak form with displacements and stresses as process variables is derived. This weak form is the basis for a finite element with an advanced fulfillment of the momentum balance and therefore with a better performance. For the continuous approximation of stresses and displacements on the triangular and tetrahedral elements, lowest-order Raviart-Thomas and linear standard Lagrange interpolations can be used. It is shown that coercivity and continuity of the resulting asymmetric bilinear form could be established with respect to appropriate norms. Further on, details about the implementation of the least-squares mixed finite elements are given and some numerical examples are presented in order to demonstrate the performance of the proposed formulation. © 2009 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nme.2692

• 2010 • 21	Accurate welding line prediction in extrusion processes Kloppenborg, T. and Ben Khalifa, N. and Tekkaya, A.E. Key Engineering Materials 424 87-95 (2010) In contrast to conventional extrusion processes, where a lot of research is done on in the welding quality, in composite extrusion, research is investigated into the welding line positioning. As a result of the process principle, the reinforcing elements are embedded into the longitudinal welding line. Hence, an undefined material flow inside the welding chamber induces reinforcement deflection, which can lead to reduced mechanical properties, as momentum of inertia. Therefore and to reduce costly experimental investigations, a new method of an automated numerical welding line prediction was developed. The results form HyperXtrude finite element calculations are used for special particle tracing simulations to predict the welding line in the profile cross section accurately. The procedures of segmentation and characteristic extraction are presented to approximate the welding line by cubic spline functions. The method was fully programmed in the Java program language, and works well for all HyperXtrude process models consisting of tetrahedral elements. © (2010) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.424.87

• 2010 • 20	Adaptive least squares finite element methods in elasto-plasticity Starke, G. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5910 LNCS 671-678 (2010) In computational mechanics applications, one is often interested not only in accurate approximations for the displacements but also for the stress tensor. Least squares finite element methods are perfectly suited for such problems since they approximate both process variables simultaneously in suitable finite element spaces. We consider an least squares formulation for the incremental formulation of elasto-plasticity using a plastic flow rule of von Mises type. The nonlinear least squares functional constitutes an a posteriori error estimator on which an adaptive refinement strategy may be based. The variational formulation under plane strain and plane stress conditions is investigated in detail. Standard conforming elements are used for the displacement approximation while the stress is represented by Raviart-Thomas elements. The algebraic least squares problems arising from the finite element discretization are nonlinear and nonsmooth and may be solved by generalized Newton methods. © 2010 Springer-Verlag Berlin Heidelberg.
  	view abstract	doi: 10.1007/978-3-642-12535-5_80

• 2010 • 19	An assessment of the grain structure evolution during hot forward extrusion of aluminum alloy 7020 Foydl, A. and Ben Khalifa, N. and Brosius, A. and Tekkaya, A.E. Key Engineering Materials 424 35-41 (2010) The current investigation is concerned with the grain structure evolution in an Al-Zn alloy (EN AW-7020) during the hot forward extrusion process. In order to analyze that, a miniature hot forward extrusion setup was designed which allows the quenching of the extrusion butt immediately after extrusion. In order to gain a better understanding of the process, the shape of the deformed grains was analyzed and the process was simulated. The shape of these grains was indentified in two directions in the different grain zones, e.g. dead metal zone and shear zone. The FE simulations showing the different grain zones were also illustrated. Simulation results and the micrographs were quite promising to find parameters for simulation models in order to predict grain sizes with the method presented in the current research work. © (2010) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.424.35

• 2010 • 18	An elasto-plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling Nagel, F. and Meschke, G. International Journal for Numerical and Analytical Methods in Geomechanics 34 605-625 (2010) This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two-phase soil model is sufficient, the simulation of compressed air support demands the use of a three-phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil-the soil skeleton, the fluid and the gaseous phase-and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto-plastic, cam-clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY's law and the soil-water characteristic curve after VAN GENUCHTEN. Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. © 2009 John Wiley & Sons, Ltd.
  	view abstract	doi: 10.1002/nag.828

