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.

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  • 2020 • 201 Effective Description of Anisotropic Wave Dispersion in Mechanical Band-Gap Metamaterials via the Relaxed Micromorphic Model
    d’Agostino, M.V. and Barbagallo, G. and Ghiba, I.-D. and Eidel, B. and Neff, P. and Madeo, A.
    Journal of Elasticity 139 299-329 (2020)
    In this paper the relaxed micromorphic material model for anisotropic elasticity is used to describe the dynamical behavior of a band-gap metamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy, Cosserat, second gradient, classical Mindlin–Eringen micromorphic etc.), the relaxed micromorphic model is endowed to capture the main microscopic and macroscopic characteristics of the targeted metamaterial, namely, stiffness, anisotropy, dispersion and band-gaps. The simple structure of our material model, which simultaneously lives on a micro-, a meso- and a macroscopic scale, requires only the identification of a limited number of frequency-independent and thus truly constitutive parameters, valid for both static and wave-propagation analyses in the plane. The static macro- and micro-parameters are identified by numerical homogenization in static tests on the unit-cell level in Neff et al. (J. Elast.,, 2019, in this volume). The remaining inertia parameters for dynamical analyses are calibrated on the dispersion curves of the same metamaterial as obtained by a classical Bloch–Floquet analysis for two wave directions. We demonstrate via polar plots that the obtained material parameters describe very well the response of the structural material for all wave directions in the plane, thus covering the complete panorama of anisotropy of the targeted metamaterial. © 2019, Springer Nature B.V.
    view abstractdoi: 10.1007/s10659-019-09753-9
  • 2020 • 200 A simple finite element for the geometrically exact analysis of Bernoulli–Euler rods
    da Costa e Silva, C. and Maassen, S.F. and Pimenta, P.M. and Schröder, J.
    Computational Mechanics 65 905-923 (2020)
    This work develops a simple finite element for the geometrically exact analysis of Bernoulli–Euler rods. Transversal shear deformation is not accounted for. Energetically conjugated cross-sectional stresses and strains are defined. A straight reference configuration is assumed for the rod. The cross-section undergoes a rigid body motion. A rotation tensor with the Rodrigues formula is used to describe the rotation, which makes the updating of the rotational variables very simple. A formula for the Rodrigues parameters in function of the displacements derivative and the torsion angle is for the first time settled down. The consistent connection between elements is thoroughly discussed, and an appropriate approach is developed. Cubic Hermitian interpolation for the displacements together with linear Lagrange interpolation for the torsion incremental angle were employed within the usual Finite Element Method, leading to adequate C1 continuity. A set of numerical benchmark examples illustrates the usefulness of the formulation and numerical implementation. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
    view abstractdoi: 10.1007/s00466-019-01800-5
  • 2020 • 199 Elastic properties of single crystal Bi12SiO20 as a function of pressure and temperature and acoustic attenuation effects in Bi12 MO20 (M = Si, Ge and Ti)
    Haussühl, E. and Reichmann, H.J. and Schreuer, J. and Friedrich, A. and Hirschle, C. and Bayarjargal, L. and Winkler, B. and Alencar, I. and Wiehl, L. and Ganschow, S.
    Materials Research Express 7 (2020)
    A comprehensive study of sillenite Bi12SiO20 single-crystal properties, including elastic stiffness and piezoelectric coefficients, dielectric permittivity, thermal expansion and molar heat capacity, is presented. Brillouin-interferometry measurements (up to 27 GPa), which were performed at high pressures for the first time, and ab initio calculations based on density functional theory (up to 50 GPa) show the stability of the sillenite structure in the investigated pressure range, in agreement with previous studies. Elastic stiffness coefficients c 11 and c 12 are found to increase continuously with pressure while c 44 increases slightly for lower pressures and remains nearly constant above 15 GPa. Heat-capacity measurements were performed with a quasi-adiabatic calorimeter employing the relaxation method between 2 K and 395 K. No phase transition could be observed in this temperature interval. Standard molar entropy, enthalpy change and Debye temperature are extracted from the data. The results are found to be roughly half of the previous values reported in the literature. The discrepancy is attributed to the overestimation of the Debye temperature which was extracted from high-temperature data. Additionally, Debye temperatures obtained from mean sound velocities derived by Voigt-Reuss averaging are in agreement with our heat-capacity results. Finally, a complete set of electromechanical coefficients was deduced from the application of resonant ultrasound spectroscopy between 103 K and 733 K. No discontinuities in the temperature dependence of the coefficients are observed. High-temperature (up to 1100 K) resonant ultrasound spectra recorded for Bi12 MO20 crystals revealed strong and reversible acoustic dissipation effects at 870 K, 960 K and 550 K for M = Si, Ge and Ti, respectively. Resonances with small contributions from the elastic shear stiffness c 44 and the piezoelectric stress coefficient e 123 are almost unaffected by this dissipation. © 2020 The Author(s). Published by IOP Publishing Ltd.
    view abstractdoi: 10.1088/2053-1591/ab6ad6
  • 2020 • 198 A mixed least-squares finite element formulation with explicit consideration of the balance of moment of momentum, a numerical study
    Igelbüscher, M. and Schröder, J. and Schwarz, A.
    GAMM Mitteilungen 43 (2020)
    Important conditions in structural analysis are the fulfillment of the balance of linear momentum (vanishing resultant forces) and the balance of angular momentum (vanishing resultant moment), which is not a priori satisfied for arbitrary element formulations. In this contribution, we analyze a mixed least-squares (LS) finite element formulation for linear elasticity with explicit consideration of the balance of angular momentum. The considered stress-displacement (σ − u) formulation is based on the squared L2(ℬ)-norm minimization of the residuals of a first-order system of differential equations. The formulation is constructed by means of two residuals, that is, the balance of linear momentum and the constitutive equation. Motivated by the crucial point of weighting factors within LS formulations, a scale independent formulation is constructed. The displacement approximation is performed by standard Lagrange polynomials and the stress approximation with Raviart-Thomas functions. The latter ansatz functions do not a priori fulfill the symmetry of the Cauchy stress tensor. Therefore, a redundant residual, the balance of angular momentum ((x − x0) × (divσ + f) + axl[σ − σT]), is introduced and the results are discussed from the engineering point of view, especially for coarse mesh discretizations. However, this formulation shows an improvement compared to standard LS σ − u formulations, which is considered here in a numerical study. © 2019 The Authors. GAMM - Mitteilungen published by Wiley-VCH Verlag GmbH & Co. KGaA on behalf of Gesellschaft für Angewandte Mathematik und Mechanik
    view abstractdoi: 10.1002/gamm.202000009
  • 2020 • 197 Single-layer Janus black arsenic-phosphorus (b-AsP): Optical dichroism, anisotropic vibrational, thermal, and elastic properties
    Li, L.L. and Bacaksiz, C. and Nakhaee, M. and Pentcheva, R. and Peeters, F.M. and Yagmurcukardes, M.
    Physical Review B 101 (2020)
    By using density functional theory (DFT) calculations, we predict a puckered, dynamically stable Janus single-layer black arsenic-phosphorus (b-AsP), which is composed of two different atomic sublayers, arsenic and phosphorus atoms. The calculated phonon spectrum reveals that Janus single-layer b-AsP is dynamically stable with either pure or coupled optical phonon branches arising from As and P atoms. The calculated Raman spectrum indicates that due to the relatively strong P-P bonds, As atoms have no contribution to the high-frequency optical vibrations. In addition, the orientation-dependent isovolume heat capacity reveals anisotropic contributions of LA and TA phonon branches to the low-temperature thermal properties. Unlike pristine single layers of b-As and b-P, Janus single-layer b-AsP exhibits additional out-of-plane asymmetry which leads to important consequences for its electronic, optical, and elastic properties. In contrast to single-layer b-As, Janus single-layer b-AsP is found to possess a direct band gap dominated by the P atoms. Moreover, real and imaginary parts of the dynamical dielectric function, including excitonic effects, reveal the highly anisotropic optical feature of the Janus single-layer. A tight-binding (TB) model is also presented for Janus single-layer b-AsP, and it is shown that, with up to seven nearest hoppings, the TB model reproduces well the DFT band structure in the low-energy region around the band gap. This TB model can be used in combination with the Green's function approach to study, e.g., quantum transport in finite systems based on Janus single-layer b-AsP. Furthermore, the linear-elastic properties of Janus single-layer b-AsP are investigated, and the orientation-dependent in-plane stiffness and Poisson ratio are calculated. It is found that the Janus single layer exhibits strong in-plane anisotropy in its Poisson ratio much larger than that of single-layer b-P. This Janus single layer is relevant for promising applications in optical dichroism and anisotropic nanoelasticity. © 2020 American Physical Society.
    view abstractdoi: 10.1103/PhysRevB.101.134102
  • 2020 • 196 Experimental and analytical analysis on the stacking sequence of composite pressure vessels
    Nebe, M. and Asijee, T.J. and Braun, C. and van Campen, J.M.J.F. and Walther, F.
    Composite Structures 247 (2020)
    The industrialization of fuel cell electric vehicles demands cost efficient storage solutions for hydrogen. While gaseous storage in type IV pressure vessels is currently the most mature technology, further structure optimization needs to be undertaken in order to meet cost requirements. This research investigates the effects of stacking sequence of composite pressure vessels regarding laminate quality, structural deformation and finally burst pressure. Therefore, a known laminate is studied on a subscale vessel geometry with changing stacking sequences. The specimens are pressurized in a specially designed chamber up to burst pressures of 166.11 MPa. Through a multisensor arrangement of stereometric systems, the deformation is tracked up to burst by using 3D digital image correlation. The experimental results show a difference of 67% in burst pressure between the investigated stacking sequences. Experimental cylinder strains and burst pressures are compared to results derived from 3D elasticity theory with implemented first ply failure criterion. Additionally, using X-ray computed tomography and acid digestion tests, insights about the distribution of fiber volume fraction and porosity are provided. For the investigated sequences in this research, the results show the considerable influence of stacking sequence on the laminate quality, the structural deformation and finally the burst pressure of composite pressure vessels. Moreover, it is shown that while the used 3D elasticity approach proved to be a useful tool for the prediction of strains and failure in the cylindrical section, discrepancies between prediction and experiment can arise based on preliminary failure occuring at the cylinder-dome transition. The results therefore emphasize the need for analytical and numerical analysis strategies to consider transition-related effects between cylinder and dome. © 2020 Elsevier Ltd
    view abstractdoi: 10.1016/j.compstruct.2020.112429
  • 2020 • 195 A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity
    Schweickert, E. and Mihai, L.A. and Martin, R.J. and Neff, P.
    International Journal of Non-Linear Mechanics 119 (2020)
    It has recently been shown that for a Cauchy stress response induced by a strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy stress tensor field cannot correspond to a non-homogeneous deformation if the deformation gradient has discrete values, i.e. if the deformation is piecewise affine linear and satisfies the Hadamard jump condition. In this note, we expand upon these results and show that they do not hold for arbitrary deformations by explicitly giving an example of a strictly rank-one convex energy and a non-homogeneous deformation such that the induced Cauchy stress tensor is constant. In the planar case, our example is related to another previous result concerning criteria for generalized convexity properties of conformally invariant energy functions, which we extend to the case of strict rank-one convexity. © 2019 Elsevier Ltd
    view abstractdoi: 10.1016/j.ijnonlinmec.2019.103282
  • 2020 • 194 Effects of size and elasticity on the relation between flow velocity and wall shear stress in side-wall aneurysms: A lattice Boltzmann-based computer simulation study
    Wang, H. and Krüger, T. and Varnik, F.
    PLoS ONE 15 (2020)
    Blood flow in an artery is a fluid-structure interaction problem. It is widely accepted that aneurysm formation, enlargement and failure are associated with wall shear stress (WSS) which is exerted by flowing blood on the aneurysmal wall. To date, the combined effect of aneurysm size and wall elasticity on intra-aneurysm (IA) flow characteristics, particularly in the case of side-wall aneurysms, is poorly understood. Here we propose a model of three-dimensional viscous flow in a compliant artery containing an aneurysm by employing the immersed boundary-lattice Boltzmann-finite element method. This model allows to adequately account for the elastic deformation of both the blood vessel and aneurysm walls. Using this model, we perform a detailed investigation of the flow through aneurysm under different conditions with a focus on the parameters which may influence the wall shear stress. Most importantly, it is shown in this work that the use of flow velocity as a proxy for wall shear stress is well justified only in those sections of the vessel which are close to the ideal cylindrical geometry. Within the aneurysm domain, however, the correlation between wall shear stress and flow velocity is largely lost due to the complexity of the geometry and the resulting flow pattern. Moreover, the correlations weaken further with the phase shift between flow velocity and transmural pressure. These findings have important implications for medical applications since wall shear stress is believed to play a crucial role in aneurysm rupture. © 2020 Wang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
    view abstractdoi: 10.1371/journal.pone.0227770
  • 2020 • 193 Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics
    Zuo, D. and Avril, S. and Yang, H. and Jamaleddin Mousavi, S. and Hackl, K. and He, Y.
    Journal of the Royal Society Interface 17 (2020)
    Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel-Gasser-Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results. © 2020 The Author(s) Published by the Royal Society. All rights reserved.
    view abstractdoi: 10.1098/rsif.2019.0708
  • 2019 • 192 Local and global dynamics of the viscous ion conductors 2Ca(NO 3 ) 2 -3KNO 3 and 2Ca(NO 3 ) 2 -3RbNO 3 probed by 87 Rb nuclear magnetic resonance and shear rheology
    Beerwerth, J. and Bierwirth, S.P. and Adam, J. and Gainaru, C. and Böhmer, R.
    Journal of Chemical Physics 150 (2019)
    The microscopic and macroscopic dynamics of calcium alkali nitrate melts are studied in their supercooled regime by means of shear rheology and nuclear magnetic resonance (NMR). The structural relaxation is probed using shear rheology to access the viscoelastic flow as well as using physical aging experiments. By exploiting the strongly quadrupole-perturbed 87 Rb nucleus, the local dynamics is probed on the milliseconds to nanoseconds range using various NMR methods involving central-transition stimulated-echo techniques, line shape analyses, spin relaxations, and second-order dynamic shift effects. The time scales monitored via the local Rb probe are in harmony with the electrical conductivity relaxation times. The low-temperature NMR line shapes agree excellently with those predicted by the Czjzek model. The temperature dependent second-order dynamic frequency shift is described using the imaginary part of the spectral density. It is demonstrated how the latter quantity can be generalized to include effects of correlation time distributions. © 2019 Author(s).
    view abstractdoi: 10.1063/1.5093973
  • 2019 • 191 Local and global dynamics of the viscous ion conductors 2Ca(NO3)2-3KNO3 and 2Ca(NO3)2-3RbNO3 probed by 87Rb nuclear magnetic resonance and shear rheology
    Beerwerth, J. and Bierwirth, S.P. and Adam, J. and Gainaru, C. and Böhmer, R.
    Journal of Chemical Physics 150 (2019)
    The microscopic and macroscopic dynamics of calcium alkali nitrate melts are studied in their supercooled regime by means of shear rheology and nuclear magnetic resonance (NMR). The structural relaxation is probed using shear rheology to access the viscoelastic flow as well as using physical aging experiments. By exploiting the strongly quadrupole-perturbed 87Rb nucleus, the local dynamics is probed on the milliseconds to nanoseconds range using various NMR methods involving central-transition stimulated-echo techniques, line shape analyses, spin relaxations, and second-order dynamic shift effects. The time scales monitored via the local Rb probe are in harmony with the electrical conductivity relaxation times. The low-temperature NMR line shapes agree excellently with those predicted by the Czjzek model. The temperature dependent second-order dynamic frequency shift is described using the imaginary part of the spectral density. It is demonstrated how the latter quantity can be generalized to include effects of correlation time distributions. © 2019 Author(s).
    view abstractdoi: 10.1063/1.5093973
  • 2019 • 190 Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry
    Bertrand, F. and Cai, Z. and Park, E.Y.
    Computational Methods in Applied Mathematics 19 415-430 (2019)
    This paper develops and analyzes two least-squares methods for the numerical solution of linear elasticity and Stokes equations in both two and three dimensions. Both approaches use the L2 norm to define least-squares functionals. One is based on the stress-displacement/velocity-rotation/vorticity-pressure (SDRP/SVVP) formulation, and the other is based on the stress-displacement/velocity-rotation/vorticity (SDR/SVV) formulation. The introduction of the rotation/vorticity variable enables us to weakly enforce the symmetry of the stress. It is shown that the homogeneous least-squares functionals are elliptic and continuous in the norm of H(div; ω) for the stress, of H1(ω) for the displacement/velocity, and of L2(ω) for the rotation/vorticity and the pressure. This immediately implies optimal error estimates in the energy norm for conforming finite element approximations. As well, it admits optimal multigrid solution methods if Raviart-Thomas finite element spaces are used to approximate the stress tensor. Through a refined duality argument, an optimal L2 norm error estimates for the displacement/velocity are also established. Finally, numerical results for a Cook's membrane problem of planar elasticity are included in order to illustrate the robustness of our method in the incompressible limit. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.
    view abstractdoi: 10.1515/cmam-2018-0255
  • 2019 • 189 Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations
    Böhmer, C.G. and Lee, Y. and Neff, P.
    Wave Motion 84 110-124 (2019)
    We study the fully nonlinear dynamical Cosserat micropolar elasticity problem in three dimensions with various energy functionals dependent on the microrotation [Formula presented] and the deformation gradient tensor [Formula presented]. We derive a set of coupled nonlinear equations of motion from first principles by varying the complete energy functional. We obtain a double sine–Gordon equation and construct soliton solutions. We show how the solutions can determine the overall deformational behaviours and discuss the relations between wave numbers and wave velocities thereby identifying parameter values where the soliton solution does not exist. © 2018 The Authors
    view abstractdoi: 10.1016/j.wavemoti.2018.10.005
  • 2019 • 188 Surfactant-mediated formation of alginate layers at the water-air interface
    Degen, P. and Paulus, M. and Zwar, E. and Jakobi, V. and Dogan, S. and Tolan, M. and Rehage, H.
    Surface and Interface Analysis 51 1051-1058 (2019)
    The self-organization process of polysaccharide alginate with different cationic surfactants at the water-air interface was investigated over a wide concentration regime. The changes of surface properties determined by surface tension measurements, surface rheology, and X-ray reflectivity are correlated with changes of bulk properties measured by turbidity, light scattering, and zeta potential measurements. We demonstrate that the interactions between the alginate and cationic surfactants result in significant changes of bulk and interfacial properties. The results of surface shear experiments point to the existence of highly viscoelastic interfacial films. In combination with X-ray reflectivity, we demonstrate that these rheological features are related to polymer-surfactant associations at the interface. In the regime of high surfactant concentrations, we observed the existence of multilayer structures. © 2019 The Authors. Surface and Interface Analysis published by John Wiley & Sons Ltd
    view abstractdoi: 10.1002/sia.6691
  • 2019 • 187 New Approach to Structure–Property Correlations of Different Films of Sorbitan Esters and Their Self-Assembly into Viscoelastic Monolayers
    Demand, S. and Egger, S. and Degen, P. and Salmen, P. and Paulus, M. and Tolan, M. and Rehage, H.
    Journal of Surfactants and Detergents 22 597-611 (2019)
    This publication is focused on the structural origin of viscoelasticity in Langmuir monolayers. To improve the understanding of the structural origin of viscoelasticity of surfactant films, we systematically studied interfacial films of different sorbitan esters with saturated (Span 60 and 65) and unsaturated (Span 80 and 85) paraffin chains by means of surface rheology, Langmuir isotherms, X-ray reflectometry (XRR), and Brewster angle microscopy (BAM). The results of two-dimensional shear rheological measurements revealed the existence of temporarily cross-linked networks. In dynamic BAM experiments, we observed a swinging motion of the monolayers as a result of a sudden externally initiated mechanical perturbation. The viscoelastic film response, which relaxed with time as the external force vanished, could be traced back to the presence of foam-like supramolecular structures that interlinked solid-condensed domains. The temperature dependence of the elastic response implied that the solid domains decomposed at temperatures close to the bulk melting point of Span 60 and Span 65. We concluded that insoluble surfactants formed solid domains at the interface, which were linked with each other by nonsolid areas, giving viscoelastic films. These newly discovered insights into coherent film formations could provide new opportunities for designing mechanically stable surfactant interfaces. © 2019 AOCS
    view abstractdoi: 10.1002/jsde.12261
  • 2019 • 186 Magnetostriction in magnetic gels and elastomers as a function of the internal structure and particle distribution
    Fischer, L. and Menzel, A.M.
    Journal of Chemical Physics 151 (2019)
    Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid particles embedded in a soft elastic polymeric matrix, leading to overall deformations. It is a major challenge in theory to correctly predict from the discrete particle configuration the type of deformation resulting for a finite-sized system. Considering an elastic sphere, we here present such an approach. The method is in principle exact, at least within the framework of linear elasticity theory and for large enough interparticle distances. Different particle arrangements are considered. We find, for instance, that regular simple cubic configurations show elongation of the sphere along the magnetization if oriented along a face or space diagonal of the cubic unit cell. Contrariwise, with the magnetization along the edge of the cubic unit cell, they contract. The opposite is true in this geometry for body- and face-centered configurations. Remarkably, for the latter configurations but the magnetization along a face or space diagonal of the unit cell, contraction was observed to revert to expansion with decreasing Poisson ratio of the elastic material. Randomized configurations were considered as well. They show a tendency of elongating the sphere along the magnetization, which is more pronounced for compressible systems. Our results can be tested against actual experiments for spherical samples. Moreover, our approach shall support the search of optimal particle distributions for a maximized effect of actuation. © 2019 Author(s).
    view abstractdoi: 10.1063/1.5118875
  • 2019 • 185 Classic crystal plasticity theory vs crystal plasticity theory based on strong discontinuities—Theoretical and algorithmic aspects
    Fohrmeister, V. and Díaz, G. and Mosler, J.
    International Journal for Numerical Methods in Engineering 117 1283-1303 (2019)
    This paper deals with two different approaches suitable for the description of plasticity in single crystals. The first one is the standard approach that is based on a continuous deformation mapping. Plasticity is driven by a classic Schmid-type relation connecting the shear stresses to the shear strains at a certain slip system. By way of contrast, the second approach is nonstandard. In this novel model, localized plastic deformation at certain slip planes is approximated by a strong discontinuity (discontinuous deformation mapping). Accordingly, a modified Schmid-type model relating the shear stresses to the shear displacements (displacement jump) is considered in this model. Although both models are indeed different, it is shown that they can be characterized by almost the same set of equations, eg, by a multiplicative decomposition of the deformation gradient into an elastic part and a plastic part. This striking analogy eventually leads to a unifying algorithmic formulation covering both models. Since the set of active slip systems is not known in advance, its determination is of utmost importance. This problem is solved here by using the nonlinear complementarity problem (NCP) as advocated by Fischer and Burmeister. While this idea is not new, it is shown that the NCP problem is well posed, independent of the number of active slip systems. To be more explicit, the tangent matrix in the return-mapping scheme is regular even for more than five simultaneously active slip systems. Based on this algorithm, texture evolution in a polycrystal is analyzed by means of both models and the results are compared in detail. © 2018 John Wiley & Sons, Ltd.
    view abstractdoi: 10.1002/nme.6000
  • 2019 • 184 Tension/compression anisotropy enhanced topology design
    Gaganelis, G. and Jantos, D.R. and Mark, P. and Junker, P.
    Structural and Multidisciplinary Optimization 59 2227-2255 (2019)
    A strategy for tension/compression anisotropy enhancement of topology optimization approaches is presented. To this end, a spectral decomposition of stresses and strains into tension and compression contributions allows for a multi-material optimization that favors tension or compression affine materials, dependent on the predominant local state. Numerical computations hence yield the topology of a construction part with maximum stiffness at constraint design volume. Additionally, the spatial distribution of a tension affine and a compression affine material is optimized, which is motivated by concrete engineering: financially cheap material, for example concrete, is applied in compression dominant regions in favor of stiffer but more expensive material, which is applied only in tension dominant regions, for example steel. The enhancement is applied both to a classical (mathematical) optimization method and the thermodynamic topology optimization. Several numerical examples are investigated and yield design suggestions for tension/compression sensitive construction parts, e.g., for future lightweight structures made of reinforced concrete. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
    view abstractdoi: 10.1007/s00158-018-02189-0
  • 2019 • 183 Bitumen rheology and the impact of rejuvenators
    Ganter, D. and Mielke, T. and Maier, M. and Lupascu, D.C.
    Construction and Building Materials 222 414-423 (2019)
    Bitumen is a material used in many industrial applications. It is the primary binding material for road pavements in asphalt. To improve sustainability, it is important to be aware of the finite nature of conventional oil reserves. As a cost and energy saving material, reclaimed asphalt pavement can help preserve our resources. Virgin binder ages significantly during its service life time yielding declining mechanical properties. As material properties of bitumen are responsible for the endurance of asphalt pavements, adding rejuvenators is supposed to restore the mechanical properties like the original bitumen properties. In this paper, three different rejuvenators were studied using one common polymer modified bitumen PmB 25/55-55 A. The virgin binder was aged in two different aging steps (short and long-term) and rheological properties were determined by traditional bitumen tests and dynamic shear rheometer (DSR) tests. For a better understanding of rejuvenation on the microscale, virgin, aged, and modified bitumen samples were measured using Optical Microscopy and Atomic Force Microscopy (AFM). Aging has significant influence on the macro- and micro-Rheology of bitumen. It causes changes in viscosity and at the same time clear changes in its surface structure. All Rejuvenators positively influence the rheological properties to different extents. Atomic Force Microscopy revealed considerable changes of the morphology between virgin, aged, and rejuvenated binders. The combination of rheological properties and micro structure imaging is an important tool in advancing and optimizing reclaimed asphalt pavement. © 2019 Elsevier Ltd
    view abstractdoi: 10.1016/j.conbuildmat.2019.06.177
  • 2019 • 182 Micromechanical modelling of coupled crystal plasticity and hydrogen diffusion
    Hassan, H.U. and Govind, K. and Hartmaier, A.
    Philosophical Magazine 99 92-115 (2019)
    Hydrogen transport behaviour in metals is greatly influenced by the mechanical stress and the underlying microstructural features. In this work, a micromechanical model based on coupled crystal plasticity and hydrogen diffusion is developed and applied to model hydrogen diffusion and storage in a polycrystalline microstructure. Particular emphasis is laid on mechanical influences on hydrogen transport, invoked by internal stresses and by trapping of dislocations generated by plastic strains. First, a study of a precharged material is carried out where hydrogen is allowed to redistribute under the influence of mechanical loading. These simulations demonstrate to which extent hydrogen migrates from regions with compressive strains to those with tensile strains. In the next step, the influence of plastic prestraining on hydrogen diffusion is analysed. This prestraining produces internal residual stresses in the microstructure, that mimic residual stresses introduced into components during cold working. Lastly, a series of permeation simulations is performed to characterise the influence of hydrogen trapping on effective diffusivity. It is shown that the effective diffusivity decreases with stronger traps and the effect is more prominent at a larger predeformation, because the trapped hydrogen concentration increases considerably. The reduction of effective diffusivity with plastic deformation agrees very well with experimental findings and offers a way to validate and parameterise our model. With this work, it is demonstrated how micromechanical modelling can support the understanding of hydrogen transport on the microstructural level. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
    view abstractdoi: 10.1080/14786435.2018.1530466
  • 2019 • 181 Geometrically nonlinear simulation of textile membrane structures based on orthotropic hyperelastic energy functions
    Motevalli, M. and Uhlemann, J. and Stranghöner, N. and Balzani, D.
    Composite Structures 223 (2019)
    New hyperelastic orthotropic models are proposed for the simulation of textile membranes used in civil engineering applications. In contrast to published models, part of the new models is polyconvex and ensures thereby a physically meaningful and mathematically sound formulation. The models are adjusted to uniaxial tension tests performed in warp and fill direction, where not only the stress-strain response in tension direction is accounted for but also the lateral contraction. Thereby, the crosswise interaction between the warp and fill direction is captured. In a series of different boundary value problems the new models as well as a competitive formulation given in literature are compared with respect to the accuracy to represent the experimental data, the mathematical properties as well as the numerical robustness. As it turns out, most formulations including the model from the literature show a loss of material stability and non-converging Newton iterations in structural simulations. Only one of the proposed polyconvex formulations works robustly in numerical simulations of realistic structural engineering problems. Thereby, this new orthotropic model enables realistic simulations of textile membranes in a fully geometrically nonlinear setting, which does not require simplifications based on linearized strains, which are currently used as standard in engineering practice. © 2019 Elsevier Ltd
    view abstractdoi: 10.1016/j.compstruct.2019.110908
  • 2019 • 180 Fatigue of glued-in rods in engineered hardwood products — Part II: Numerical modelling
    Myslicki, S. and Walther, F. and Bletz-Mühldorfer, O. and Diehl, F. and Lavarec, C. and Beber, V.C. and Vallée, T.
    Journal of Adhesion 95 702-722 (2019)
    Fatigue behaviour of materials is traditionally performed on probes that ensure that stresses (or strains) are very uniform. This is a situation seldom encountered in most adhesively bonded joints, where stresses usually peak at the end of the overlaps. This paper presents a relatively simple model to predict the fatigue behaviour of glued-in rods (GiR) involving hardwood in previously investigated in an extensive experimental campaign. The model is based on strength and stiffness degradation of the components of the GiR, which were experimentally estimated in small scale tests. Based thereupon, Finite Element Analysis (FEA) was used to estimate the effect of material degradation on the residual strength of the GiR, which was then interpreted as S-N-curves. The influence of several parameters, e.g. strength and stiffness degradation rates and the magnitude of the residual strength threshold were numerically investigated. The result showed that it is possible, using a practitioner adapted numerical model, to predict the fatigue behaviour of GiR, based upon comparatively simple fatigue characterisation on their components. © 2019, © 2019 Taylor & Francis Group, LLC.
    view abstractdoi: 10.1080/00218464.2018.1555478
  • 2019 • 179 Modelling cyclic behaviour of martensitic steel with J2 plasticity and crystal plasticity
    Sajjad, H.M. and Hanke, S. and Güler, S. and ul Hassan, H. and Fischer, A. and Hartmaier, A.
    Materials 12 (2019)
    In order to capture the stress-strain response of metallic materials under cyclic loading, it is necessary to consider the cyclic hardening behaviour in the constitutive model. Among different cyclic hardening approaches available in the literature, the Chaboche model proves to be very efficient and convenient to model the kinematic hardening and ratcheting behaviour of materials observed during cyclic loading. The purpose of this study is to determine the material parameters of the Chaboche kinematic hardening material model by using isotropic J2 plasticity and micromechanical crystal plasticity (CP) models as constitutive rules in finite element modelling. As model material, we chose a martensitic steel with a very fine microstructure. Thus, it is possible to compare the quality of description between the simpler J2 plasticity and more complex micromechanical material models. The quality of the results is rated based on the quantitative comparison between experimental and numerical stress-strain hysteresis curves for a rather wide range of loading amplitudes. It is seen that the ratcheting effect is captured well by both approaches. Furthermore, the results show that concerning macroscopic properties, J2 plasticity and CP are equally suited to describe cyclic plasticity. However, J2 plasticity is computationally less expensive whereas CP finite element analysis provides insight into local stresses and plastic strains on the microstructural length scale. With this study, we show that a consistent material description on the microstructural and the macroscopic scale is possible, which will enable future scale-bridging applications, by combining both constitutive rules within one single finite element model. © 2019 by the authors.
    view abstractdoi: 10.3390/ma12111767
  • 2019 • 178 Phase-field simulation of martensite microstructure in low-carbon steel
    Shchyglo, O. and Du, G. and Engels, J.K. and Steinbach, I.
    Acta Materialia 175 415-425 (2019)
    We present three-dimensional phase-field simulations of martensite microstructure formation in low-carbon steel. In this study, a full set of 24 Kurdjumov-Sachs symmetry variants of martensite is considered. Three different carbon compositions are investigated in order to reveal the effect of carbon content on the martensite microstructure formation. The simulations are performed using the finite strain framework which allows considering real martensite transformation strains. Using Neuber elasto-plastic approximation to the mechanical equilibrium solution, realistic stresses and strains can be obtained during martensite formation resulting in realistic mechanical driving forces for the transformation. The simulated microstructures are compared to experimental results for three carbon compositions. Good agreement between simulated and experimental results is achieved. © 2019 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2019.06.036
  • 2018 • 177 Numerical Benchmark of Phase-Field Simulations with Elastic Strains: Precipitation in the Presence of Chemo-Mechanical Coupling
    Darvishi Kamachali, R. and Schwarze, C. and Lin, M. and Diehl, M. and Shanthraj, P. and Prahl, U. and Steinbach, I. and Raabe, D.
    Computational Materials Science 155 541-553 (2018)
    Phase-field studies of solid-state precipitation under strong chemo-mechanical coupling are performed and benchmarked against the existing analytical solutions. The open source software packages OpenPhase and DAMASK are used for the numerical studies. Solutions for chemical diffusion and static mechanical equilibrium are investigated individually followed by a chemo-mechanical coupling effect arising due to composition dependence of the elastic constants. The accuracy of the numerical solutions versus the analytical solutions is quantitatively discussed. For the chemical diffusion benchmark, an excellent match, with a deviation <0.1%, was obtained. For the static mechanical equilibrium benchmark Eshelby problem was considered where a deviation of 5% was observed in the normal component of the stress, while the results from the diffuse interface (OpenPhase) and sharp interface (DAMASK) models were slightly different. In the presence of the chemo-mechanical coupling, the concentration field around a static precipitate was benchmarked for different coupling coefficients. In this case, it is found that the deviation increases proportional to the coupling coefficient that represents the strength of coupling concentration and elastic constants. Finally, the interface kinetics in the presence of the considered chemo-mechanical coupling were studied using OpenPhase and a hybrid OpenPhase–DAMASK implementation, replacing the mechanical solver of OpenPhase with DAMASK's. The observed deviations in the benchmark studies are discussed to provide guidance for the use of these results in studying further phase transformation models and implementations involving diffusion, elasticity and chemo-mechanical coupling effect. © 2018 Elsevier B.V.
    view abstractdoi: 10.1016/j.commatsci.2018.09.011
  • 2018 • 176 Elastic properties and plastic deformation of TiC- and VC-based pseudobinary alloys
    Edström, D. and Sangiovanni, D.G. and Hultman, L. and Petrov, I. and Greene, J.E. and Chirita, V.
    Acta Materialia 144 376-385 (2018)
    Transition-metal (TM) carbides are an important class of hard, protective coating materials; however, their brittleness often limits potential applications. We use density functional theory to investigate the possibility of improving ductility by forming pseudobinary cubic M1M2C alloys, for which M1 = Ti or V and M2 = W or Mo. The alloying elements are chosen based on previous results showing improved ductility of the corresponding pseudobinary nitride alloys with respect to their parent compounds. While commonly-used empirical criteria do not indicate enhanced ductility in the carbide alloys, calculated stress/strain curves along known slip systems, supported by electronic structure analyses, indicate ductile behavior for VMoC. As VMoC layers are sheared along the 11¯0 direction on {111} planes, the stress initially increases linearly up to a yield point where the accumulated stress is partially dissipated. With further increase in strain, the stress increases again until fracture occurs. A similar mechanical behavior is observed for the corresponding TM nitride VMoN, known to be a ductile ceramic material [1]. Thus, our results show that VMoC is a TM carbide alloy which may be both hard and ductile, i.e. tough. © 2017 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2017.10.047
  • 2018 • 175 Variational updates for thermomechanically coupled gradient-enhanced elastoplasticity — Implementation based on hyper-dual numbers
    Fohrmeister, V. and Bartels, A. and Mosler, J.
    Computer Methods in Applied Mechanics and Engineering 339 239-261 (2018)
    This paper deals with the implementation of thermomechanically coupled gradient-enhanced elastoplasticity at finite strains. The presented algorithmic formulation heavily relies on the variational structure of the considered initial boundary value problem. Consequently, such a variational structure is elaborated. While variational formulations are well-known in the case of isothermal plasticity theory, thermomechanically coupled gradient-enhanced plasticity theory has not been considered before. The resulting time-continuous variational principle allows the computation of all unknown variables jointly and naturally from the stationarity condition of an incremental potential. By discretization of this time-continuous potential in time, a discrete approximation is obtained which represents the foundation of the algorithmic formulation. As a matter of fact, stationarity of the respective potential again defines all unknown variables — now in a time-discrete fashion. Within this paper, the necessary condition associated with stationarity – a vanishing first gradient – is solved numerically by means of Newton's method. Hence, the first as well as the second derivatives of the incremental potential are required. They are computed by numerical differentiation based on hyper-dual numbers. By considering a perturbation with respect to hyper-dual numbers, the first as well as the second derivatives are computed in an exact manner without introducing any numerical errors. Although numerical differentiation based on hyper-dual numbers is numerically more extensive than real-valued perturbations, it is shown that the scalability of the resulting parallel finite element implementation is not dominated by this effect for sufficiently large problems. © 2018 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2018.04.047
  • 2018 • 174 Pendant capsule elastometry
    Hegemann, J. and Knoche, S. and Egger, S. and Kott, M. and Demand, S. and Unverfehrt, A. and Rehage, H. and Kierfeld, J.
    Journal of Colloid and Interface Science 513 549-565 (2018)
    We provide a C/C++ software for the shape analysis of deflated elastic capsules in a pendant capsule geometry, which is based on an elastic description of the capsule material as a quasi two-dimensional elastic membrane using shell theory. Pendant capsule elastometry provides a new in situ and non-contact method for interfacial rheology of elastic capsules that goes beyond determination of the Gibbs- or dilational modulus from area-dependent measurements of the surface tension using pendant drop tensiometry, which can only give a rough estimate of the elastic capsule properties as they are based on a purely liquid interface model. Given an elastic model of the capsule membrane, pendant capsule elastometry determines optimal elastic moduli by fitting numerically generated axisymmetric shapes optimally to an experimental image. For each digitized image of a deflated capsule elastic moduli can be determined, if another image of its undeformed reference shape is provided. Within this paper, we focus on nonlinear Hookean elasticity because of its low computational cost and its wide applicability, but also discuss and implement alternative constitutive laws. For Hookean elasticity, Young's surface modulus (or, alternatively, area compression modulus) and Poisson's ratio are determined; for Mooney-Rivlin elasticity, the Rivlin modulus and a dimensionless shape parameter are determined; for neo-Hookean elasticity, only the Rivlin modulus is determined, using a fixed dimensionless shape parameter. Comparing results for different models we find that nonlinear Hookean elasticity is adequate for most capsules. If series of images are available, these moduli can be evaluated as a function of the capsule volume to analyze hysteresis or aging effects depending on the deformation history or to detect viscoelastic effects for different volume change rates. An additional wrinkling wavelength measurement allows the user to determine the bending modulus, from which the layer thickness can be derived. We verify the method by analyzing several materials, compare the results to available rheological measurements, and review several applications. We make the software available under the GPL license at © 2017
    view abstractdoi: 10.1016/j.jcis.2017.11.048
  • 2018 • 173 Using algebraic multigrid in inexact BDDC domain decomposition methods
    Klawonn, A. and Lanser, M. and Rheinbach, O.
    Lecture Notes in Computational Science and Engineering 125 425-433 (2018)
    A highly scalable implementation of an inexact BDDC (Balancing Domain Decomposition by Constraints) method is presented, and scalability results for linear elasticity problems in two and three dimensions for up to 131,072 computational cores of the JUQUEEN BG/Q are shown. In this method, the inverse action of the partially coupled stiffness matrix is replaced by V-cycles of an AMG (algebraic multigrid) method. The use of classical AMG for systems of PDEs, based on a nodal coarsening approach is compared with a recent AMG method using an explicit interpolation of the rigid body motions (global matrix approach; GM). It is illustrated, that for systems of PDEs an appropriate AMG interpolation is mandatory for fast convergence, i.e., using exact interpolation of rigid body modes in elasticity. © 2018, Springer International Publishing AG, part of Springer Nature.
    view abstractdoi: 10.1007/978-3-319-93873-8_40
  • 2018 • 172 Martensite aging in 〈0 0 1〉 oriented Co49Ni21Ga30 single crystals in tension
    Lauhoff, C. and Krooß, P. and Langenkämper, D. and Somsen, C. and Eggeler, G. and Kireeva, I. and Chumlyakov, Y.I. and Niendorf, T.