• 2010 • 17	An image morphing method for 3D reconstruction and FE-analysis of pore networks in thermal spray coatings Wiederkehr, T. and Klusemann, B. and Gies, D. and Müller, H. and Svendsen, B. Computational Materials Science 47 881-889 (2010) Using thermal spraying various surface coatings consisting of different material compositions can be manufactured. Besides different solid phases the resulting coating microstructure often contains a non-negligible amount of pores altering their mechanical properties. A common practice to analyze the porosity and composition of a coating is to create cross section images using standard light microscopy equipment or a scanning electron microscope. In this paper a method is presented to construct a three-dimensional multiphase model of the coating from a number of such cross section images by means of an image morphing technique. The resulting model can then be used for visualization purposes or further analysis e.g. within a finite element simulation. The described method has been applied to the construction of a finite element model of a porous coating sample which is used in a compaction simulation to determine its behavior in a rolling process. The required cross section images were obtained using a successive grinding and microscopy procedure. The material behavior of the porous material is modeled by using a modified Johnson-Cook material model formulation for an elasto-viscoplastic material. Comparison of 2D and 3D-simulation results are shown. © 2009 Elsevier B.V. All rights reserved.
  	view abstract	doi: 10.1016/j.commatsci.2009.11.019

• 2010 • 16	Application of the multiscale FEM to the modeling of cancellous bone Ilic, S. and Hackl, K. and Gilbert, R. Biomechanics and Modeling in Mechanobiology 9 87-102 (2010) This paper considers the application of multiscale finite element method (FEM) to the modeling of cancellous bone as an alternative for Biot's model, the main intention of which is to decrease the extent of the necessary laboratory tests. At the beginning, the paper gives a brief explanation of the multiscale concept and thereafter focuses on the modeling of the representative volume element and on the calculation of the effective material parameters, including an analysis of their change with respect to increasing porosity. The latter part of the paper concentrates on the macroscopic calculations, which is illustrated by the simulation of ultrasonic testing and a study of the attenuation dependency on material parameters and excitation frequency. The results endorse conclusions drawn from the experiments: increasing excitation frequency and material density cause increasing attenuation. © 2009 Springer-Verlag.
  	view abstract	doi: 10.1007/s10237-009-0161-6

• 2010 • 15	Bending of single crystal microcantilever beams of cube orientation: Finite element model and experiments Demir, E. and Roters, F. and Raabe, D. Journal of the Mechanics and Physics of Solids 58 1599-1612 (2010) The aim of this work is to investigate the microstructure evolution, stressstrain response and strain hardening behavior of microscale beams. For that purpose, two single crystal cantilever beams in the size dependent regime were manufactured by ion beam milling and beams were bent with an indenter device. A crystal plasticity material model for large deformations was implemented in a finite element framework to further investigate the effect of boundary constraints. Simulations were performed using bulk material properties of single crystal copper without any special treatment for the strain gradients. The difference between the slopes of the experimental and the simulated force displacement curves suggested negligible amount of strain gradient hardening compared to the statistical hardening mechanisms. © 2010 Elsevier Ltd. All rights reserved.
  	view abstract	doi: 10.1016/j.jmps.2010.07.007

• 2010 • 14	Comparison of finite element and fast Fourier transform crystal plasticity solvers for texture prediction Liu, B. and Raabe, D. and Roters, F. and Eisenlohr, P. and Lebensohn, R.A. Modelling and Simulation in Materials Science and Engineering 18 (2010) We compare two full-field formulations, i.e. a crystal plasticity fast Fourier transform-based (CPFFT) model and the crystal plasticity finite element model (CPFEM) in terms of the deformation textures predicted by both approaches. Plane-strain compression of a 1024-grain ensemble is simulated with CPFFT and CPFEM to assess the models in terms of their predictions of texture evolution for engineering applications. Different combinations of final textures and strain distributionsare obtained with the CPFFT and CPFEM models for this 1024-grain polycrystal. To further understand these different predictions, the correlation between grain rotations and strain gradients is investigated through the simulation of plane-strain compression of bicrystals. Finally, a study of the influence of the initial crystal orientation and the crystallographic neighborhood on grain rotations and grain subdivisions is carried out by means of plane-strain compression simulations of a 64-grain cluster. © 2010 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/0965-0393/18/8/085005

• 2010 • 13	Crystal plasticity modelling and experiments for deriving microstructure-property relationships in γ-TiAl based alloys Zambaldi, C. and Raabe, D. Journal of Physics: Conference Series 240 (2010) Single-crystals of γ-TiAl cannot be grown for the compositions present inside the two-phase γ/α 2-microstructures that show good mechanical properties. Therefore the single crystal constitutive behaviour of γ-TiAl was studied by nanoindentation experiments in single phase regions of these microstructures. The experiments were extensively characterized by a combined experimental approach to clarify the orientation dependent mechanical response during nanoindentation. They further were analyzed by a three-dimensional crystal plasticity finite element model that incorporated the deformation behaviour of γ-TiAl. The spatially resolved activation of competing deformation mechanisms during indentation was used to assess their relative strengths. On the length-scale of multi-grain aggregates two kinds of microstructures were investigated. The lamellar microstructure was analyzed in terms of kinematic constraints perpendicular to densely spaced lamellar boundaries which lead to pronounced plastic anisotropy. Secondly, the mechanical behaviour of massively transformed microstructures was modelled by assuming a lower degree of kinematic constraints. This resulted in less plastic anisotropy on a single grain scale and lower compatibility stresses in a 64-grain aggregate. On the macroscopic length scale, the results could possibly explain the pre-yielding of lamellar microstructures. © 2010 IOP Publishing Ltd.
  	view abstract	doi: 10.1088/1742-6596/240/1/012140

• 2010 • 12	Finite element modeling and three-dimensional simulation of the turning process incorporating the material hardness Biermann, D. and Höhne, F. and Sieben, B. and Zabel, A. International Journal of Material Forming 3 459-462 (2010) Newly developed functionally graded workpieces made of AISI 6150 (51CrV4), pose great challenges to the machining process due to the combination of different material properties (e. g., hardness) within one workpiece. A material model including more information than experimentally identified stress-strain curves for different temperatures is necessary to model the process more realistically. Therefore, the Johnson-Cook material model has been implemented for three-dimensional turning simulations within the Finite Element software DEFORMTM 3D. This paper outlines the adopted method to modify the parameters of the Johnson-Cook material model for two-dimensional and three-dimensional FE-simulations in order to take material hardness into account. The primary objective was to improve passive and feed force computation by using this modeling approach, as it was observed that common material modeling showed large deviations of the feed force and passive force from the measured force components. The calculated feed force and passive force, as well as the cutting force, are validated experimentally. In conclusion it is shown that the application of the Johnson-Cook material model reveals more valid results for modeling the turning of workpieces with varying hardness values. © 2010 Springer-Verlag France.
  	view abstract	doi: 10.1007/s12289-010-0806-0

• 2010 • 11	Friction model selection in FEM simulations of aluminium extrusion Donati, L. and Tomesani, L. and Schikorra, M. and Ben Khalifa, N. and Tekkaya, A.E. International Journal of Surface Science and Engineering 4 27-41 (2010) Visioplastic analyses with the rod technique were performed in the extrusion of AA6060 alloy at different processing conditions in order to measure the friction effect at the billet-container interface. During the trials an accurate monitoring of the relevant process variables such as punch force and temperatures was performed in order to validate FEM simulations. Different FE codes were used to carry out the simulations: Deform, HyperXtrude, and Superform. A particular attention was given on evaluating the several coefficients of the available friction models by comparing the FEM results with experimental results. Copyright © 2010 Inderscience Enterprises Ltd.
  	view abstract	doi: 10.1504/IJSURFSE.2010.029627

• 2010 • 10	Goal-oriented a posteriori error estimates for transport problems Kuzmin, D. and Korotov, S. Mathematics and Computers in Simulation 80 1674-1683 (2010) Some aspects of goal-oriented a posteriori error estimation are addressed in the context of steady convection-diffusion equations. The difference between the exact and approximate values of a linear target functional is expressed in terms of integrals that depend on the solutions to the primal and dual problems. Gradient averaging techniques are employed to separate the element residual and diffusive flux errors without introducing jump terms. The dual solution is computed numerically and interpolated using higher-order basis functions. A node-based approach to localization of global errors in the quantities of interest is pursued. A possible violation of Galerkin orthogonality is taken into account. Numerical experiments are performed for centered and upwind-biased approximations of a 1D boundary value problem. © 2009 IMACS.
  	view abstract	doi: 10.1016/j.matcom.2009.03.008

• 2010 • 9	Grinding of arc-sprayed tungsten carbide coatings on machining centers - Process configuration and simulation Biermann, D. and Mohn, T. and Blum, H. and Kleemann, H. Key Engineering Materials 438 115-122 (2010) This paper describes the special demands placed on the grinding of arc-sprayed WC-Fe coatings on a conventional machining center. Basic process configuration, experimental results, measurement methods and an approach for a hybrid simulation system are presented. © (2010) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.438.115