    Functional Materials Letters 11 (2018)
    Co-Ni-Ga high-temperature shape memory alloys (HT-SMAs) are well-known candidate materials for damping applications at elevated temperatures. Recent studies showed that upon heat treatment in stress-induced martensite under compressive loads transformation temperatures can be increased significantly, qualifying Co-Ni-Ga for HT-actuation. The increase in transformation temperatures is related to a change in chemical order recently validated via neutron diffraction experiments. Since SMAs show distinct tension-compression asymmetry in terms of theoretical transformation strains and bearable stresses, understanding the impact of martensite aging in tension is crucial for future applications. The current results indicate that martensite aging in tension provides for a further improvement in functional properties. © 2018 The Author(s).
    view abstractdoi: 10.1142/S1793604718500248
  • 2018 • 171 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 abstractdoi: 10.1016/j.jnnfm.2018.03.015
  • 2018 • 170 Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy
    Münch, I. and Neff, P.
    Mathematics and Mechanics of Solids 23 3-42 (2018)
    For homogeneous higher-gradient elasticity models we discuss frame-indifference and isotropy requirements. To this end, we introduce the notions of local versus global SO(3)-invariance and identify frame-indifference (traditionally) with global left SO(3)-invariance and isotropy with global right SO(3)-invariance. For specific restricted representations, the energy may also be local left SO(3)-invariant as well as local right SO(3)-invariant. Then we turn to linear models and consider a consequence of frame-indifference together with isotropy in nonlinear elasticity and apply this joint invariance condition to some specific linear models. The interesting point is the appearance of finite rotations in transformations of a geometrically linear model. It is shown that when starting with a linear model defined already in the infinitesimal symmetric strain ε = sym Grad[u], the new invariance condition is equivalent to the isotropy of the linear formulation. Therefore, it may also be used in higher-gradient elasticity models for a simple check of isotropy and for extensions to anisotropy. In this respect we consider in more detail variational formulations of the linear indeterminate couple-stress model, a new variant of it with symmetric force stresses and general linear gradient elasticity. © The Author(s) 2016.
    view abstractdoi: 10.1177/1081286516666134
  • 2018 • 169 Reconstructing disturbance zones ahead of the tunnel face by elastic waveform inversion supported by a parametric level-set representation
    Nguyen, L.T. and Nestorović, T.
    Soil Dynamics and Earthquake Engineering 115 606-621 (2018)
    This work presents a flexible and effective methodology for locating and characterizing the disturbance zones ahead of the underground tunnel face by elastic full-waveform inversion (FWI) enhanced with the parametric level-set representation. By using the unscented Kalman filter as the inversion machinary, the inversion process is completely free from gradient calculations and able to provide uncertainty bounds of the estimated model. The conceptual methodology is verified through successful reconstructions of single- and multiple-disturbance objects in a simple 2D frequency domain model. In the synthetic tunnel reconnaissance tests, the special characteristics of the tunnel seismic waves in the time domain are described, and the results of SPECFEM2D simulation and a qualitative evaluation of the simulated tunnel seismic waveforms are shown. The computer model and its simulated tunnel seismic waveform data are eventually used to reconstruct the geological scenarios, whose disturbance is present in the form of a single object and multiple discontinuous objects, in a parsimonious and flexible manner. Although further validations using laboratory or in-situ measurements and the use of fully 3D model are needed to prove the practicality of this approach, the current results are encouraging and promising to apply FWI in tunneling practice as an advanced tool for looking ahead of the tunnel face. © 2018 Elsevier Ltd
    view abstractdoi: 10.1016/j.soildyn.2018.09.025
  • 2018 • 168 Synthetic DNA filaments: From design to applications
    Pfeifer, W. and Saccà, B.
    Biological Chemistry 399 773-785 (2018)
    Natural filaments, such as microtubules and actin filaments, are fundamental components of the cell. Despite their relatively simple linear structure, filaments play a number of crucial roles in living organisms, from scaffolding to cellular adhesion and motility. The mechanical properties of natural filaments mostly rely on the structural features of the component units and on the way they are connected together, thus providing an ideal molecular model for emulation purposes. In this review, we describe the progresses done in this field using DNA for the rational design of synthetic filamentous-like materials with tailored structural and physical characteristics. We firstly survey the strategies that have been adopted until now for the construction of individual DNA building components and their programmable self-assembly into linear oligomeric structures. We then describe the theoretical models of polymer elasticity applied to calculate the bending strength of DNA filaments, expressed in terms of persistence length. Finally, we report some of the most exciting examples of truly biomimetic DNA filaments, which are capable of mimicking not only the sophisticated structural features of their natural counterparts but also their responsiveness to external stimuli, thus resulting in active motion and growing networks between distant loci. © 2018 Walter de Gruyter GmbH, Berlin/Boston.
    view abstractdoi: 10.1515/hsz-2018-0110
  • 2018 • 167 Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures
    Schwarz, A. and Steeger, K. and Igelbüscher, M. and Schröder, J.
    International Journal for Numerical Methods in Engineering 115 1138-1153 (2018)
    We present geometrically nonlinear formulations based on a mixed least-squares finite element method. The L2-norm minimization of the residuals of the given first-order system of differential equations leads to a functional, which is a two-field formulation dependent on displacements and stresses. Based thereon, we discuss and investigate two mixed formulations. Both approaches make use of the fact that the stress symmetry condition is not fulfilled a priori due to the row-wise stress approximation with vector-valued functions belonging to a Raviart-Thomas space, which guarantees a conforming discretization of H(div). In general, the advantages of using the least-squares finite element method lie, for example, in an a posteriori error estimator without additional costs or in the fact that the choice of the polynomial interpolation order is not restricted by the Ladyzhenskaya-Babuška-Brezzi condition (inf-sup condition). We apply a hyperelastic material model with logarithmic deformation measures and investigate various benchmark problems, adaptive mesh refinement, computational costs, and accuracy. Copyright © 2018 John Wiley & Sons, Ltd.
    view abstractdoi: 10.1002/nme.5838
  • 2018 • 166 A simple and efficient Hellinger–Reissner type mixed finite element for nearly incompressible elasticity
    Viebahn, N. and Steeger, K. and Schröder, J.
    Computer Methods in Applied Mechanics and Engineering 340 278-295 (2018)
    The mixed finite element method is a promising approach in order to overcome locking phenomena of classical displacement based finite elements in the (nearly) incompressible regime for the elasticity problem. In this work we present a novel element based on Hellinger–Reissner's principle for linear elasticity. Essential for the construction of the element is a restriction of the solution space for the stresses, resulting in a formulation with displacements in H1(B) and stresses in H(div,B). The symmetry of the stresses is achieved in a weak sense, without the necessity of additional degrees of freedom. This formulation leads for the case of lowest order interpolation to a very efficient and robust finite element, even satisfying the numerical inf–sup test in two and three dimensions. © 2018 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2018.06.001
  • 2018 • 165 Strong Deformation of Ferrofluid-Filled Elastic Alginate Capsules in Inhomogenous Magnetic Fields
    Wischnewski, C. and Zwar, E. and Rehage, H. and Kierfeld, J.
    Langmuir 34 13534-13543 (2018)
    We present a new system based on alginate gels for the encapsulation of a ferrofluid drop, which allows us to create millimeter-sized elastic capsules that are highly deformable by inhomogeneous magnetic fields. We use a combination of experimental and theoretical work in order to characterize and quantify the deformation behavior of these ferrofluid-filled capsules. We introduce a novel method for the direct encapsulation of unpolar liquids by sodium alginate. By adding 1-hexanol to the unpolar liquid, we can dissolve sufficient amounts of CaCl2 in the resulting mixture for ionotropic gelation of sodium alginate. The addition of polar alcohol molecules allows us to encapsulate a ferrofluid as a single phase rather than an emulsion without impairing ferrofluid stability. This encapsulation method increases the amount of encapsulated magnetic nanoparticles resulting in high deformations of approximately 30% (in height-to-width ratio) in inhomogeneous magnetic field with magnetic field variations of 50 mT over the size of the capsule. This offers possible applications of capsules as actuators, switches, or valves in confined spaces like microfluidic devices. We determine both elastic moduli of the capsule shell, Young's modulus and Poisson's ratio, by employing two independent mechanical methods, spinning capsule measurements and capsule compression between parallel plates. We then show that the observed magnetic deformation can be fully understood from magnetic forces exerted by the ferrofluid on the capsule shell if the magnetic field distribution and magnetization properties of the ferrofluid are known. We perform a detailed analysis of the magnetic deformation by employing a theoretical model based on nonlinear elasticity theory. Using an iterative solution scheme that couples a finite element/boundary element method for the magnetic field calculation to the solution of the elastic shape equations, we achieve quantitative agreement between theory and experiment for deformed capsule shapes using the Young modulus from mechanical characterization and the surface Poisson ratio as a fit parameter. This detailed analysis confirms the results from mechanical characterization that the surface Poisson ratio of the alginate shell is close to unity, that is, deformations of the alginate shell are almost area conserving. © 2018 American Chemical Society.
    view abstractdoi: 10.1021/acs.langmuir.8b02357
  • 2017 • 164 Geometrically nonlinear cosserat elasticity in the plane: Applications to chirality
    Bahamonde, S. and Böhmer, C.G. and Neff, P.
    Journal of Mechanics of Materials and Structures 12 689-710 (2017)
    Modeling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become nonchiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically nonlinear Cosserat-type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our nonlinear approach. Plane wave solutions are briefly discussed within this model. © 2017 Mathematical Sciences Publishers.
    view abstractdoi: 10.2140/jomms.2017.12.689
  • 2017 • 163 Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics
    Barbagallo, G. and Madeo, A. and d'Agostino, M.V. and Abreu, R. and Ghiba, I.-D. and Neff, P.
    International Journal of Solids and Structures 120 7-30 (2017)
    In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual micromorphic theories, in our relaxed micromorphic model only classical elasticity-tensors with at most 21 independent components are studied together with rotational coupling tensors with at most 6 independent components. We show that in the limit case Lc → 0 (which corresponds to considering very large specimens of a microstructured metamaterial) the meso- and micro-coefficients of the relaxed model can be put in direct relation with the macroscopic stiffness of the medium via a fundamental homogenization formula. We also show that a similar homogenization formula is not possible in the case of the standard Mindlin-Eringen-format of the anisotropic micromorphic model. Our results allow us to forecast the successful short term application of the relaxed micromorphic model to the characterization of anisotropic mechanical metamaterials. © 2017 Elsevier Ltd
    view abstractdoi: 10.1016/j.ijsolstr.2017.01.030
  • 2017 • 162 A phenomenological model for the simulation of functional fatigue in shape memory alloy wires
    Bartel, T. and Osman, M. and Menzel, A.
    Meccanica 52 973-988 (2017)
    In this contribution, a modelling framework for functional fatigue in shape memory alloy wires is introduced. The approach is in particular designed to reproduce the effective response determined by experiments as published in, e.g., Eggeler et al. (Mat Sci Eng A 378:24–33, 2004). In this context, the decrease of transformation stresses, the increase of irreversible strains, and the occurrence of “characteristic points” with respect to the stress-strain relation is explicitly covered in the model formulation. The modelling approach for the phase transformations itself offers a large potential for further micromechanically well-motivated model extensions. © 2016, Springer Science+Business Media Dordrecht.
    view abstractdoi: 10.1007/s11012-016-0419-x
  • 2017 • 161 Inverse Ripening and Rearrangement of Precipitates under Chemomechanical Coupling
    Darvishi Kamachali, R. and Schwarze, C.
    Computational Materials Science 130 292-296 (2017)
    A coupling between diffusional and mechanical relaxation raised from composition-dependent elastic constants, and its effects on the evolution of precipitates with finite misfit strain are investigated. Inverse ripening has been observed where smaller precipitate grows at the expense of a larger one. This occurs due to fluxes generated under elastically-strained solute gradients around precipitates that scales with Rr6 where R and r are the precipitate radius and the radial coordinate, respectively. Both isotropic and anisotropic dependency of elastic constants on the composition were considered. The latter leads to the emergence of new patterns of elastic anisotropy and rearrangement of precipitates in the matrix. © 2017
    view abstractdoi: 10.1016/j.commatsci.2017.01.024
  • 2017 • 160 3D discrete dislocation dynamics study of creep behavior in Ni-base single crystal superalloys by a combined dislocation climb and vacancy diffusion model
    Gao, S. and Fivel, M. and Ma, A. and Hartmaier, A.
    Journal of the Mechanics and Physics of Solids 102 209-223 (2017)
    A three-dimensional (3D) discrete dislocation dynamics (DDD) creep model is developed to investigate creep behavior under uniaxial tensile stress along the crystallographic [001] direction in Ni-base single crystal superalloys, which takes explicitly account of dislocation glide, climb and vacancy diffusion, but neglects phase transformation like rafting of γ′ precipitates. The vacancy diffusion model takes internal stresses by dislocations and mismatch strains into account and it is coupled to the dislocation dynamics model in a numerically efficient way. This model is helpful for understanding the fundamental creep mechanisms in superalloys and clarifying the effects of dislocation glide and climb on creep deformation. In cases where the precipitate cutting rarely occurs, e.g. due to the high anti-phase boundary energy and the lack of superdislocations, the dislocation glide in the γ matrix and the dislocation climb along the γ/γ′ interface dominate plastic deformation. The simulation results show that a high temperature or a high stress both promote dislocation motion and multiplication, so as to cause a large creep strain. Dislocation climb accelerated by high temperature only produces a small plastic strain, but relaxes the hardening caused by the filling γ channels and lets dislocations further glide and multiply. The strongest variation of vacancy concentration occurs in the horizontal channels, where more mixed dislocations exit and tend to climb. The increasing internal stresses due to the increasing dislocation density are easily overcome by dislocations under a high external stress that leads to a long-term dislocation glide accompanied by multiplication. © 2017 Elsevier Ltd
    view abstractdoi: 10.1016/j.jmps.2017.02.010
  • 2017 • 159 A variant of the linear isotropic indeterminate couple-stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and orthogonal boundary conditions
    Ghiba, I.-D. and Neff, P. and Madeo, A. and Münch, I.
    Mathematics and Mechanics of Solids 22 1221-1266 (2017)
    In this paper we venture a new look at the linear isotropic indeterminate couple-stress model in the general framework of second-gradient elasticity and we propose a new alternative formulation which obeys Cauchy-Boltzmann's axiom of the symmetry of the force-stress tensor. For this model we prove the existence of solutions for the equilibrium problem. Relations with other gradient elastic theories and the possibility of switching from a fourth-order (gradient elastic) problem to a second-order micromorphic model are also discussed with the view of obtaining symmetric force-stress tensors. It is shown that the indeterminate couple-stress model can be written entirely with symmetric force-stress and symmetric couple-stress. The difference of the alternative models rests in specifying traction boundary conditions of either rotational type or strain type. If rotational-type boundary conditions are used in the integration by parts, the classical anti-symmetric nonlocal force-stress tensor formulation is obtained. Otherwise, the difference in both formulations is only a divergence-free second-order stress field such that the field equations are the same, but the traction boundary conditions are different. For these results we employ an integrability condition, connecting the infinitesimal continuum rotation and the infinitesimal continuum strain. Moreover, we provide the orthogonal boundary conditions for both models. © SAGE Publications.
    view abstractdoi: 10.1177/1081286515625535
  • 2017 • 158 Precipitation of T1 and θ' phase in Al-4Cu-1Li-0.25Mn during age hardening: Microstructural investigation and phase-field simulation
    Häusler, I. and Schwarze, C. and Bilal, M.U. and Ramirez, D.V. and Hetaba, W.d and Kamachali, R.D. and Skrotzki, B.
    Materials 10 (2017)
    Experimental and phase field studies of age hardening response of a high purity Al-4Cu-1Li-0.25Mn-alloy (mass %) during isothermal aging are conducted. In the experiments, two hardening phases are identified: the tetragonal θ' (Al2Cu) phase and the hexagonal T1 (Al2CuLi) phase. Both are plate shaped and of nm size. They are analyzed with respect to the development of their size, number density and volume fraction during aging by applying different analysis techniques in TEM in combination with quantitative microstructural analysis. 3D phase-field simulations of formation and growth of θ' phase are performed in which the full interfacial, chemical and elastic energy contributions are taken into account. 2D simulations of T1 phase are also investigated using multi-component diffusion without elasticity. This is a first step toward a complex phase-field study of T1 phase in the ternary alloy. The comparison between experimental and simulated data shows similar trends. The still unsaturated volume fraction indicates that the precipitates are in the growth stage and that the coarsening/ripening stage has not yet been reached. © 2017 by the authors.
    view abstractdoi: 10.3390/ma10020117
  • 2017 • 157 Parallel overlapping Schwarz with an energy-minimizing coarse space
    Heinlein, A. and Klawonn, A. and Rheinbach, O.
    Lecture Notes in Computational Science and Engineering 116 353-360 (2017)
    Parallel results obtained with a new implementation of an overlapping Schwarz method using an energy minimizing coarse space are presented. We consider structured and unstructured domain decompositions for scalar elliptic and linear elasticity model problems in two dimensions. In particular, strong and weak parallel scalability studies for up to 1024 processor cores are presented for both types of problems. Additionally, weak scalability results for a three-dimensional linear elasticity model problem using up to 4096 processor cores are discussed. Finally, an application from fully-coupled fluid-structure interaction using a nonlinear hyperelastic material model for the structure is shown. © Springer International Publishing AG 2017.
    view abstractdoi: 10.1007/978-3-319-52389-7_36
  • 2017 • 156 Characterization of hybrid joining techniques for FRP/Steel-structures under combined mechanical and thermal loading
    Hoepfner, M. and Becker, T. and Hülsbusch, D. and Walther, F.
    Key Engineering Materials 742 KEM 358-365 (2017)
    In order to optimize the design of vibrating screening machines and realize significant weight reductions, the use of hybrid structures is gaining importance. In this context, the joining of FRP and steel and their interactions due to different material properties were investigated. Therefore, quasi-static tests with combined mechanical and thermal loads were carried out. To realize the simultaneous application of physical measurement techniques, e.g. optical and acoustic measurements, and thermal loads, short-wave infrared emitter technique was used instead of thermal chambers. Thus, the mechanical characteristics and acoustic emissions could be determined and assessed. The results show different structural mechanisms of hybrid joining at room and elevated temperatures. The characteristics of failure modes, shear stresses, strains and acoustic emissions could be correlated to determine the damage developments and mechanisms. © 2017 Trans Tech Publications, Switzerland.
    view abstractdoi: 10.4028/
  • 2017 • 155 Modelling of grain boundary dynamics using amplitude equations
    Hüter, C. and Neugebauer, J. and Boussinot, G. and Svendsen, B. and Prahl, U. and Spatschek, R.
    Continuum Mechanics and Thermodynamics 29 895-911 (2017)
    We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity of the system and coincidence site lattices at grain boundaries is investigated. Within the amplitude equations framework, we recover predictions of the geometrical model by Cahn and Taylor for coupled grain boundary motion, and find both (Formula presented.) and (Formula presented.) coupling. No spontaneous transition between these modes occurs due to restrictions related to the rotational invariance of the amplitude equations. Grain rotation due to coupled motion is also in agreement with theoretical predictions. Whereas linear elasticity is correctly captured by the amplitude equations model, open questions remain for the case of nonlinear deformations. © 2015 Springer-Verlag Berlin Heidelberg
    view abstractdoi: 10.1007/s00161-015-0424-7
  • 2017 • 154 Optimized growth and reorientation of anisotropic material based on evolution equations
    Jantos, D.R. and Junker, P. and Hackl, K.
    Computational Mechanics 1-20 (2017)
    Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton’s principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously. © 2017 Springer-Verlag GmbH Germany
    view abstractdoi: 10.1007/s00466-017-1483-3
  • 2017 • 153 Micro-to-macro transition accounting for general imperfect interfaces
    Javili, A. and Steinmann, P. and Mosler, J.