• 2010 • 8	Joining of lightweight frame structures by die-less hydroforming Marré, M. and Gies, S. and Maevus, F. and Tekkaya, A.E. International Journal of Material Forming 3 1031-1034 (2010) A successful approach to achieve a reduction of a car's total weight is the implementation of lightweight strategies in the design process, e. g. using lightweight materials. An interesting alternative to conventional welding and riveting processes is joining by die-less hydroforming. This work describes an analytical model which can be used to calculate the strengths of these joints, taking into account the material parameters, joint geometry and process parameters. Additionally, validation of the model by both finite element simulations and experiments will be provided. Furthermore, investigations were carried out to implement the described methodology for a multi-joint used in a space frame structure. © 2010 Springer-Verlag France.
  	view abstract	doi: 10.1007/s12289-010-0946-2

• 2010 • 7	Numerical investigations of a multi-walled carbon nanotube-based multi-segmented optical antenna Cui, X. and Dong, L. and Zhang, W. and Wu, W. and Tang, Y. and Erni, D. Applied Physics B: Lasers and Optics 101 601-609 (2010) Motivated by the fabrication potential of multi-walled carbon nanotube structures, we numerically investigated a paired structure consisting of two metallic spheres each grown on one end of a multi-walled nanotube. The paired two-segmented structure is capable to convert free-space radiation into an intense near-field, and, hence, acting as an optical antenna. Vice versa the presence of the two nanotubes enable a current source at the antenna feed to more efficiently energy into the radiation modes, resulting e.g. in correspondingly altered luminescence lifetimes when an excited single molecule is placed in the feed point. Furthermore, the structure represents a mean to localize light on a sub-wavelength scale within different materials, which is interesting in the context of a fabrication technology for integrated nanophotonic components with different material combinations. The optical properties of the nano-antenna are analyzed by means of numerical simulations using the finite element method. Our investigations have revealed that the field enhancement, the resonances, and the radiation patterns can be easily tuned since all these quantities strongly depend on the size of the nanotubes and the metallic spheres, as well as on their material properties The structure we propose here carries a great potential for bio-sensing, for tip-enhanced spectroscopy applications, and for interfacing integrated photonic nano circuits. © 2010 Springer-Verlag.
  	view abstract	doi: 10.1007/s00340-010-4220-6

• 2010 • 6	Numerical material flow optimization of a multi-hole extrusion process Kloppenborg, T. and Brosius, A. and Tekkaya, A.E. Advanced Materials Research 83-86 826-833 (2010) The decrease of the bearing length in the aluminum extrusion processes results in an increase of the material flow and offers, through this, the possibility for correction and optimization. This study presents a simulation-based optimization technique which uses this effect for optimizing the material flow in a direct multi-hole extrusion process. First the extrusion process was numerically calculated to simulate the production of three rectangular profiles with equal cross sections. Here, the die orifices were arranged at various distances to the die centre, which lead to different profile exit speeds. Based on the initial numerical calculation, an automated optimization of the bearing length with the adaptive-response-surface-method was set up to achieve uniform exit speeds for all profiles. Finally, an experimental verification carried out to show the influence of the optimized die design. © (2010) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/AMR.83-86.826

• 2010 • 5	On the mechanical modeling of anisotropic biological soft tissue and iterative parallel solution strategies Balzani, D. and Brands, D. and Klawonn, A. and Rheinbach, O. and Schröder, J. Archive of Applied Mechanics 80 479-488 (2010) Biological soft tissues appearing in arterial walls are characterized by a nearly incompressible, anisotropic, hyperelastic material behavior in the physiological range of deformations. For the representation of such materials we apply a polyconvex strain energy function in order to ensure the existence of minimizers and in order to satisfy the Legendre-Hadamard condition automatically. The 3D discretization results in a large system of equations; therefore, a parallel algorithm is applied to solve the equilibrium problem. Domain decomposition methods like the Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) method are designed to solve large linear systems of equations, that arise from the discretization of partial differential equations, on parallel computers. Their numerical and parallel scalability, as well as their robustness, also in the incompressible limit, has been shown theoretically and in numerical simulations. We are using a dual-primal FETI method to solve nonlinear, anisotropic elasticity problems for 3D models of arterial walls and present some preliminary numerical results. © 2009 Springer-Verlag.
  	view abstract	doi: 10.1007/s00419-009-0379-x