    Computer Methods in Applied Mechanics and Engineering 317 274-317 (2017)
    The objective of this contribution is to establish a micro-to-macro transition framework to study the behavior of heterogeneous materials whereby the influence of interfaces at the microscale is taken into account. The term “interface” refers to a zero-thickness model that represents the finite thickness “interphase” between the constituents of the micro-structure. For geometrically equivalent samples, due to increasing area-to-volume ratio with decreasing size, interfaces demonstrate a more pronounced effect on the material response at small scales. A remarkable outcome is that including interfaces introduces a length-scale and our interface-enhanced computational homogenization captures a size effect in the material response even if linear prolongation conditions are considered. Furthermore, the interface model in this contribution is general imperfect in the sense that it allows for both jumps of the deformation as well as for the traction across the interface. Both cohesive zone model and interface elasticity theory can be derived as two limit cases of this general model. We establish a consistent computational homogenization scheme accounting for general imperfect interfaces. Suitable boundary conditions to guarantee meaningful averages are derived. Clearly, this general framework reduces to classical computational homogenization if the effect of interfaces is ignored. Finally, the proposed theory is elucidated via a series of numerical examples. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2016.12.025
  • 2017 • 152 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 abstractdoi: 10.1016/j.compstruc.2017.06.015
  • 2017 • 151 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 abstractdoi: 10.1142/S1758825117500697
  • 2017 • 150 Effect of temperature and texture on the reorientation of martensite variants in NiTi shape memory alloys
    Laplanche, G. and Birk, T. and Schneider, S. and Frenzel, J. and Eggeler, G.
    Acta Materialia 127 143-152 (2017)
    Martensitic Ni50Ti50 wires and sheets with different textures were tensile tested in the temperature range between −100 °C and 60 °C. The effect of texture and temperature on reorientation of martensite variants was investigated. After deformation, all material states were heated into the austenite regime to study their shape memory behavior. During room temperature tensile testing, in-situ digital image correlation revealed that the reorientation of martensite variants is associated with the nucleation and propagation of a macroscopic Lüders band. A comparison between the mechanical data obtained for wire and sheet specimens revealed a strong effect of texture. The plateau stresses of sheets were found to be 25–33% larger and their recoverable strains were 30% lower than for wires. However, the product of plateau stress and recoverable strain, which represents the external work per unit volume required for martensite variants reorientation does not depend on texture. The tensile tests performed at different temperatures revealed that in the temperature range considered the recoverable strain does not depend significantly on temperature. In contrast, the plateau stress as well as the external work required to reorient martensite decrease with increasing testing temperature. We use a thermodynamic approach involving the elastic strain energy associated with the growth of reoriented martensite variants to rationalize these temperature dependencies. © 2017 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2017.01.023
  • 2017 • 149 Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations
    Mihai, L.A. and Neff, P.
    International Journal of Non-Linear Mechanics 89 93-100 (2017)
    We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank-one convex elastic energy. © 2016 The Authors
    view abstractdoi: 10.1016/j.ijnonlinmec.2016.12.003
  • 2017 • 148 Correlative plasma-surface model for metastable Cr-Al-N: Frenkel pair formation and influence of the stress state on the elastic properties
    Music, D. and Banko, L. and Ruess, H. and Engels, M. and Hecimovic, A. and Grochla, D. and Rogalla, D. and Brögelmann, T. and Ludwig, Al. and Von Keudell, A. and Bobzin, K. and Schneider, J.M.
    Journal of Applied Physics 121 (2017)
    Correlatively employing density functional theory and experiments congregated around high power pulsed magnetron sputtering, a plasma-surface model for metastable Cr0.8Al0.2N (space group Fm 3 m) is developed. This plasma-surface model relates plasma energetics with film composition, crystal structure, mass density, stress state, and elastic properties. It is predicted that N Frenkel pairs form during Cr0.8Al0.2N growth due to high-energy ion irradiation, yielding a mass density of 5.69 g cm-3 at room temperature and Young's modulus of 358-130 GPa in the temperature range of 50-700 K for the stress-free state and about 150 GPa larger values for the compressive stress of 4 GPa. Our measurements are consistent with the quantum mechanical predictions within 5% for the mass density and 3% for Young's modulus. The hypothesis of a stress-induced Young's modulus change may at least in part explain the spread in the reported elasticity data ranging from 250 to 420 GPa. © 2017 Author(s).
    view abstractdoi: 10.1063/1.4985172
  • 2017 • 147 Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition
    Neff, P. and Mihai, L.A.
    Journal of Elasticity 127 309-315 (2017)
    In this note, we show that the Cauchy stress tensor (Formula presented.) in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that (Formula presented.) implies (Formula presented.) under strict rank-one convexity. As a consequence of this seemingly unnoticed observation, it follows that rank-one convexity and a homogeneous Cauchy stress imply that the left Cauchy-Green strain is homogeneous, as is shown in Mihai and Neff (Int. J. Non-Linear Mech., 2016, to appear). © 2016 Springer Science+Business Media Dordrecht
    view abstractdoi: 10.1007/s10659-016-9609-y
  • 2017 • 146 Real wave propagation in the isotropic-relaxed micromorphic model
    Neff, P. and Madeo, A. and Barbagallo, G. and D'Agostino, M.V. and Abreu, R. and Ghiba, I.-D.
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2017)
    For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity. © 2017 The Author(s) Published by the Royal Society. All rights reserved.
    view abstractdoi: 10.1098/rspa.2016.0790
  • 2017 • 145 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 abstractdoi: 10.1016/j.ijsolstr.2017.02.010
  • 2017 • 144 A Prange–Hellinger–Reissner type finite element formulation for small strain elasto-plasticity
    Schröder, J. and Igelbüscher, M. and Schwarz, A. and Starke, G.
    Computer Methods in Applied Mechanics and Engineering 317 400-418 (2017)
    In this contribution we propose a mixed variational formulation of the Prange–Hellinger–Reissner type for elasto-plasticity at small strains. Here, the displacements and the stresses are interpolated independently, which are balanced within the variational functional by the relation of the elastic strains and the partial derivative of the complementary stored energy with respect to the stresses. For the elasto-plastic material behavior a von Mises yield criterion is considered, where we restrict ourselves w.l.o.g. to linear isotropic hardening. In the proposed formulation we enforce the constraints arising from plasticity point-wise in contrast to the element-wise realization of the plastic return mapping algorithm suggested in Simo et al. (1989). The performance of the new formulation is demonstrated by the analysis of several benchmark problems. Here, we compare the point-wise treatment of elasto-plasticity with the original element-wise formulation of Simo et al. (1989). Furthermore, we derive an algorithmic consistent treatment for plane stress as well as for plane strain condition. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2016.12.005
  • 2017 • 143 On the Convexity of Nonlinear Elastic Energies in the Right Cauchy-Green Tensor
    Yang Gao, D. and Neff, P. and Roventa, I. and Thiel, C.
    Journal of Elasticity 127 303-308 (2017)
    We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic energy functional. This criterion is applicable to energies W(F) = Wˆ (FTF) = Wˆ (C) which are convex with respect to the right Cauchy-Green tensor C= FTF, where F denotes the gradient of deformation. Examples of such energies exhibiting a blow up for det F→ 0 are given. © 2016, Springer Science+Business Media Dordrecht.
    view abstractdoi: 10.1007/s10659-016-9601-6
  • 2016 • 142 Scalability of classical algebraic multigrid for elasticity to half a million parallel tasks
    Baker, A.H. and Klawonn, A. and Kolev, T. and Lanser, M. and Rheinbach, O. and Yang, U.M.
    Lecture Notes in Computational Science and Engineering 113 113-140 (2016)
    The parallel performance of several classical AlgebraicMultigrid (AMG) methods applied to linear elasticity problems is investigated. These methods include standard AMG approaches for systems of partial differential equations such as the unknown and hybrid approaches, as well as the more recent globalmatrix (GM) and local neighborhood (LN) approaches, which incorporate rigid body modes (RBMs) into the AMG interpolation operator. Numerical experiments are presented for both two- and three-dimensional elasticity problems on up to 131,072 cores (and 262,144 MPI processes) on the Vulcan supercomputer (LLNL, USA) and up to 262,144 cores (and 524,288 MPI processes) on the JUQUEEN supercomputer (JSC, Jülich, Germany). It is demonstrated that incorporating all RBMs into the interpolation leads generally to faster convergence and improved scalability. © Springer International Publishing Switzerland 2016.
    view abstractdoi: 10.1007/978-3-319-40528-5_6
  • 2016 • 141 Numerical modeling of fluid–structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains
    Balzani, D. and Deparis, S. and Fausten, S. and Forti, D. and Heinlein, A. and Klawonn, A. and Quarteroni, A. and Rheinbach, O. and Schröder, J.
    International Journal for Numerical Methods in Biomedical Engineering 32 (2016)
    The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid–structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid–structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid–structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple – but nonsymmetric – curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid–structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid–structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    view abstractdoi: 10.1002/cnm.2756
  • 2016 • 140 One-way and fully-coupled FE2 methods for heterogeneous elasticity and plasticity problems: Parallel scalability and an application to thermo-elastoplasticity of dual-phase steels
    Balzani, D. and Gandhi, A. and Klawonn, A. and Lanser, M. and Rheinbach, O. and Schröder, J.
    Lecture Notes in Computational Science and Engineering 113 91-112 (2016)
    In this paper, aspects of the two-scale simulation of dual-phase steels are considered. First, we present two-scale simulations applying a top-down oneway coupling to a full thermo-elastoplastic model in order to study the emerging temperature field. We find that, for our purposes, the consideration of thermomechanics at the microscale is not necessary. Second, we present highly parallel fully-coupled two-scale FE2 simulations, now neglecting temperature, using up to 458;752 cores of the JUQUEEN supercomputer at Forschungszentrum Jülich. The strong and weak parallel scalability results obtained for heterogeneous nonlinear hyperelasticity exemplify the massively parallel potential of the FE2 multiscale method. © Springer International Publishing Switzerland 2016.
    view abstractdoi: 10.1007/978-3-319-40528-5_5
  • 2016 • 139 Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity
    Böhmer, C.G. and Neff, P. and Seymenoğlu, B.
    Wave Motion 60 158-165 (2016)
    The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. We present the geometrically nonlinear theory taking into account all possible interaction terms between the elastic and microelastic structures. This is achieved by considering the irreducible pieces of the deformation gradient and of the dislocation curvature tensor. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small. By choosing a particular ansatz we are able to reduce the system of equations to a sine-Gordon type equation which is known to have soliton solutions. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.wavemoti.2015.09.006
  • 2016 • 138 Optimal control of static elastoplasticity in primal formulation
    De Los Reyes, J.C. and Herzog, R. and Meyer, C.
    SIAM Journal on Control and Optimization 54 3016-3039 (2016)
    An optimal control problem of static plasticity with linear kinematic hardening and von Mises yield condition is studied. The problem is treated in its primal formulation, where the state system is a variational inequality of the second kind. First-order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by Huber-type smoothing, and a subsequent limit analysis. The equivalence of the optimality conditions with the C-stationarity system for the equivalent dual formulation of the problem is proved. Numerical experiments are presented, which demonstrate the viability of the Huber-type smoothing approach. © 2016 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/130920861
  • 2016 • 137 Superelasticity and Tunable Thermal Expansion across a Wide Temperature Range
    Hao, Y. L. and Wang, H. L. and Li, T. and Cairney, J. M. and Ceguerra, A. V. and Wang, Y. D. and Wang, Y. and Wang, D. and Obbard, E. G. and Li, S. J. and Yang, R.
    Journal of Materials Science & Technology 32 705--709 (2016)
    Materials that undergo a reversible change of crystal structure through martensitic transformation (MT) possess unusual functionalities including shape memory, superelasticity, and low/negative thermal expansion. These properties have many advanced applications, such as actuators, sensors, and energy conversion, but are limited typically in a narrow temperature range of tens of Kelvin. Here we report that, by creating a nano-scale concentration modulation via phase separation, the MT can be rendered continuous by an in-situ elastic confinement mechanism. Through a model titanium alloy, we demonstrate that the elastically confined continuous MT has unprecedented properties, such as superelasticity from below 4.2 K to 500 K, fully tunable and stable thermal expansion, from positive, through zero, to negative, from below 4.2 K to 573 K, and high strength-to-modulus ratio across a wide temperature range. The elastic tuning on the MT, together with a significant extension of the crystal stability limit, provides new opportunities to explore advanced materials. Copyright (C) 2016, The editorial office of Journal of Materials Science & Technology. Published by Elsevier Limited.
    view abstractdoi: 10.1016/j.jmst.2016.06.017
  • 2016 • 136 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 abstractdoi: 10.1137/15M1049610
  • 2016 • 135 Crystal plasticity study of monocrystalline stochastic honeycombs under in-plane compression
    Ma, D. and Eisenlohr, P. and Epler, E. and Volkert, C.A. and Shanthraj, P. and Diehl, M. and Roters, F. and Raabe, D.
    Acta Materialia 103 796-808 (2016)
    We present a study on the plastic deformation of single crystalline stochastic honeycombs under in-plane compression using a crystal plasticity constitutive description for face-centered cubic (fcc) materials, focusing on the very early stage of plastic deformation, and identifying the interplay between the crystallographic orientation and the cellular structure during plastic deformation. We observe that despite the stochastic structure, surprisingly, the slip system activations in the honeycombs are almost identical to their corresponding bulk single crystals at the early stage of the plastic deformation. On the other hand, however, the yield stresses of the honeycombs are nearly independent of their crystallographic orientations. Similar mechanical response is found in compression testing of nanoporous gold micro-pillars aligned with various crystallographic orientations. The macroscopic stress tensors of the honeycombs show the same anisotropy as their respective bulk single crystals. Locally, however, there is an appreciable fluctuation in the local stresses, which are even larger than for polycrystals. This explains why the Taylor/Schmid factor associated with the crystallographic orientation is less useful to estimate the yield stresses of the honeycombs than the bulk single crystals and polycrystals, and why the plastic deformation occurs at smaller strains in the honeycombs than their corresponding bulk single crystals. Besides these findings, the observations of the crystallographic reorientation suggest that conventional orientation analysis tools, such as inverse pole figure and related tools, would in general fail to study the plastic deformation mechanism of monocrystalline cellular materials. © 2015 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2015.11.016
  • 2016 • 134 First evidence of non-locality in real band-gap metamaterials: Determining parameters in the relaxed micromorphic model
    Madeo, A. and Barbagallo, G. and D'Agostino, M.V. and Placidi, L. and Neff, P.
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472 (2016)
    In this paper, we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of the relaxed micromorphic model by superimposing the experimentally based profile of the reflection coefficient (plotted as function of the wave-frequency) with the analogous profile obtained via numerical simulations. We determine five out of six constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulus μc, still remains undetermined, since experiments on transverse incident waves are not yet available. A fundamental result of this paper is the estimate of the non-locality intrinsically associated with the underlying microstructure of the metamaterial. We show that the characteristic length Lc measuring the non-locality of the phononic crystal is of the order of 1/3 of the diameter of its fluidfilled holes. © 2016 The Author(s).
    view abstractdoi: 10.1098/rspa.2016.0169
  • 2016 • 133 Investigation of the self-healing sliding wear characteristics of NiTi-based PVD coatings on tool steel
    Momeni, S. and Tillmann, W.
    Wear 368-369 53-59 (2016)
    Excellent damping capacity and superelasticity of the bulk NiTi shape memory alloy (SMA) makes it a suitable material of choice for tools in machining process as well as tribological systems. Although thin film of NiTi SMA has a same damping capacity as NiTi bulk alloys, it has a poor mechanical properties and undesirable tribological performance. This study aims at eliminating these application limitations for NiTi thin films. In order to achieve this goal, NiTi thin films were magnetron sputtered as an interlayer between reactively sputtered hard TiCN coatings and hot work tool steel substrates. The microstructure, composition, crystallographic phases, mechanical and tribological properties of the deposited thin films were analyzed by using field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), nanoindentation, ball-on-disc, scratch test, and three dimensional (3D) optical microscopy. It was found that under a specific coating architecture, the superelasticity of NiTi inter-layer can be combined with high hardness and wear resistance of TiCN protective layers. The obtained results revealed that the thickness of NiTi interlayers is an important factor controlling mechanical and tribological performance of bilayer composite coating systems. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.wear.2016.08.004
  • 2016 • 132 The Exponentiated Hencky Strain Energy in Modeling Tire Derived Material for Moderately Large Deformations
    Montella, G. and Govindjee, S. and Neff, P.
    Journal of Engineering Materials and Technology, Transactions of the ASME 138 (2016)
    This work presents a hyperviscoelastic model, based on the Hencky-logarithmic strain tensor, to model the response of a tire derived material (TDM) undergoing moderately large deformations. The TDM is a composite made by cold forging a mix of rubber fibers and grains, obtained by grinding scrap tires, and polyurethane binder. The mechanical properties are highly influenced by the presence of voids associated with the granular composition and low tensile strength due to the weak connection at the grain-matrix interface. For these reasons, TDM use is restricted to applications involving a limited range of deformations. Experimental tests show that a central feature of the response is connected to highly nonlinear behavior of the material under volumetric deformation which conventional hyperelastic models fail in predicting. The strain energy function presented here is a variant of the exponentiated Hencky strain energy, which for moderate strains is as good as the quadratic Hencky model and in the large strain region improves several important features from a mathematical point of view. The proposed form of the exponentiated Hencky energy possesses a set of parameters uniquely determined in the infinitesimal strain regime and an orthogonal set of parameters to determine the nonlinear response. The hyperelastic model is additionally incorporated in a finite deformation viscoelasticity framework that accounts for the two main dissipation mechanisms in TDMs, one at the microscale level and one at the macroscale level. The new model is capable of predicting different deformation modes in a certain range of frequency and amplitude with a unique set of parameters with most of them having a clear physical meaning. This translates into an important advantage with respect to overcoming the difficulties related to finding a unique set of optimal material parameters as are usually encountered fitting the polynomial forms of strain energies. Moreover, by comparing the predictions from the proposed constitutive model with experimental data we conclude that the new constitutive model gives accurate prediction. © 2016 by ASME.
    view abstractdoi: 10.1115/1.4032749
  • 2016 • 131 On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
    Neff, P. and Münch, I. and Ghiba, I.-D. and Madeo, A.
    International Journal of Solids and Structures 81 233-243 (2016)
    In a series of papers which are either published [Hadjesfandiari, A., Dargush, G. F., 2011a. Couple stress theory for solids. Int. J. Solids Struct. 48 (18), 2496-2510; Hadjesfandiari, A., Dargush, G. F., 2013. Fundamental solutions for isotropic size-dependent couple stress elasticity. Int. J. Solids Struct. 50 (9), 1253-1265.] or available as preprints [Hadjesfandiari, A., Dargush, G. F., 2010. Polar continuum mechanics. Preprint arXiv:1009.3252; Hadjesfandiari, A. R., Dargush, G. F., 2011b. Couple stress theory for solids. Int. J. Solids Struct. 48, 2496-2510; Hadjesfandiari, A. R., 2013. On the skew-symmetric character of the couple-stress tensor. Preprint arXiv:1303.3569; Hadjesfandiari, A. R., Dargush, G. F., 2015a. Evolution of generalized couple-stress continuum theories: a critical analysis. Preprint arXiv:1501.03112; Hadjesfandiari, A. R., Dargush, G. F., 2015b. Foundations of consistent couple stress theory. Preprint arXiv:1509.06299] Hadjesfandiari and Dargush have reconsidered the linear indeterminate couple stress model. They are postulating a certain physically plausible split in the virtual work principle. Based on this postulate they claim that the second-order couple stress tensor must always be skew-symmetric. Since they do not consider that the set of boundary conditions intervening in the virtual work principle is not unique, their statement is not tenable and leads to some misunderstandings in the indeterminate couple stress model. This is shown by specifying their development to the isotropic case. However, their choice of constitutive parameters is mathematically possible and we show that it still yields a well-posed boundary value problem. © 2015 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.ijsolstr.2015.11.028
  • 2016 • 130 Rediscovering GF Becker's early axiomatic deduction of a multiaxial nonlinear stress-strain relation based on logarithmic strain
    Neff, P. and Münch, I. and Martin, R.
    Mathematics and Mechanics of Solids 21 856-911 (2016)
    We discuss a completely forgotten work of the geologist GF Becker on the ideal isotropic nonlinear stress-strain function (Am J Sci 1893; 46: 337-356). Due to the fact that the mathematical modelling of elastic deformations has evolved greatly since the original publication we give a modern reinterpretation of Becker's work, combining his approach with the current framework of the theory of nonlinear elasticity. Interestingly, Becker introduces a multiaxial constitutive law incorporating the logarithmic strain tensor, more than 35 years before the quadratic Hencky strain energy was introduced by Heinrich Hencky in 1929. Becker's deduction is purely axiomatic in nature. He considers the finite strain response to applied shear stresses and spherical stresses, formulated in terms of the principal strains and stresses, and postulates a principle of superposition for principal forces which leads, in a straightforward way, to a unique invertible constitutive relation, which in today's notation can be written as TBiot= 2 G · dev3 log (U) + K · tr [ log (U) ] · 11 = 2 G · log (U) + Λ · tr [ log (U) ] · 11, where TBiot is the Biot stress tensor, log(U) is the principal matrix logarithm of the right Biot stretch tensor U = √FTF, tr X = ∑i=13 Xi,i denotes the trace and dev3 X = X - (1/3) tr (X) · 11 denotes the deviatoric part of a matrix X ∈ ℝ3 × 3. Here, G is the shear modulus and K is the bulk modulus. For Poisson's number ν = 0 the formulation is hyperelastic and the corresponding strain energy WBeckerν= 0 (U) = 2 G [ < U, log (U) - 11 &gt; + 3 ] has the form of the maximum entropy function. © The Author(s) 2016.
    view abstractdoi: 10.1177/1081286514542296
  • 2016 • 129 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 abstractdoi: 10.1007/s10237-015-0685-x
  • 2016 • 128 A novel mixed finite element for finite anisotropic elasticity; the SKA-element Simplified Kinematics for Anisotropy
    Schröder, J. and Viebahn, N. and Balzani, D. and Wriggers, P.
    Computer Methods in Applied Mechanics and Engineering 310 475-494 (2016)
    A variety of numerical approximation schemes for boundary value problems suffer from so-called locking-phenomena. It is well known that in such cases several finite element formulations exhibit poor convergence rates in the basic variables. A serious locking phenomenon can be observed in the case of anisotropic elasticity, due to high stiffness in preferred directions. The main goal of this paper is to overcome this locking problem in anisotropic hyperelasticity by introducing a novel mixed variational framework. Therefore we split the strain energy into two main parts, an isotropic and an anisotropic part. For the isotropic part we can apply different well-established approximation schemes and for the anisotropic part we apply a constant approximation of the deformation gradient or the right Cauchy–Green tensor. This additional constraint is attached to the strain energy function by a second-order tensorial Lagrange-multiplier, governed by a Simplified Kinematic for the Anisotropic part. As a matter of fact, for the tested boundary value problems the SKA-element based on quadratic ansatz functions for the displacements, performs excellent and behaves more robust than competitive formulations. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2016.06.029
  • 2016 • 127 Atomistically informed extended Gibbs energy description for phase-field simulation of tempering of martensitic steel
    Shchyglo, O. and Hammerschmidt, T. and Čak, M. and Drautz, R. and Steinbach, I.
    Materials 9 (2016)
    In this study we propose a unified multi-scale chemo-mechanical description of the BCT (Body-Centered Tetragonal) to BCC (Body-Centered Cubic) order-disorder transition in martensitic steel by adding the mechanical degrees of freedom to the standard CALPHAD (CALculation of PHAse Diagrams) type Gibbs energy description. The model takes into account external strain, the effect of carbon composition on the lattice parameter and elastic moduli. The carbon composition effect on the lattice parameters and elastic constants is described by a sublattice model with properties obtained from DFT (Density Functional Theory) calculations; the temperature dependence of the elasticity parameters is estimated from available experimental data. This formalism is crucial for studying the kinetics of martensite tempering in realistic microstructures. The obtained extended Gibbs energy description opens the way to phase-field simulations of tempering of martensitic steel comprising microstructure evolution, carbon diffusion and lattice symmetry change due to the ordering/disordering of carbon atoms under multiaxial load. © 2016 by the authors.
    view abstractdoi: 10.3390/ma9080669
  • 2016 • 126 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 abstractdoi: 10.1007/978-3-319-39022-2_1
  • 2016 • 125 A cascade continuum micromechanics model for the effective elastic properties of porous materials
    Timothy, J.J. and Meschke, G.
    International Journal of Solids and Structures 83 1-12 (2016)
    The elastic properties of porous materials with a disordered pore structure are estimated using the mean-field Eshelby homogenization scheme together with the principle of recurrence to generate a cascade of effective microstructures as a function of the porosity and the cascade level n. Starting with the Hashin-Shtrikman upper bound for porous materials, the proposed cascade micromechanics model generates a hierarchy of micro-structures which evolve from an initial configuration of a porous material with spherical pores embedded within an elastic solid phase consistent with the Mori-Tanaka matrix inclusion morphology to a porous material characterized by a hierarchic distribution of spherical elastic grains. The model is explicit and allows for an easy computational implementation. It predicts physically consistent threshold porosities, characteristic for the specific morphology of the porous material under consideration, beyond which the material loses its stiffness. The validity of the cascade micromechanics model is evaluated against experimental data for various materials ranging from foam to ceramics with different pore structures. © 2015 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijsolstr.2015.12.010
  • 2016 • 124 Cyclic degradation in bamboo-like Fe-Mn-Al-Ni shape memory alloys - The role of grain orientation
    Vollmer, M. and Krooß, P. and Kriegel, M.J. and Klemm, V. and Somsen, C. and Ozcan, H. and Karaman, I. and Weidner, A. and Rafaja, D. and Biermann, H. and Niendorf, T.
    Scripta Materialia 114 156-160 (2016)
    In the present study the cyclic deformation behavior within differently oriented grains in Fe-34.8Mn-13.5Al-7.4Ni (at.%) shape memory polycrystals featuring a bamboo-like structure was investigated. In cyclic tensile tests up to 50 cycles, the degree of degradation in pseudoelasticity was evaluated and contributing elementary mechanisms are discussed. The results reveal rapid cyclic degradation in the bamboo-like samples. The unexpected stabilization of parent phase in reverse transformed areas and the proceeding activation of new martensite variants in subsequent cycles were found to be the prevailing degradation mechanisms. Dislocation activity is found to be the most detrimental factor. © 2015 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.scriptamat.2015.12.007
  • 2015 • 123 Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening
    Betz, T. and Meyer, C.
    ESAIM - Control, Optimisation and Calculus of Variations 21 271-300 (2015)
    The paper is concerned with the optimal control of static elastoplasticity with linear kinematic hardening. This leads to an optimal control problem governed by an elliptic variational inequality (VI) of first kind in mixed form. Based on Lp-regularity results for the state equation, it is shown that the control-to-state operator is Bouligand differentiable. This enables to establish second-order sufficient optimality conditions by means of a Taylor expansion of a particularly chosen Lagrange function. © EDP Sciences, SMAI 2014.
    view abstractdoi: 10.1051/cocv/2014024
  • 2015 • 122 Shapes of sedimenting soft elastic capsules in a viscous fluid
    Boltz, H.-H. and Kierfeld, J.
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 92 (2015)
    Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid at low Reynolds numbers. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical rest shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force. This type of instability should be observable for generic synthetic capsules. All shape bifurcations can be resolved in the force-velocity relation of sedimenting capsules, where up to three capsule shapes with different velocities can occur for the same driving force. All three types of possible axisymmetric stationary shapes are stable with respect to rotation during sedimentation. Additionally, we study capsules pushed or pulled by a point force, where we always find capsule shapes to transform smoothly without bifurcations. © 2015 American Physical Society.
    view abstractdoi: 10.1103/PhysRevE.92.033003
  • 2015 • 121 Numerical simulation of polymer film stretching
    Damanik, H. and Ouazzi, A. and Turek, S.
    Lecture Notes in Computational Science and Engineering 103 709-716 (2015)
    We present numerical simulations of a film stretching process between two rolls of different temperature and rotational velocity. Film stretching is part of the industrial production of sheets of plastics which takes place after the extrusion process. The goal of the stretching of the sheet material is to rearrange the orientation of the polymer chains. Thus, the final products have more smooth surfaces and homogeneous properties. In numerical simulation, the plastic sheet is modelled geometrically as a membrane and rheologically as a polymer melt. The thickness of the membrane is not assumed to be constant but rather depends on the rheology of the polymer and the heat transfer. The rheology of the sheet material is governed by a viscoelastic fluid and is coupled to the flow model. An A-stable time integrator is applied to the systems in which the continuous spatial system is discretized within the FEM framework at each time step. The resulting discrete systems are solved via Newton-multigrid techniques. Moreover, a level set method is used to capture the free surface. We obtain similar results for test configurations with available results from literature and present “neck-in” as well as “dog-bone” effects. © Springer International Publishing Switzerland 2015.
    view abstractdoi: 10.1007/978-3-319-10705-9_70
  • 2015 • 120 Influence of microstructure on macroscopic elastic properties and thermal expansion of nickel-base superalloys ERBO/1 and LEK94
    Demtröder, K. and Eggeler, G. and Schreuer, J.
    Materialwissenschaft und Werkstofftechnik 46 563-576 (2015)
    In the present work the thermal expansion and the elastic properties of second generation nickel-base superalloy single crystals ERBO/1 (CMSX-4 variation) and LEK94 have been studied between about 100 K and 1273 K using dilatometry and resonant ultrasound spectroscopy, respectively. Inhomogeneity related to the large scale microstructure of the samples can act as a potential source of scatter for the propagation of ultrasonic waves. This can be overcome by choosing samples of sufficient size so that they appear as homogeneous media at the scale of the elastic wave length. Our final results are in good agreement with data reported in literature for similar alloy systems. In particular, the elastic material properties are only weekly affected by moderate variations in chemical composition and microstructure. Taking into account literature data for other superalloys like CMSX-4, we derive general polynomial functions which describe the temperature dependence of the elastic moduli E<inf>〈100〉</inf>, E<inf>〈110〉</inf> and E<inf>〈111〉</inf> in nickel-base superalloys to within about ±3%. It was also observed that the alloys ERBO/1 and LEK94 show weak but significant anomalies in both thermal expansion and temperature coefficients of elastic constants above about 900 K. These anomalies are probably related to the gradual dissolution of the γ′-precipitates at higher temperatures. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/mawe.201500406
  • 2015 • 119 Synergy of atom-probe structural data and quantum-mechanical calculations in a theory-guided design of extreme-stiffness superlattices containing metastable phases
    Friák, M. and Tytko, D. and Holec, D. and Choi, P.-P. and Eisenlohr, P. and Raabe, D. and Neugebauer, J.
    New Journal of Physics 17 (2015)
    A theory-guided materials design of nano-scaled superlattices containing metastable phases is critically important for future development of advanced lamellar composites with application-dictated stiffness and hardness. Our study combining theoretical and experimental methods exemplifies the strength of this approach for the case of the elastic properties of AlN/CrN superlattices that were deposited by reactive radio-frequency magnetron sputtering with a bilayer period of 4 nm. Importantly, CrN stabilizes AlN in a metastable B1 (rock salt) cubic phase only in the form of a layer that is very thin, up to a few nanometers. Due to the fact that B1-AlN crystals do not exist as bulk materials, experimental data for this phase are not available. Therefore, quantum-mechanical calculations have been applied to simulate an AlN/CrN superlattice with a similar bilayer period. The ab initio predicted Young's modulus (428 GPa) along the [001] direction is in excellent agreement with measured nano-indentation values (408 32 GPa). Aiming at a future rapid high-throughput materials design of superlattices, we have also tested predictions obtained within linear-elasticity continuum modeling using elastic properties of B1-CrN and B1-AlN phases as input. Using single-crystal elastic constants from ab initio calculations for both phases, we demonstrate the reliability of this approach to design nano-patterned coherent superlattices with unprecedented and potentially superior properties. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
    view abstractdoi: 10.1088/1367-2630/17/9/093004
  • 2015 • 118 An ellipticity domain for the distortional Henckylogarithmic strain energy
    Ghiba, I.-D. and Neff, P. and Martin, R.J.
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2015)
    We describe ellipticity domains for the isochoric elastic energy F →||devn logU||2 = ||log √ FTF (det F)1/n||2 = 1/4||log C (detC)1/n || 2 for n=2, 3, where C=FTF for F ε GL+(n). Here, devn logU =logU - (1/n) tr(logU) 1 is the deviatoric part of the logarithmic strain tensor logU. For n=2, we identify the maximal ellipticity domain, whereas for n=3, we show that the energy is Legendre- Hadamard (LH) elliptic in the set E3(Wiso H , LH,U, 23 ) := U PSym(3)| dev3 logU2 ≤ 23 , which is similar to the von Mises-Huber-Hencky maximum distortion strain energy criterion. Our results complement the characterization of ellipticity domains for the quadratic Hencky energy WH(F)=μ dev3 logU2 + (k/2)[tr(logU)]2, U = √ FTF with μ&gt;0 andk &gt; 23 μ, previously obtained by Bruhns et al.
    view abstractdoi: 10.1098/rspa.2015.0510
  • 2015 • 117 The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics
    Ghiba, I.-D. and Neff, P. and Madeo, A. and Placidi, L. and Rosi, G.
    Mathematics and Mechanics of Solids 20 1171-1197 (2015)
    We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. Another interesting feature concerns the prescription of boundary values for the micro-distortion field: only tangential traces may be determined which are weaker than the usual strong anchoring boundary condition. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch, and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. © The Author(s) 2014.
    view abstractdoi: 10.1177/1081286513516972
  • 2015 • 116 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 abstractdoi: 10.1007/978-3-319-10705-9_56
  • 2015 • 115 Toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations
    Klawonn, A. and Lanser, M. and Rheinbach, O.
    SIAM Journal on Scientific Computing 37 C667-C696 (2015)
    The solution of nonlinear problems, e.g., in material science, requires fast and highly scalable parallel solvers. Finite element tearing and interconnecting dual primal (FETI-DP) domain decomposition methods are parallel solution methods for implicit problems discretized by finite elements. Recently, nonlinear versions of the well-known FETI-DP methods for linear problems have been introduced. In these methods, the nonlinear problem is decomposed before linearization. This approach can be viewed as a strategy to further localize computational work and to extend the parallel scalability of FETI-DP methods toward extreme-scale supercomputers. Here, a recent nonlinear FETI-DP method is combined with an approach that allows an inexact solution of the FETI-DP coarse problem. We combine the nonlinear FETI-DP domain decomposition method with an algebraic multigrid (AMG) method and thus obtain a hybrid nonlinear domain decomposition/multigrid method. We consider scalar nonlinear problems as well as nonlinear hyperelasticity problems in two and three space dimensions. For the first time for a domain decomposition method, weak parallel scalability can be shown beyond half a million cores and subdomains. We can show weak parallel scalability for up to 524 288 cores on the Mira Blue Gene/Q supercomputer for our new implementation and discuss the steps necessary to obtain these results. We solve a heterogeneous nonlinear hyperelasticity problem discretized using piecewise quadratic finite elements with a total of 42 billion degrees of freedom in about six minutes. Our analysis reveals that scalability beyond 524 288 cores depends critically on both efficient construction and solution of the coarse problem. © 2015 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/140997907
  • 2015 • 114 Elasticity of interfacial rafts of hard particles with soft shells
    Knoche, S. and Kierfeld, J.
    Langmuir 31 5364-5376 (2015)
    We study an elasticity model for compressed protein monolayers or particle rafts at a liquid interface. Based on the microscopic view of hard-core particles with soft shells, a bead-spring model is formulated and analyzed in terms of continuum elasticity theory. The theory can be applied, for example, to hydrophobin-coated air-water interfaces or, more generally, to liquid interfaces coated with an adsorbed monolayer of interacting hard-core particles. We derive constitutive relations for such particle rafts and describe the buckling of compressed planar liquid interfaces as well as their apparent Poisson ratio. We also use the constitutive relations to obtain shape equations for pendant or buoyant capsules attached to a capillary, and to compute deflated shapes of such capsules. A comparison with capsules obeying the usual Hookean elasticity (without hard cores) reveals that the hard cores trigger capsule wrinkling. Furthermore, it is shown that a shape analysis of deflated capsules with hard-core/soft-shell elasticity gives apparent elastic moduli which can be much higher than the original values if Hookean elasticity is assumed. © 2015 American Chemical Society.
    view abstractdoi: 10.1021/acs.langmuir.5b00083
  • 2015 • 113 Analytical bounds of in-plane Young's modulus and full-field simulations of two-dimensional monocrystalline stochastic honeycomb structures
    Ma, D. and Eisenlohr, P. and Shanthraj, P. and Diehl, M. and Roters, F. and Raabe, D.
    Computational Materials Science 109 323-329 (2015)
    Abstract In this study, we focus on the interplay between the honeycomb structure and the crystallographic orientation. Specifically, the in-plane Young's moduli of monocrystalline stochastic honeycombs are calculated by a numerical and an analytical approach. The in-plane Young's moduli of the honeycombs were calculated numerically using a solution scheme for the full-field mechanical equilibrium based on spectral methods and anisotropic crystal elasticity. The analytical approach formulates two alternative assumptions, i.e. uniform force and uniform strain per strut, considers the elastic anisotropy of the base material, and depends on the two-variable distribution of the strut length and inclination angle as the structural parameters characterizing the stochastic honeycombs. The uniform strain assumption agrees closely with the numerical simulation results and constitutes an improvement compared to analytical solutions proposed in previous studies. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.commatsci.2015.07.041
  • 2015 • 112 Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices
    Martin, R.J. and Neff, P.
    Archive of Applied Mechanics 85 1761-1778 (2015)
    This note contains some observations on primary matrix functions and different notions of monotonicity with relevance toward constitutive relations in nonlinear elasticity. Focusing on primary matrix functions on the set of symmetric matrices, we discuss and compare different criteria for monotonicity. The demonstrated results are particularly applicable to computations involving the true-stress–true-strain monotonicity condition, a constitutive inequality recently introduced in an Arch. Appl. Mech. article by C.S. Jog and K.D. Patil. We also clarify a statement by Jog and Patil from the same article which could be misinterpreted. © 2015, Springer-Verlag Berlin Heidelberg.
    view abstractdoi: 10.1007/s00419-015-1017-4
  • 2015 • 111 The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity
    Neff, P. and Ghiba, I.-D. and Lankeit, J.
    Journal of Elasticity 121 143-234 (2015)
    We investigate a family of isotropic volumetric-isochoric decoupled strain energies (Formula Presented.) based on the Hencky-logarithmic (true, natural) strain tensor logU, where μ&gt;0 is the infinitesimal shear modulus, (Formula Presented.) is the infinitesimal bulk modulus with λ the first Lamé constant, k, are additional dimensionless material parameters, F=∇φ is the gradient of deformation, (Formula Presented.) is the right stretch tensor and [InlineEquation not available: see fulltext.] is the n-dimensional deviatoric part of the strain tensor logU. For small elastic strains, WeH approximates the classical quadratic Hencky strain energy (Formula Presented.) which is not everywhere rank-one convex. In plane elastostatics, i.e., n=2, we prove the everywhere rank-one convexity of the proposed family WeH, for (Formula Presented.). Moreover, we show that the corresponding Cauchy (true)-stress-true-strain relation is invertible for n=2,3 and we show the monotonicity of the Cauchy (true) stress tensor as a function of the true strain tensor in a domain of bounded distortions. We also prove that the rank-one convexity of the energies belonging to the family WeH is not preserved in dimension n=3 and that the energies (Formula Presented.) are also not rank-one convex. © 2015, Springer Science+Business Media Dordrecht.
    view abstractdoi: 10.1007/s10659-015-9524-7
  • 2015 • 110 Existence Theorem for Geometrically Nonlinear Cosserat Micropolar Model Under Uniform Convexity Requirements
    Neff, P. and Bîrsan, M. and Osterbrink, F.
    Journal of Elasticity 121 119-141 (2015)
    We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium system as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of minimizers. We present a clear proof based on the coercivity of the elastically stored energy density and on the weak lower semi-continuity of the total energy functional. Use is made of the dislocation density tensor $\overline{\boldsymbol{K}}= \overline{\boldsymbol{R}}^{T}\operatorname{Curl}\overline{\boldsymbol{R}}$ as a suitable Cosserat curvature measure. © 2015, Springer Science+Business Media Dordrecht.
    view abstractdoi: 10.1007/s10659-015-9517-6
  • 2015 • 109 The relaxed linear micromorphic continuum: Well-posedness of the static problem and relations to the gauge theory of dislocations
    Neff, P. and Ghiba, I.D. and Lazar, M. and Madeo, A.