• 2010 • 4	Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation Zambaldi, C. and Raabe, D. Acta Materialia 58 3516-3530 (2010) Single crystals of γ-TiAl cannot be grown in the near-stoichiometric compositions that are present inside two-phase γ / α2-microstructures with attractive mechanical properties. Therefore, the single-crystal constitutive behavior of γ-TiAl was studied by nanoindentation experiments in single-phase regions of these γ / α2-microstructures. The experiments were characterized by orientation microscopy and atomic force microscopy to quantify the orientation-dependent mechanical response during nanoindentation. Further, they were analyzed by a three-dimensional crystal plasticity finite element model that incorporated the deformation behavior of γ-TiAl. The spatially resolved activation of competing deformation mechanisms during indentation was used to assess their relative strengths. A convention was defined to unambiguously relate any indentation axis to a crystallographic orientation. Experiments and simulations were combined to study the orientation-dependent surface pile-up. The characteristic pile-up topographies were simulated throughout the unit triangle of γ-TiAl and represented graphically in the newly introduced inverse pole figure of pile-up patterns. Through this approach, easy activation of ordinary dislocation glide in stoichiometric γ-TiAl was confirmed independently from dislocation observation by transmission electron microscopy. © 2010 Acta Materialia Inc.
  	view abstract	doi: 10.1016/j.actamat.2010.02.025

• 2010 • 3	Simulation of the quench sensitivity of the aluminum alloy 6082 Güzel, A. and Jäger, A. and Ben Khalifa, N. and Tekkaya, A.E. Key Engineering Materials 424 51-56 (2010) A method for the numerical estimation of the final hardness distribution of heat treated aluminum alloys was developed and implemented into a commercial finite element (FE) tool. Jominy end-quench tests were carried out in order to determine the quench sensitivity of the aluminum alloy EN AW-6082. The hardness distribution of the alloy after end-quenching was related to the corresponding cooling rates. The derived relation was tested for an industrial application by investigating the local heat treatment of a prototype crash absorbing structure. Numerical estimations were validated with experimental measurements. Effectiveness of the derived method and possible improvements were discussed. © (2010) Trans Tech Publications.
  	view abstract	doi: 10.4028/www.scientific.net/KEM.424.51

• 2010 • 2	Simulation of tube wrinkling in electromagnetic compression Demir, O.K. and Psyk, V. and Tekkaya, A.E. Production Engineering 4 421-426 (2010) Wrinkle formation at electromagnetic tube compression was simulated using finite element (FE) method. Three-dimensional (3D) calculations were performed using a staggered coupling scheme between the electromagnetic and structural sides of the problem. Introducing the tube's contour imperfections into the FE model makes the simulation of the wrinkle formation possible. The results show good correspondence with the experiments. © 2010 German Academic Society for Production Engineering (WGP).
  	view abstract	doi: 10.1007/s11740-010-0243-4

• 2010 • 1	Sphere-on-pillar optical nano-antennas Cui, X. and Fan, Z. and Tao, X. and Zhang, W. and Erni, D. and Fan, X. and Zhang, X. and Dong, L. 2010 IEEE Nanotechnology Materials and Devices Conference, NMDC2010 171-176 (2010) We propose an optical nano-antenna consisting of a pair of sphere-on-pillar structures. Experiments show that the controlled fabrication of metallic nanospheres on the tip of carbon nanotubes (CNTs) is effective, and numerical investigation revealed that a pair of such structures are capable to convert free space radiation into an intense near-field; hence can function as an optical antenna. The fabrication process, electron-beam-induced bubbling (EBIB) and electromigration-based bubbling (EMBB), are based on nanofluidic mass delivery at the attogram scale using metal-filled CNTs. Under the irradiation of a high energy electron beam of a transmission electron microscope (TEM), the encapsulated metal is melted and extruded out from the tip of the nanotube; generating a metallic sphere. In the case that the encapsulated materials inside the CNT have a higher melting point than that of the beam energy can reach, electromigration-based mass delivery is an optional process to apply. Under a low bias (2-2.5V), spherical nanoparticles are formed on the tips of nanotubes. The optical properties of the nano-antenna are analyzed numerically using the finite element method. Our investigations have revealed that the field enhancement, the resonances, and the radiation patterns can be easily tuned since all these quantities strongly depend on the size of the nanotubes and the metallic spheres, as well as on their material properties. Sphere-on-pillar optical antennas carry a great potential for bio-sensing, tip-enhanced spectroscopy applications, and interfacing integrated nanophotonic circuits. © 2010 IEEE.
  	view abstract	doi: 10.1109/NMDC.2010.5652241