    Quarterly Journal of Mechanics and Applied Mathematics 68 53-84 (2015)
    We consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement u ε R3 and the non-symmetric micro-distortion density tensor P ε R3×3. In this relaxed theory, a symmetric force-stress tensor arises despite the presence of microstructure and the curvature contribution depends solely on the micro-dislocation tensor Curl P. However, the relaxed model is able to fully describe rotations of the microstructure and to predict non-polar size-effects. In contrast to classical linear micromorphic models, we allow the usual elasticity tensors to become positive-semidefinite. We prove that, nevertheless, the equilibrium problem has a unique weak solution in a suitable Hilbert space. The mathematical framework also settles the question of which boundary conditions to take for the micro-distortion. Similarities and differences between linear micromorphic elasticity and dislocation gauge theory are discussed and pointed out. © The Author, 2015.
    view abstractdoi: 10.1093/qjmam/hbu027
  • 2015 • 108 Mechanical Properties of a Calcium Dietary Supplement, Calcium Fumarate Trihydrate
    Sun, S. and Henke, S. and Wharmby, M.T. and Yeung, H.H.-M. and Li, W. and Cheetham, A.K.
    Inorganic Chemistry 54 11186-11192 (2015)
    The mechanical properties of calcium fumarate trihydrate, a 1D coordination polymer considered for use as a calcium source for food and beverage enrichment, have been determined via nanoindentation and high-pressure X-ray diffraction with single crystals. The nanoindentation studies reveal that the elastic modulus (16.7-33.4 GPa, depending on crystallographic orientation), hardness (1.05-1.36 GPa), yield stress (0.70-0.90 GPa), and creep behavior (0.8-5.8 nm/s) can be rationalized in view of the anisotropic crystal structure; factors include the directionality of the inorganic Ca-O-Ca chain and hydrogen bonding, as well as the orientation of the fumarate ligands. High-pressure single-crystal X-ray diffraction studies show a bulk modulus of ∼20 GPa, which is indicative of elastic recovery intermediate between small molecule drug crystals and inorganic pharmaceutical ingredients. The combined use of nanoindentation and high-pressure X-ray diffraction techniques provides a complementary experimental approach for probing the critical mechanical properties related to tableting of these dietary supplements. © 2015 American Chemical Society.
    view abstractdoi: 10.1021/acs.inorgchem.5b01466
  • 2015 • 107 Deformation, orientation and bursting of microcapsules in simple shear flow: Wrinkling processes, tumbling and swinging motions
    Unverfehrt, A. and Koleva, I. and Rehage, H.
    Journal of Physics: Conference Series 602 (2015)
    In a series of experiments we studied the deformation and orientation behaviour of microcapsules in simple shear flow. For a large number of capsules we observed folding processes which were induced by the bending resistance, by membrane pre-stresses or the mechanical asymmetry of the surrounding viscoelastic wall materials. Periodic oscillations of the inclination angle were detected for non-spherical particles. At low shear rates a tumbling motion occurred in which the capsule turned around its axis. A swinging mode at evaluated shear rates was accompanied by tank-treading motions, a rotation of the membrane around the capsule core. Between these two well-known motions we also observed an intermittent regime. © Published under licence by IOP Publishing Ltd.
    view abstractdoi: 10.1088/1742-6596/602/1/012002
  • 2015 • 106 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 abstractdoi: 10.1016/j.jmps.2015.03.009
  • 2015 • 105 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 abstractdoi: 10.1007/s10439-014-1200-8
  • 2015 • 104 Routes towards catalytically active TiO2 doped porous cellulose
    Wittmar, A. and Thierfeld, H. and Köcher, S. and Ulbricht, M.
    RSC Advances 5 35866-35873 (2015)
    Cellulose-TiO<inf>2</inf> nanocomposites have been successfully prepared by non-solvent induced phase separation, either from cellulose solutions in ionic liquids or from cellulose acetate solutions in classical organic solvents followed by deacetylation ("regeneration"). Commercially available titania nanoparticles from gas phase synthesis processes have been used and processed as dispersions in the respective polymer solution. The used TiO<inf>2</inf> nanoparticles have been characterized by means of transmission electron microscopy (TEM) and X-ray diffraction (XRD), and their dispersions in ionic liquids and organic solvents have been evaluated by dynamic light scattering (DLS) and advanced rheology. The intermediate polymer solutions used in the phase separation process have been studied by advanced rheology. The resulting nanocomposites have been characterized by means of scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FT-IR). Special attention has been given to the complex relationship between the characteristics of the phase separation process and the porous structure of the formed nanocomposites. Two catalytic tests, based on the photocatalytic degradation of model organic dyes under UV irradiation, have been used for the characterization of the TiO<inf>2</inf> doped nanocomposites. The proof-of-concept experiments demonstrated the feasibility of photocatalyst immobilization in porous cellulose via phase separation of nanoparticle dispersions in polymer solutions, as indicated by UV-activated dye degradation in aqueous solution. © The Royal Society of Chemistry.2015.
    view abstractdoi: 10.1039/c5ra03707g
  • 2014 • 103 Shells without drilling rotations: A representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory
    Bîrsan, M. and Neff, P.
    International Journal of Engineering Science 80 32-42 (2014)
    In the framework of the geometrically nonlinear 6-parameter resultant shell theory we give a characterization of the shells without drilling rotations. These are shells for which the strain energy function W is invariant under the superposition of drilling rotations, i.e. W is insensible to the arbitrary local rotations about the third director d3. For this type of shells we show that the strain energy density W can be represented as a function of certain combinations of the shell deformation gradient F and the surface gradient of d3, namely W(FTF,FT d3,FTGrads d3). For the case of isotropic shells we present explicit forms of the strain energy function W having this property. © 2014 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.ijengsci.2014.02.027
  • 2014 • 102 Depinning of stiff directed lines in random media
    Boltz, H.-H. and Kierfeld, J.
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 90 (2014)
    Driven elastic manifolds in random media exhibit a depinning transition to a state with nonvanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than line tension. Their equation of motion is the (quenched) Herring-Mullins equation, which also describes surface growth governed by surface diffusion. Stiff directed lines are particularly interesting as there is a localization transition in the static problem at a finite temperature and the commonly exploited time ordering of states by means of Middleton's theorems [Phys. Rev. Lett. 68, 670 (1992)PRLTAO0031-900710.1103/PhysRevLett.68.670] is not applicable. We employ analytical arguments and numerical simulations to determine the critical exponents and compare our findings with previous works and functional renormalization group results, which we extend to the different line elasticity. We see evidence for two distinct correlation length exponents. © 2014 American Physical Society.
    view abstractdoi: 10.1103/PhysRevE.90.012101
  • 2014 • 101 Effects of atomic ordering on the elastic properties of TiN- and VN-based ternary alloys
    Edström, D. and Sangiovanni, D.G. and Hultman, L. and Chirita, V.
    Thin Solid Films 571 145-153 (2014)
    Improved toughness is one of the central goals in the development of wear-resistant coatings. Previous studies of toughness in transition metal nitride alloys have addressed the effects of chemical composition in these compounds. Herein, we use density functional theory to study the effects of various metal sublattice configurations, ranging from fully ordered to fully disordered, on the mechanical properties of VM2N and TiM2N (M2 = W, Mo) ternary alloys. Results show that all alloys display high incompressibility, indicating strong Me-N bonds. Disordered atomic arrangements yield lower values of bulk moduli and C11 elastic constants, as well as higher values of C44 elastic constants, compared to ordered structures. We attribute the low C44 values of ordered structures to the formation of fully-bonding states perpendicular to the applied stress. We find that the ductility of these compounds is primarily an effect of the increased valence electron concentration induced upon alloying. © 2014 Elsevier B.V.
    view abstractdoi: 10.1016/j.tsf.2014.09.048
  • 2014 • 100 Quantum-mechanical study of single-crystalline and polycrystalline elastic properties of Mg-substituted calcite crystals
    Friák, M. and Zhu, L.-F. and Lymperakis, L. and Titrian, H. and Aydin, U. and Janus, A.M. and Fabritius, H.-O. and Ziegler, A. and Nikolov, S. and Hemzalová, P. and Raabe, D. and Neugebauer, J.
    Key Engineering Materials 592-593 335-341 (2014)
    We use quantum-mechanical calculations to study single-crystalline elastic properties of (Ca,Mg)CO3 crystals with concentrations ranging from calcite CaCO3 to magnesite MgCO3. By analyzing results for a dense set of distributions of Ca and Mg atoms within 30-atom supercells, our theoretical study shows that those atomic configurations, that minimize the total energy for a given concentration, are characterized by elastic constants that either increase with the Mg content or remain nearly constants. Employing these ab initio calculated single-crystalline elastic parameters, the polycrystalline elastic properties of (Ca,Mg)CO3 aggregates are determined using a mean-field self-consistent homogenization method. The computed integral elastic moduli (bulk and shear) show a significant stiffening impact of Mg atoms on calcite crystals. Our analysis also demonstrates that it is not advantageous to use a granular two-phase composite of stoichiometric calcite and magnesite instead of substituting individual Ca and Mg atoms. Such two-phase aggregates are not significantly thermodynamically favorable and do not offer any strong additional stiffening effect. © (2014) Trans Tech Publications.
    view abstractdoi: 10.4028/
  • 2014 • 99 Oscillatory shear and high-pressure dielectric study of 5-methyl-3-heptanol
    Gainaru, C. and Wikarek, M. and Pawlus, S. and Paluch, M. and Figuli, R. and Wilhelm, M. and Hecksher, T. and Jakobsen, B. and Dyre, J.C. and Böhmer, R.
    Colloid and Polymer Science 292 1913-1921 (2014)
    The monohydroxy alcohol 5-methyl-3-heptanol is studied using rheology at ambient pressure and using dielectric spectroscopy at elevated pressures up to 1.03 GPa. Both experimental techniques reveal that the relaxational behavior of this liquid is intermediate between those that show a large Debye process, such as 2-ethyl-1-hexanol, or a small Debye-like feature, such as 4-methyl-3-heptanol, with which comparisons are made. Various phenomenological approaches assigning a time scale for the rheological signature of supramolecular dynamics in monohydroxy alcohols are discussed. © 2014 Springer-Verlag.
    view abstractdoi: 10.1007/s00396-014-3274-0
  • 2014 • 98 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 abstractdoi: 10.1016/j.ultras.2014.02.004
  • 2014 • 97 Rheology of dense suspensions of elastic capsules: Normal stresses, yield stress, jamming and confinement effects
    Gross, M. and Krüger, T. and Varnik, F.
    Soft Matter 10 4360-4372 (2014)
    We study the shearing rheology of dense suspensions of elastic capsules, taking aggregation-free red blood cells as a physiologically relevant example. Particles are non-Brownian and interact only via hydrodynamics and short-range repulsive forces. An analysis of the different stress mechanisms in the suspension shows that the viscosity is governed by the shear elasticity of the capsules, whereas the repulsive forces are subdominant. Evidence for a dynamic yield stress above a critical volume fraction is provided and related to the elastic properties of the capsules. The shear stress is found to follow a critical jamming scenario and is rather insensitive to the tumbling-to-tank- treading transition. The particle pressure and normal stress differences display some sensitivity to the dynamical state of the cells and exhibit a characteristic scaling, following the behavior of a single particle, in the tank-treading regime. The behavior of the viscosity in the fluid phase is rationalized in terms of effective medium models. Furthermore, the role of confinement effects, which increase the overall magnitude and enhance the shear-thinning of the viscosity, is discussed. © 2014 the Partner Organisations.
    view abstractdoi: 10.1039/c4sm00081a
  • 2014 • 96 Shear-induced mixing governs codeformation of crystalline-amorphous nanolaminates
    Guo, W. and Jägle, E.A. and Choi, P.-P. and Yao, J. and Kostka, A. and Schneider, J.M. and Raabe, D.
    Physical Review Letters 113 (2014)
    Deformation of ductile crystalline-amorphous nanolaminates is not well understood due to the complex interplay of interface mechanics, shear banding, and deformation-driven chemical mixing. Here we present indentation experiments on 10 nm nanocrystalline Cu-100 nm amorphous CuZr model multilayers to study these mechanisms down to the atomic scale. By using correlative atom probe tomography and transmission electron microscopy we find that crystallographic slip bands in the Cu layers coincide with noncrystallographic shear bands in the amorphous CuZr layers. Dislocations from the crystalline layers drag Cu atoms across the interface into the CuZr layers. Also, crystalline Cu blocks are sheared into the CuZr layers. In these sheared and thus Cu enriched zones the initially amorphous CuZr layer is rendered into an amorphous plus crystalline nanocomposite. © 2014 American Physical Society.
    view abstractdoi: 10.1103/PhysRevLett.113.035501
  • 2014 • 95 Structure-property relations of orthorhombic [(CH 3) 3 NCH 2COO ] 2(CuCl 2) 3·2 H 2O
    Haussühl, E. and Schreuer, J. and Wiehl, L. and Paulsen, N.
    Journal of Solid State Chemistry 212 205-212 (2014)
    Large single crystals of orthorhombic [(CH3)3 NCH2COO]2(CuCl2)3·2H2O with dimensions up to 40×40×30 mm3 were grown from aqueous solutions. The elastic and piezoelastic coefficients were derived from ultrasonic resonance frequencies and their shifts upon variation of pressure, respectively, using the plate-resonance technique. Additionally, the coefficients of thermal expansion were determined between 95 K and 305 K by dilatometry. The elastic behaviour at ambient conditions is dominated by the 2-dimensional network of strong hydrogen bonds within the (001) plane leading to a corresponding pseudo-tetragonal anisotropy of the longitudinal elastic stiffness. The variation of elastic properties with pressure, however, as well as the thermal expansion shows strong deviations from the pseudo-tetragonal symmetry. These deviations are probably correlated with tilts of the elongated tri-nuclear betaine-CuCl 2-water complexes. Neither the thermal expansion nor the specific heat capacity gives any hint on a phase transition in the investigated temperature range. © 2014 Elsevier Inc.
    view abstractdoi: 10.1016/j.jssc.2014.01.004
  • 2014 • 94 Modeling of the effective elastic properties of multifunctional carbon nanocomposites due to agglomeration of straight circular carbon nanotubes in a polymer matrix
    Jarali, C.S. and Basavaraddi, S.R. and Kiefer, B. and Pilli, S.C. and Lu, Y.C.
    Journal of Applied Mechanics, Transactions ASME 81 (2014)
    In the present study, the effective elastic properties of multifunctional carbon nanotube composites are derived due to the agglomeration of straight circular carbon nanotubes dispersed in soft polymer matrices. The agglomeration of CNTs is common due to the size of nanotubes, which is at nanoscales. Furthermore, it has been proved that straight circular CNTs provide higher stiffness and elastic properties than any other shape of the nanofibers. Therefore, in the present study, the agglomeration effect on the effective elastic moduli of the CNT polymer nanocomposites is investigated when circular CNTs are aligned straight as well as distributed randomly in the matrix. The Mori-Tanaka micromechanics theory is adopted to newly derive the expressions for the effective elastic moduli of the CNT composites including the effect of agglomeration. In this direction, analytical expressions are developed to establish the volume fraction relationships for the agglomeration regions with high, and dilute CNT concentrations. The volume of the matrix in which there may not be any CNTs due to agglomeration is also included in the present formulation. The agglomeration volume fractions are subsequently adopted to develop the effective relations of the composites for transverse isotropy and isotropic straight CNTs. The validation of the modeling technique is assessed with results reported, and the variations in the effective properties for high and dilute agglomeration concentrations are investigated. Copyright © 2014 by ASME.
    view abstractdoi: 10.1115/1.4024414
  • 2014 • 93 DFT-supported phase-field study on the effect of mechanically driven fluxes in Ni4Ti3 precipitation
    Kamachali, R.D. and Borukhovich, E. and Hatcher, N. and Steinbach, I.
    Modelling and Simulation in Materials Science and Engineering 22 (2014)
    Formation of the Ni4Ti3 precipitate has a strong effect on the shape memory properties of NiTi alloys. In this work, growth of this precipitate is studied using phase-field modelling and density functional theory (DFT) calculations. Using first-principles calculations, the composition-dependent stability and elastic properties of the B2 phase are obtained. Composition-dependent elastic constants are incorporated into our phase-field model to investigate the interplay between stress and concentration fields around the precipitate. The model introduces a source of diffusion due to mechanical relaxation which is accompanied by local softening/hardening of the B2 phase. The results are discussed in light of previous experimental and simulation studies. © 2014 IOP Publishing Ltd.
    view abstractdoi: 10.1088/0965-0393/22/3/034003
  • 2014 • 92 Thermal cycling behavior of an aged FeNiCoAlTa single-crystal shape memory alloy
    Krooß, P. and Holzweissig, M.J. and Niendorf, T. and Somsen, C. and Schaper, M. and Chumlyakov, Y.I. and Maier, H.J.
    Scripta Materialia 81 28-31 (2014)
    In this study the thermal cycling behavior of differently aged [1 0 0]-oriented Fe-28Ni-17Co-11.5Al-2.5Ta (at.%) shape memory single crystals was investigated. The strain-temperature response determined from thermal cycling experiments revealed a strong dependency on the precipitate morphology, which was adjusted by aging heat treatments. Specifically, a high precipitate density in the microstructure leads to small phase transformation-induced strains and low stresses necessary for activation of the martensitic phase transformation. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.scriptamat.2014.02.020
  • 2014 • 91 Temperature dependencies of the elastic moduli and thermal expansion coefficient of an equiatomic, single-phase CoCrFeMnNi high-entropy alloy
    Laplanche, G. and Gadaud, P. and Horst, O. and Otto, F. and Eggeler, G. and George, E.P.
    Journal of Alloys and Compounds 623 348-353 (2014)
    The equiatomic CoCrFeMnNi alloy is now regarded as a model face-centered cubic single-phase high-entropy alloy. Therefore, determination of its intrinsic properties such as the temperature dependencies of elastic moduli and thermal expansion coefficient are important to improve understanding of this new class of material. These temperature dependencies were measured over a large temperature range (200-1270 K) in this study. © 2014 Elsevier B.V.
    view abstractdoi: 10.1016/j.jallcom.2014.11.061
  • 2014 • 90 On the convexity of the function C → f(det C) on positive-definite matrices
    Lehmich, S. and Neff, P. and Lankeit, J.
    Mathematics and Mechanics of Solids 19 369-375 (2014)
    Let n≥2. We prove a condition on f ∈ C2(ℝ+,ℝ) for the convexity of f o det on ℙ ym(n), namely that f o det is convex on ℙ ym(n) if and only if f''(s)+ n-1/ns · f'(s) ≥ 0 and f'(s)≤ 0 ∀ s ∈ ℝ+.This generalizes the observation that C → - ln det C is convex as a function of C. © The Author(s) 2013.
    view abstractdoi: 10.1177/1081286512466099
  • 2014 • 89 Wrinkling of random and regular semiflexible polymer networks
    Müller, P. and Kierfeld, J.
    Physical Review Letters 112 (2014)
    We investigate wrinkling of two-dimensional random and triangular semiflexible polymer networks under shear. Both types of semiflexible networks exhibit wrinkling above a small critical shear angle, which scales with an exponent of the bending modulus between 1.9 and 2.0. Random networks exhibit hysteresis at the wrinkling threshold. Wrinkling lowers the total elastic energy by up to 20% and strongly affects the elastic properties of all semiflexible networks such as the crossover between bending and stretching dominated behavior. In random networks, we also find evidence for metastable wrinkled configurations. While the disordered microstructure of random networks affects the scaling behavior of wrinkle amplitudes, it has little effect on wrinkle wavelength. Therefore, wrinkles represent a robust, microstructure-independent assay of shear strain or elastic properties. © 2014 American Physical Society.
    view abstractdoi: 10.1103/PhysRevLett.112.094303
  • 2014 • 88 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 abstractdoi: 10.1137/130937573
  • 2014 • 87 A Riemannian approach to strain measures in nonlinear elasticity
    Neff, P. and Eidel, B. and Osterbrink, F. and Martin, R.
    Comptes Rendus - Mecanique 342 254-257 (2014)
    The isotropic Hencky strain energy appears naturally as a distance measure of the deformation gradient to the set SO(n) of rigid rotations in the canonical left-invariant Riemannian metric on the general linear group GL(n). Objectivity requires the Riemannian metric to be left-GL(n)-invariant, isotropy requires the Riemannian metric to be right-O(n)-invariant. The latter two conditions are only satisfied for a three-parameter family of Riemannian metrics on the tangent space of GL(n). Surprisingly, the final result is basically independent of the chosen parameters.In deriving the result, geodesics on GL(n) have to be parameterized and a novel minimization problem, involving the matrix logarithm for non-symmetric arguments, has to be solved. © 2014.
    view abstractdoi: 10.1016/j.crme.2013.12.005
  • 2014 • 86 Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity
    Schwarz, A. and Steeger, K. and Schröder, J.
    Computational Mechanics 54 603-612 (2014)
    The main goal of this contribution is the improvement of the approximation quality of least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity. Compared with other variational approaches as for example the Galerkin method, the main drawback of least-squares formulations is the unsatisfying approximation quality in terms of accuracy and robustness. Here, lower-order elements are especially affected, see e.g. [33]. In order to circumvent these problems, we introduce overconstrained first-order systems with suited weights. We consider different mixed least-squares formulations depending on stresses and displacements with a maximal cubical polynomial interpolation. For the continuous approximation of the stresses Raviart-Thomas elements are used, while for the displacements standard conforming elements are employed. Some numerical benchmarks are presented in order to validate the performance and efficiency of the proposed formulations. © 2014 Springer-Verlag Berlin Heidelberg.
    view abstractdoi: 10.1007/s00466-014-1009-1
  • 2014 • 85 Extremal states of energy of a double-layered thick-walled tube - application to residually stressed arteries
    Waffenschmidt, T. and Menzel, A.
    Journal of the Mechanical Behavior of Biomedical Materials 29 635-654 (2014)
    Various biological tissues are designed to optimally support external loads for complex geometries and mechanobiological structures. This results in complex microstructures of such materials. The design of, for instance, (healthy) arteries, which are in the focus of this work, is characterised by a residually stressed fibre-reinforced multi-layered composite with highly non-linear elastic response. The complex interaction of material properties with the geometry and residual stress effects enables the optimal support under different blood pressures, respectively blood flow, within the vessel. The fibres reinforcing the arterial wall, as well as residual stresses present in the vessel, strongly influence its overall behaviour and performance. Turn-over and remodelling processes of the collagenous fibres occurring in the respective layers - either resulting from natural growth phenomena or from artificially induced changes in loading condition such as stent deployment - support the optimisation of the multi-layered composite structure of arteries for the particular loading conditions present in the artery. Within this contribution, the overall energetic properties of an artery are discussed by means of the inflation, bending and extension of a double-layered cylindrical tube. Different states of residual stresses and different fibre orientations are considered so that, for instance, representative fibre angles that result in extremal states of the total potential energy can be identified. In view of turn-over and remodelling processes, these orientations are considered to constitute preferred directions of fibre alignment. In summary, the main goal of this work is to calculate optimal material, structural and loading parameters by concepts of energy-minimisation. Several numerical studies show that the obtained values - such as the fibre orientations, the residual axial stretch and the opening angle - are in good agreement with respective physiological parameters reported in the literature. © 2013 Elsevier Ltd.
    view abstractdoi: 10.1016/j.jmbbm.2013.05.023
  • 2014 • 84 PH controlled condensation of polysiloxane networks at the water-air interface
    Wieland, D.C.F. and Degen, P. and Paulus, M. and Schroer, M.A. and Rehage, H. and Tolan, M.
    Colloids and Surfaces A: Physicochemical and Engineering Aspects 455 44-48 (2014)
    Structural and mechanical properties of molecularly thick polysiloxane membranes were studied on different liquid subphases to investigate the impact of the subphase's pH value on the cross-linking process. The lateral structure of these films was studied in-situ by grazing incidence diffraction while torsions pendulum experiments reveal the response of the system to mechanical stress. The results show a hindered cross-linking on acidic subphases. At alkaline and neutral pH conditions the cross-linking process was not effected. The data revealed that the degree of polymerization can be tuned by regulating the subphase's pH value, which opens the opportunity to build complex polysiloxane membranes in a controlled manner. © 2014 Elsevier B.V.
    view abstractdoi: 10.1016/j.colsurfa.2014.03.099
  • 2014 • 83 Stable zinc oxide nanoparticle dispersions in ionic liquids
    Wittmar, A. and Gautam, D. and Schilling, C. and Dörfler, U. and Mayer-Zaika, W. and Winterer, M. and Ulbricht, M.
    Journal of Nanoparticle Research 16 (2014)
    The influence of the hydrophilicity and length of the cation alkyl chain in imidazolium-based ionic liquids on the dispersability of ZnO nanoparticles by ultrasound treatment was studied by dynamic light scattering and advanced rheology. ZnO nano-powder synthesized by chemical vapor synthesis was used in parallel with one commercially available material. Before preparation of the dispersion, the nanoparticles characteristics were determined by transmission electron microscopy, X-ray diffraction, nitrogen adsorption with BET analysis, and FT-IR spectroscopy. Hydrophilic ionic liquids dispersed all studied nanopowders better and in the series of hydrophilic ionic liquids, an improvement of the dispersion quality with increasing length of the alkyl chain of the cation was observed. Especially, for ionic liquids with short alkyl chain, additional factors like nanoparticle concentration in the dispersion and the period of the ultrasonic treatment had significant influence on the dispersion quality. Additionally, nanopowder characteristics (crystallite shape and size as well as the agglomeration level) influenced the dispersion quality. The results indicate that the studied ionic liquids are promising candidates for absorber media at the end of the gas phase synthesis reactor allowing the direct preparation of non-agglomerated nanoparticle dispersions without supplementary addition of dispersants and stabilizers. © Springer Science+Business Media 2014.
    view abstractdoi: 10.1007/s11051-014-2341-2
  • 2014 • 82 Ab initio based study of finite-temperature structural, elastic and thermodynamic properties of FeTi
    Zhu, L.-F. and Friák, M. and Udyansky, A. and Ma, D. and Schlieter, A. and Kühn, U. and Eckert, J. and Neugebauer, J.
    Intermetallics 45 11-17 (2014)
    We employ density functional theory (DFT) to calculate pressure dependences of selected thermodynamic, structural and elastic properties as well as electronic structure characteristics of equiatomic B2 FeTi. We predict ground-state single-crystalline Young's modulus and its two-dimensional counterpart, the area modulus, together with homogenized polycrystalline elastic parameters. Regarding the electronic structure of FeTi, we analyze the band structure and electronic density of states. Employing (i) an analytical dynamical matrix parametrized in terms of elastic constants and lattice parameters in combination with (ii) the quasiharmonic approximation we then obtained free energies, the thermal expansion coefficient, heat capacities at constant pressure and volume, as well as isothermal bulk moduli at finite temperatures. Experimental measurements of thermal expansion coefficient complement our theoretical investigation and confirm our theoretical predictions. It is worth mentioning that, as often detected in other intermetallics, some materials properties of FeTi strongly differ from the average of the corresponding values found in elemental Fe and Ti. These findings can have important implications for future materials design of new intermetallic materials. © 2013 The Authors. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.intermet.2013.09.008
  • 2013 • 81 The rubber elasticity of poly(N-isopropylacrylamide) hydrogel networks
    Adrus, N. and Ulbricht, M.
    Advanced Materials Research 812 210-215 (2013)
    We report here on the characterization of classical bulk poly(N-isopropylacrylamide) (PNIPAAm) hydrogel networks. The classical PNIPAAm hydrogels were prepared from Nisopropylacrylamide (NIPAAm) as a main monomer and N,N'-methylenebisacrylamide (MBAAm) as a crosslinker. The viscoelastic character of bulk hydrogels was examined using rheological measurements under frequency sweep mode (20 °C). A range of frequency, ω from 0.1 to 100 rad/s, was employed as this is a typical range for 'rubber plateau'. Within this range, almost frequency independent of storage moduli (G'; ~ 104 Pa as a function of hydrogel compositions were obtained. Indeed, the 'perfect' soft-rubbery behaviour of PNIPAAm hydrogels could be confirmed and thus enabled the estimation of mesh size. Interestingly, the mesh size rubbery hydrogels determined from rheological data was in a good agreement to that from swelling experiments (~ 4 to 9 nm). © (2013) Trans Tech Publications, Switzerland.
    view abstractdoi: 10.4028/
  • 2013 • 80 Rheological studies on PNIPAAm hydrogel synthesis via in situ polymerization and on resulting viscoelastic properties
    Adrus, N. and Ulbricht, M.
    Reactive and Functional Polymers 73 141-148 (2013)
    Bulk poly(N-isopropylacrylamide) hydrogels were prepared via free radical polymerization. Two different initiation methods were studied: redox- and photoinitiation. It was demonstrated that the desired final properties of resulting hydrogels, i.e., high monomer conversion (>95%) and adjustable swelling were only obtained by selecting best suited initiation conditions. For redox polymerization, this was achieved by tuning the ratio of accelerator N,N,N′,N′-tetramethylethylenediamine to initiator ammonium persulfate. The key parameters for achieving optimum photopolymerization conditions were photoinitiator concentration and UV irradiation time. With help of in situ rheological measurements, optimum conditions could be further verified and quantified by monitoring the liquid-to-gel transition. Overall, photoiniated crosslinking copolymerization was postulated to offer better options for in situ preparation of tailored functional hydrogels, in particular for the integration of smart soft matrices within membrane pores or other microsystems via a rapid reaction. Rheology was also used to investigate the hydrogel after ex situ preparation, revealing "perfect" soft-rubbery behavior. A good correlation between the mesh sizes determined from swelling and rheology was also found. In conclusion, rheology has been found to be a powerful tool because it provides valuable data on polymerization and gelation kinetics as well as information about the hydrogels microstructure based on their viscoelastic character. © 2012 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.reactfunctpolym.2012.08.015
  • 2013 • 79 A simple finite strain non-linear visco-plastic model for thermoplastics and its application to the simulation of incremental cold forming of polyvinylchloride (PVC)
    Alkas Yonan, S. and Soyarslan, C. and Haupt, P. and Kwiatkowski, L. and Tekkaya, A.E.
    International Journal of Mechanical Sciences 66 192-201 (2013)
    This paper introduces a finite strain extension of a non-linear visco-plastic material model, previously proposed by the authors, and its application to the finite element simulation of incremental cold forming processes of thermoplastics, demonstrated on PVC. Preserving the original structure of the model, its finite strain extension does not rely on any presumed kinematic split, either multiplicative or additive, among elastic and inelastic parts. It uses a systematic replacement of the strain and stress tensors and their rates by their respective spatial counterparts. A deviatoric Oldroyd rate is introduced to preserve the objectivity as well as the deviatoricity of the integration of the rate forms of deviatoric tensors. To cope with the incremental loading paths within the process, where through-thickness variations of the variables gain importance, the material model is posed in 3D formulation. The developed model is implemented as an ABAQUS®/UMAT subroutine and used in the simulations following parameter identification studies. The numerical results are compared with analogous experimental ones to evaluate the performance of the material model where PVC sheets of three different thicknesses are formed incrementally with path controlled tool force monitoring. The investigations have the following consequences: the deformation-limited homogeneous stress-strain portion at uni-axial tensile tests, which is generally used in parameter identification of the constitutive model, is not able to reflect the post necking regime and its extrapolation ends up with a stiffer response with much less retained strains. Once a semi-inverse parameter identification is followed by taking into account the overall experimental outputs, one ends up with a considerable improvement in the tool force, geometry and the wall thickness predictions. Nevertheless, these improvements are inversely proportional with the sheet thickness where the local indentation effects (strains and stresses) become larger. © 2012 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.ijmecsci.2012.11.007
  • 2013 • 78 Interplay between Coulomb interaction and quantum-confined Stark-effect in polar and nonpolar wurtzite InN/GaN quantum dots
    Barthel, S. and Schuh, K. and Marquardt, O. and Hickel, T. and Neugebauer, J. and Jahnke, F. and Czycholl, G.
    European Physical Journal B 86 (2013)
    In this paper we systematically analyze the electronic structures of polar and nonpolar wurtzite-InN/GaN quantum dots and their modification due to the quantum-confined Stark effect caused by intrinsic fields. This is achieved by combining continuum elasticity theory with an effective-bond orbital model to describe the elastic and single-particle electronic properties in these nitride systems. Based on these results, a many-body treatment is used to determine optical absorption spectra. The efficiency of optical transitions depends on the interplay between the Coulomb interaction and the quantum-confined Stark effect. We introduce an effective confinement potential which represents the electronic structure under the influence of the intrinsic polarization fields and calculate the needed strength of Coulomb interaction to diminish the separation of electrons and holes. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
    view abstractdoi: 10.1140/epjb/e2013-40542-0
  • 2013 • 77 Energy substitution: When model selection depends on the focus
    Behl, P. and Dette, H. and Frondel, M. and Tauchmann, H.
    Energy Economics 39 233-238 (2013)
    In contrast to conventional model selection criteria, the Focused Information Criterion (FIC) allows for the purpose-specific choice of model specifications. This accommodates the idea that one kind of model might be highly appropriate for inferences on a particular focus parameter, but not for another. Ever since its development, the FIC has been increasingly applied in the realm of statistics, but this concept appears to be virtually unknown in the literature on energy and production economics. Using the classical example of the Translog cost function and production data for 35 U.S. industry sectors (1960-2005), this paper provides for an empirical illustration of the FIC and demonstrates its usefulness in selecting production models, thereby focusing on the ease of substitution between energy and capital versus energy and labor. © 2013 Elsevier B.V.
    view abstractdoi: 10.1016/j.eneco.2013.04.013
  • 2013 • 76 Existence theorems in the geometrically non-linear 6-parameter theory of elastic plates
    Bîrsan, M. and Neff, P.
    Journal of Elasticity 112 185-198 (2013)
    In this paper we show the existence of global minimizers for the geometrically non-linear equations of elastic plates, in the framework of the general 6-parameter shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. © 2012 Springer Science+Business Media B.V.
    view abstractdoi: 10.1007/s10659-012-9405-2
  • 2013 • 75 Augmented Lagrange methods for quasi-incompressible materials-Applications to soft biological tissue
    Brinkhues, S. and Klawonn, A. and Rheinbach, O. and Schröder, J.
    International Journal for Numerical Methods in Biomedical Engineering 29 332-350 (2013)
    Arterial walls in the healthy physiological regime are characterized by quasi-incompressible, anisotropic, hyperelastic material behavior. Polyconvex material functions representing such materials typically incorporate a penalty function to account for the incompressibility. Unfortunately, the penalty will affect the conditioning of the stiffness matrices. For high penalty parameters, the performance of iterative solvers will degrade, and when direct solvers are used, the quality of the solutions will deteriorate. In this paper, an augmented Lagrange approach is used to cope with the quasi-incompressibility condition. Here, the penalty parameter can be chosen much smaller, and as a consequence, the arising linear systems of equations have better properties. An improved convergence is then observed for the finite element tearing and interconnecting-dual primal domain decomposition method, which is used as an iterative solver. Numerical results for an arterial geometry obtained from ultrasound imaging are presented. © 2012 John Wiley & Sons, Ltd.
    view abstractdoi: 10.1002/cnm.2504
  • 2013 • 74 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 abstractdoi: 10.1007/s00466-012-0823-6
  • 2013 • 73 B-and strong stationarity for optimal control of static plasticity with hardening
    Herzog, R. and Meyer, C. and Wachsmuth, G.
    SIAM Journal on Optimization 23 321-352 (2013)
    Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The control-to-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly stationary type. © 2013 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/110821147
  • 2013 • 72 A supramolecular gel from a quadruple zwitterion that responds to both acid and base
    Hisamatsu, Y. and Banerjee, S. and Avinash, M.B. and Govindaraju, T. and Schmuck, C.
    Angewandte Chemie - International Edition 52 12550-12554 (2013)
    Four arms: A quadruple zwitterion based on a pentaerythritol core forms thermoreversible gels in DMSO driven by the formation of ion-paired dimers between the zwitterionic units. Furthermore, it exhibits reversible gel-sol transitions in response to both acid and base. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/anie.201306986
  • 2013 • 71 Determination of the geometry of the RVE for cancellous bone by using the effective complex shear modulus
    Klinge, S.
    Biomechanics and Modeling in Mechanobiology 12 401-412 (2013)
    This contribution deals with the application of the inverse homogenization method to the determination of geometrical properties of cancellous bone. The approach represents a combination of an extended version of the Marquardt-Levenberg method with the multiscale finite element method. The former belongs to the group of gradient-based optimization strategies, while the latter is a numerical homogenization method, suitable for the modeling of materials with a highly heterogeneous microstructure. The extension of the Marquardt-Levenberg method is concerned with the selection strategy for distinguishing the global minimum from the plethora of local minima. Within the numerical examples, the bone is modeled as a biphasic viscoelastic medium and three different representative volume elements are taken into consideration. Different models enable the simulation of the bone either as a purely isotropic or as a transversally anisotropic medium. Main geometrical properties of trabeculae are determined from data on effective shear modulus but alternative schemes are also possible. © 2012 Springer-Verlag.
    view abstractdoi: 10.1007/s10237-012-0408-5
  • 2013 • 70 Elastometry of deflated capsules: Elastic moduli from shape and wrinkle analysis
    Knoche, S. and Vella, D. and Aumaitre, E. and Degen, P. and Rehage, H. and Cicuta, P. and Kierfeld, J.
    Langmuir 29 12463-12471 (2013)
    Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We compare this method with previous approaches using the Laplace-Young equation and illustrate the method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles, the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having a rigid core surrounded by a softer shell. © 2013 American Chemical Society.
    view abstractdoi: 10.1021/la402322g
  • 2013 • 69 Uniqueness of integrable solutions to ∇ ζ=G ζ, ζ{pipe}Gamma = 0 for integrable tensor coefficients G and applications to elasticity
    Lankeit, J. and Neff, P. and Pauly, D.
    Zeitschrift fur Angewandte Mathematik und Physik 64 1679-1688 (2013)
    Let Ω ⊂ ℝN be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ∂Ω. We show that the solution to the linear first-order system (Formula is Presented) is unique if (Formula is Presented) and (Formula is Presented). As a consequence, we prove (Formula is Presented) to be a norm for (Formula is Presented) for some p, q &gt; 1 with 1/p + 1/q = 1 as well as det (Formula is Presented). We also give a new and different proof for the so-called 'infinitesimal rigid displacement lemma' in curvilinear coordinates: Let (Formula is Presented) satisfy sym (Formula is Presented) for some (Formula is Presented). Then, there exist a constant translation vector (Formula is Presented). © 2013 Springer Basel.
    view abstractdoi: 10.1007/s00033-013-0314-4
  • 2013 • 68 Polarization effects due to thickness fluctuations in nonpolar InGaN/GaN quantum wells
    Marquardt, O. and Hickel, T. and Neugebauer, J. and Van De Walle, C.G.
    Applied Physics Letters 103 (2013)
    We have employed continuum elasticity theory and an eight band k·p model to study the influence of thickness fluctuations in In 0.2Ga0.8N quantum wells grown along the [11 2 ̄ 0] direction in GaN. Such fluctuations are the origin of polarization potentials that may spatially separate electrons and holes in the vicinity of a thickness fluctuation and therefore reduce the efficiency of light emitters. Our calculations reveal that even shallow fluctuations of one or two monolayers can induce a significant spatial separation of electrons and holes, in particular, if the lateral extent of such a fluctuation is large. © 2013 AIP Publishing LLC.
    view abstractdoi: 10.1063/1.4818752
  • 2013 • 67 A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: Continuum basis, computational aspects and applications
    Pierce, D.M. and Ricken, T. and Holzapfel, G.A.
    Computer Methods in Biomechanics and Biomedical Engineering 16 1344-1361 (2013)
    Cartilage is a multi-phase material composed of fluid and electrolytes (68-85% by wet weight), proteoglycans (5-10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness. The same two components control diffusion of the fluid phase, e.g. as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network. We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen-proteoglycan solid matrix. The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be 'squeezed out' from the tissue. Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature. © 2013 © 2013 Taylor & Francis.
    view abstractdoi: 10.1080/10255842.2012.670854
  • 2013 • 66 Self-consistent scale-bridging approach to compute the elasticity of multi-phase polycrystalline materials
    Titrian, H. and Aydin, U. and Friák, M. and Ma, D. and Raabe, D. and Neugebauer, J.
    Materials Research Society Symposium Proceedings 1524 17-23 (2013)
    A necessary prerequisite for a successful theory-guided up-scale design of materials with application-driven elastic properties is the availability of reliable homogenization techniques. We report on a new software tool that enables us to probe and analyze scale-bridging structure-property relations in the elasticity of materials. The newly developed application, referred to as SC-EMA (Self-consistent Calculations of Elasticity of Multi-phase Aggregates) computes integral elastic response of randomly textured polycrystals. The application employs a Python modular library that uses single-crystalline elastic constants Cij as input parameters and calculates macroscopic elastic moduli (bulk, shear, and Young's) and Poisson ratio of both single-phase and multi-phase aggregates. Crystallites forming the aggregate can be of cubic, tetragonal, hexagonal, orthorhombic, or trigonal symmetry. For cubic polycrystals the method matches the Hershey homogenization scheme. In case of multi-phase polycrystalline composites, the shear moduli are computed as a function of volumetric fractions of phases present in aggregates. Elastic moduli calculated using the analytical self-consistent method are computed together with their bounds as determined by Reuss, Voigt and Hashin-Shtrikman homogenization schemes. The library can be used as (i) a toolkit for a forward prediction of macroscopic elastic properties based on known single-crystalline elastic characteristics, (ii) a sensitivity analysis of macro-scale output parameters as function of input parameters, and, in principle, also for (iii) an inverse materials-design search for unknown phases and/or their volumetric ratios. © 2013 Materials Research Society.
    view abstractdoi: 10.1557/opl.2013.41
  • 2013 • 65 Influence of the cation alkyl chain length of imidazolium-based room temperature ionic liquids on the dispersibility of TiO2 nanopowders
    Wittmar, A. and Gajda, M. and Gautam, D. and Dörfler, U. and Winterer, M. and Ulbricht, M.
    Journal of Nanoparticle Research 15 (2013)
    The influence of the length of the cation alkyl chain on the dispersibility by ultrasonic treatment of TiO2 nanopowders in hydrophilic imidazolium-based room temperature ionic liquids was studied for the first time by dynamic light scattering and advanced rheology. TiO2 nanopowders had been synthesized by chemical vapor synthesis (CVS) under varied conditions leading to two different materials. A commercial nanopowder had been used for comparison. Characterizations had been done using transmission electron microscopy, X-ray diffraction, nitrogen adsorption with BET analysis, and FT-IR spectroscopy. Primary particle sizes were about 6 and 8 nm for the CVS-based and 26 nm for the commercial materials. The particle size distribution in the dispersion was strongly influenced by the length of the cation alkyl chain for all the investigated powders with different structural characteristics and concentrations in the dispersion. It was found that an increase of the alkyl chain length was beneficial, leading to a narrowing of the particle size distribution and a decrease of the agglomerate size in dispersion. The smallest average nanoparticle sizes in dispersion were around 30 nm. Additionally, the surface functionality of the nanoparticles, the concentration of the solid material in the liquid, and the period of ultrasonic treatment control the dispersion quality, especially in the case of the ionic liquids with the shorter alkyl chain. The influence of the nanopowders characteristics on their dispersibility decreases considerably with increasing cation alkyl chain length. The results indicate that ionic liquids with adapted structure are candidates as absorber media for nanoparticles synthesized in gas phase processes to obtain liquid dispersions directly without redispergation. © 2013 Springer Science+Business Media Dordrecht.
    view abstractdoi: 10.1007/s11051-013-1463-2
  • 2013 • 64 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 abstractdoi: 10.1002/nag.2184
  • 2013 • 63 Ab initio study of single-crystalline and polycrystalline elastic properties of Mg-substituted calcite crystals
    Zhu, L.-F. and Friák, M. and Lymperakis, L. and Titrian, H. and Aydin, U. and Janus, A.M. and Fabritius, H.-O. and Ziegler, A. and Nikolov, S. and Hemzalová, P. and Raabe, D. and Neugebauer, J.
    Journal of the Mechanical Behavior of Biomedical Materials 20 296-304 (2013)
    We employ ab initio calculations and investigate the single-crystalline elastic properties of (Ca,Mg)CO3 crystals covering the whole range of concentrations from pure calcite CaCO3 to pure magnesite MgCO3. Studying different distributions of Ca and Mg atoms within 30-atom supercells, our theoretical results show that the energetically most favorable configurations are characterized by elastic constants that nearly monotonously increase with the Mg content. Based on the first principles-derived single-crystalline elastic anisotropy, the integral elastic response of (Ca,Mg)CO3 polycrystals is determined employing a mean-field self-consistent homogenization method. As in case of single-crystalline elastic properties, the computed polycrystalline elastic parameters sensitively depend on the chemical composition and show a significant stiffening impact of Mg atoms on calcite crystals in agreement with the experimental findings. Our analysis also shows that it is not advantageous to use a higher-scale two-phase mix of stoichiometric calcite and magnesite instead of substituting Ca atoms by Mg ones on the atomic scale. Such two-phase composites are not significantly thermodynamically favorable and do not provide any strong additional stiffening effect. © 2013 Elsevier Ltd.
    view abstractdoi: 10.1016/j.jmbbm.2013.01.030
  • 2012 • 62 Novel hydrogel pore-filled composite membranes with tunable and temperature-responsive size-selectivity
    Adrus, N. and Ulbricht, M.
    Journal of Materials Chemistry 22 3088-3098 (2012)
    Hydrogel pore-filled composite membranes (HPFCM) based on polyethylene terephthalate (PET) track-etched membranes with pore diameters between 200 and 5000 nm and temperature-responsive poly(N-isopropylacrylamide) (PNIPAAm) hydrogels were successfully prepared. A premodification of the pore walls by grafted linear PNIPAAm led to stable anchoring of crosslinked PNIPAAm prepared in a subsequent step. Proper tuning of photopolymerization conditions resulted in a desired microstructure of the hydrogels and thus tailored barrier properties of the composite membranes. The very interesting separation performance of HPFCM was due to diversification of the hydrogel network that caused adjustable sieving properties via synthesis conditions and also largely switchable barrier properties in response to the temperature. The interplay between the immobilized hydrogel and various pore sizes of the membrane support was also investigated. The base membrane provides mechanical support and confines the hydrogel within its pores, and it thus allows using the hydrogel mesh size for size-selective solute transport. Completely stable and selective HPFCM were only obtained with base pore sizes of about 2 μm or smaller. The size-selectivity (molecular weight cut-off) of the same HPFCM was higher under diffusive than under convective flow conditions; this is presumably mainly caused by elasticity deformation of the hydrogel network. The apparent cut-off from diffusion experiments was well correlated to the mesh-size of the hydrogel determined from the Darcy model applied to permeability data obtained under convective flow conditions. Upon temperature increase beyond 32 °C, flux increased and rejection decreased very strongly; this remarkable change between macromolecule-size selective ultrafiltration and microfiltration/filtration behavior was fully reversible. © 2012 The Royal Society of Chemistry.
    view abstractdoi: 10.1039/c2jm15022k
  • 2012 • 61 Inverse-motion based modeling for electromechanics with application to electrostrictive polyurethane
    Ask, A. and Denzer, R. and Menzel, A. and Ristinmaa, M.
    ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2012 2 167-173 (2012)
    In this work the inverse motion problem for electro elasticity is considered. For given loads and boundary conditions, and a given deformed shape of the electro elastic body, the initially unknown undeformed configuration is sought. The boundary-value problem for the inverse motion is obtained by reparameterization of the forward motion equations in terms of the inverse deformation map. In order to account for incompressibility, a mixed formulation is adopted. The finite element method is used to calculate the undeformed configuration for an electro-active gripper application. Copyright © 2012 by ASME.
    view abstractdoi: 10.1115/SMASIS2012-8049
  • 2012 • 60 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 abstractdoi: 10.3390/ma5101853
  • 2012 • 59 Analysis of FETI-DP and BDDC for linear elasticity in 3D with almost incompressible components and varying coefficients inside subdomains
    Gippert, S. and Klawonn, A. and Rheinbach, O.
    SIAM Journal on Numerical Analysis 50 2208-2236 (2012)
    FETI-DP (dual-primal finite element tearing and interconnecting) methods are nonoverlapping domain decomposition methods which are used to solve large algebraic systems of equations that arise, e.g., from problems in linear elasticity. Good convergence bounds for problems of compressible linear elasticity are well known for two- and three-dimensional problems. More recently, FETI-DP and BDDC (balancing domain decomposition by constraints) methods have been developed that are robust also in the regime of homogeneous almost incompressible linear elasticity. The coarse space of such methods is large especially in 3D (three dimensions) and its implementation needs knowledge of geometrical information. Here, the convergence of FETI-DP methods for problems in 3D with almost incompressible inclusions or compressible inclusions with different material parameters embedded in a compressible matrix material is analyzed. For such problems, where the material is compressible in the vicinity of the subdomain interface, a polylogarithmic condition number estimate is shown for the preconditioned FETI-DP system. This bound depends only on the thickness of the compressible hull but is otherwise independent of coefficient jumps between subdo-mains and also between the hull and the inclusion. The bound is also valid for corresponding BDDC methods. The new contribution of the current paper is a theory that provides condition number bounds for the case of varying incompressibility and also varying Young moduli inside subdomains without changing the coarse space. © 2012 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/110838315
  • 2012 • 58 Deposition and characteristics of submicrometer-structured thermal barrier coatings by suspension plasma spraying
    Guignard, A. and Mauer, G. and Vaßen, R. and Stöver, D.
    Journal of Thermal Spray Technology 21 416-424 (2012)
    In the field of thermal barrier coatings (TBCs) for gas turbines, suspension plasma sprayed (SPS) submicrometer-structured coatings often show unique mechanical, thermal, and optical properties compared to conventional atmospheric plasma sprayed ones. They have thus the potential of providing increased TBC performances under severe thermo-mechanical loading. Experimental results showed the capability of SPS to obtain yttria stabilized zirconia coatings with very fine porosity and high density of vertical segmentation cracks, yielding high strain tolerance, and low Young's modulus. The evolution of the coating microstructure and properties during thermal cycling test at very high surface temperature (1400 °C) in our burner rigs and under isothermal annealing was investigated. Results showed that, while segmentation cracks survive, sintering occurs quickly during the first hours of exposure, leading to pore coarsening and stiffening of the coating. In-situ measurements at 1400 °C of the elastic modulus were performed to investigate in more detail the sintering-related stiffening. © ASM International.
    view abstractdoi: 10.1007/s11666-012-9762-1
  • 2012 • 57 Structure-property relations and thermodynamic properties of monoclinic petalite, LiAlSi 4O 10
    Haussühl, E. and Schreuer, J. and Winkler, B. and Haussühl, S. and Bayarjargal, L. and Milman, V.
    Journal of Physics Condensed Matter 24 (2012)
    Structure-property relations of monoclinic petalite, LiAlSi 4O 10, were determined by experiment and atomistic modeling based on density functional theory. The elastic stiffness coefficients were measured between room temperature and 570K using a combination of the plate-resonance technique and resonant ultrasound spectroscopy. The thermal expansion was studied between 100 and 740K by means of dilatometry. The heat capacity between 2 and 398K has been obtained by microcalorimetry using a quasi-adiabatic calorimeter. The experimentally determined elastic stiffness coefficients were employed to benchmark the results of density functional theory based model calculations. The values in the two data sets agreed to within a few GPa and the anisotropy was very well reproduced. The atomistic model was then employed to predict electric field gradients, the lattice dynamics and thermodynamic properties. The theoretical charge density was analyzed to investigate the bonding between atoms. © 2012 IOP Publishing Ltd.
    view abstractdoi: 10.1088/0953-8984/24/34/345402
  • 2012 • 56 Stress-induced melting of crystals in natural rubber: A new way to tailor the transition temperature of shape memory polymers
    Heuwers, B. and Quitmann, D. and Katzenberg, F. and Tiller, J.C.
    Macromolecular Rapid Communications 33 1517-1522 (2012)
    Lightly cross-linked natural rubber (NR, cis-1,4-polyisoprene) was found to be an exceptional cold programmable shape memory polymer (SMP) with strain storage of up to 1000%. These networks are stabilized by strain-induced crystals. Here, we explore the influence of mechanical stress applied perpendicular to the elongation direction of the network on the stability of these crystals. We found that the material recovers its original shape at a critical transverse stress. It could be shown that this is due to a disruption of the strain-stabilizing crystals, which represents a completely new trigger for SMPs. The variation of transverse stress allows tuning of the trigger temperature Ttrig(σ) in a range of 45 to 0 °C, which is the first example of manipulating the transition of a crystal-stabilized SMP after programming. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/marc.201200313
  • 2012 • 55 Deflation, projector preconditioning, and balancing in iterative substructuring methods: Connections and new results
    Klawonn, A. and Rheinbach, O.
    SIAM Journal on Scientific Computing 34 A459-A484 (2012)
    In this paper, projector preconditioning, also known as the deflation method, as well as the balancing preconditioner are applied to the dual-primal finite element tearing and interconnecting (FETI-DP) and balancing domain decomposition by constraints (BDDC) methods in order to create a second, independent coarse problem. This may help to extend the parallel scalability of classical FETI-DP and BDDC methods without the use of inexact solvers and may also be used to improve the robustness, e.g., for almost incompressible elasticity problems. Connections of FETIDP methods applying a transformation of basis using a larger coarse space with a corresponding FETI-DP method using projector preconditioning or balancing are pointed out. It is then shown that the methods have essentially the same spectrum. Numerical results for compressible and almost incompressible linear elasticity are provided. The sensitivity of the projection methods to an inexact computation of the projections is numerically investigated and a different behavior for projector preconditioning and the balancing preconditioner is found. © 2012 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/100811118
  • 2012 • 54 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 abstractdoi: 10.1016/j.compstruc.2012.02.008
  • 2012 • 53 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 abstractdoi: 10.1615/IntJMultCompEng.2012002946
  • 2012 • 52 Thermal expansion and elastic properties of mullite-type Bi 2Ga 4O 9 and Bi 2Fe 4O 9 single crystals
    Krenzel, T.F. and Schreuer, J. and Gesing, T.M. and Burianek, M. and Mühlberg, M. and Schneider, H.
    International Journal of Materials Research 103 438-448 (2012)
    Resonant ultrasound spectroscopy was used to characterize the elastic properties of single crystal orthorhombic Bi 2Ga 4O 9 and Bi 2Fe 4O 9 between room temperature and about 1200 K. Additionally, the coefficients of thermal expansion were studied in the range 100 K to 1 280 K using high-resolution dilatometry and X-ray powder diffraction. The elastic constants at 295 K are in GPa c 11 = 143.4(1), c 22 = 161.9(1), c 33 = 224.5(1), c 44 = 68.4(1), c 55 = 49.3(1), c 66 = 76.6(1), c 12 = 74.2(1), c 13 = 62.2(1), c 23 = 70.5(1) for Bi 2Ga 4O 9, and c 11 = 106.7(1), c 22 = 141.2(1), c 33 = 183.7(2), c 44 = 53.7(1), c 55 = 41.9(1), c 66 = 63.8(1), c 12 = 63.5(1), c 13 = 59.8(1), c 23 = 63.4(2) for Bi 2Fe 4O 9. In both mullite-type compounds the strong bond chains built up by edge-sharing coordination octahedra extending parallel to [001] dominate the anisotropy of their elastic and thermoelastic properties. Smaller variations of elastic anisotropy within the (001) plane can be attributed to the specific type of cross-linking of the octahedral chains. The temperature evolution of the c ij shows no hint on any structural instability or glass-like transition that might be related to the suspected ion conductivity at high temperatures. However, in both crystal species characteristic anelastic relaxation phenomena occur in the ultrasonic frequency regime close to room temperature. The smallest thermal expansion is observed in the plane perpendicular to the stiffest octahedral chains. A model is discussed to explain the apparent discrepancy in terms of cross-correlations within the three-dimensional framework of edge- and corner- linked coordination polyhedra. © 2012 Carl Hanser Verlag.
    view abstractdoi: 10.3139/146.110718
  • 2012 • 51 Spark plasma sintering synthesis and mechanical spectroscopy of the ω-Al 0.7Cu 0.2Fe 0.1 phase
    Laplanche, G. and Gadaud, P. and Bonneville, J. and Joulain, A. and Gauthier-Brunet, V. and Dubois, S. and Jay, F.
    Journal of Materials Science 47 169-175 (2012)
    Starting from a mixture of Al-Cu-Fe quasicrystalline (QC) particles and Al powder, a fully dense and almost Al-Cu-Fe ω single-phase alloy was produced by spark plasma sintering. This technique allows synthesising large samples with sizes suitable for mechanical spectroscopy experiments. Mechanical spectroscopy was selected because it is a relevant tool for detecting the presence of structural defects at both nano and microscopic scales. Young's moduli were measured in the 15 kHz range as a function of temperature by the resonant frequency method. Young's moduli behave similarly for typical metals and exhibit values that are comparable to those of the Al-Cu-Fe QC phase. The damping coefficient Q -1 was determined at various temperatures between room temperature and 840 K over a large frequency range, i.e. between 10 -3 and 10 Hz. The results suggest that solid friction effects do occur. In addition, a relaxation peak is observed in the intermediate temperature range. © 2011 Springer Science+Business Media, LLC.
    view abstractdoi: 10.1007/s10853-011-5784-1
  • 2012 • 50 Critical motor number for fractional steps of cytoskeletal filaments in gliding assays
    Li, X. and Lipowsky, R. and Kierfeld, J.
    PLoS ONE 7 (2012)
    In gliding assays, filaments are pulled by molecular motors that are immobilized on a solid surface. By varying the motor density on the surface, one can control the number N of motors that pull simultaneously on a single filament. Here, such gliding assays are studied theoretically using Brownian (or Langevin) dynamics simulations and taking the local force balance between motors and filaments as well as the force-dependent velocity of the motors into account. We focus on the filament stepping dynamics and investigate how single motor properties such as stalk elasticity and step size determine the presence or absence of fractional steps of the filaments. We show that each gliding assay can be characterized by a critical motor number, Nc. Because of thermal fluctuations, fractional filament steps are only detectable as long as N < Nc. The corresponding fractional filament step size is ℓ/N where ℓ is the step size of a single motor. We first apply our computational approach to microtubules pulled by kinesin-1 motors. For elastic motor stalks that behave as linear springs with a zero rest length, the critical motor number is found to be Nc=4, and the corresponding distributions of the filament step sizes are in good agreement with the available experimental data. In general, the critical motor number Nc depends on the elastic stalk properties and is reduced to Nc=3 for linear springs with a nonzero rest length. Furthermore, Nc is shown to depend quadratically on the motor step size ℓ. Therefore, gliding assays consisting of actin filaments and myosin-V are predicted to exhibit fractional filament steps up to motor number N=31. Finally, we show that fractional filament steps are also detectable for a fixed average motor number 〈N〉 as determined by the surface density (or coverage) of the motors on the substrate surface. © 2012 Li et al.
    view abstractdoi: 10.1371/journal.pone.0043219
  • 2012 • 49 Do cement nanotubes exist?
    Manzano, H. and Enyashin, A.N. and Dolado, J.S. and Ayuela, A. and Frenzel, J. and Seifert, G.
    Advanced Materials 24 3239-3245 (2012)
    Using atomistic simulations, this work indicates that cement nanotubes can exist. The chemically compatible nanotubes are constructed from the two main minerals in ordinary Portland cement pastes, namely calcium hydroxide and a calcium silicate hydrate called tobermorite. These results show that such nanotubes are stable and have outstanding mechanical properties, unique characteristics that make them ideally suitable for nanoscale reinforcements of cements. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/adma.201103704
  • 2012 • 48 Prediction of ship response statistics in severe sea conditions using RANS
    Oberhagemann, J. and Ley, J. and El Moctar, B.O.
    Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE 2 583-593 (2012)
    The International Association of Classification Societies (IACS) promotes the paradigm shift in structural design rules for ships towards risk based approaches. This requires improvements in the assessment of structural design loads and new methods for estimation of wave loads and responses, amongst others with respect to extreme value distributions. In this paper we present a numerical method based on the solution of RANS equations to deal with large wave-induced ship motions and corresponding loads for different ship types. Nonlinearities of wave excitation and ship response are included. Short-term ship response distributions from time domain simulations are compared with model test data. Significant deviations from Rayleigh distribution of amplitudes are observed, especially for hull girder loads including effects of structural elasticity. Copyright © 2012 by ASME.
    view abstractdoi: 10.1115/OMAE2012-83995
  • 2012 • 47 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 abstractdoi: 10.1016/j.apnum.2010.12.010
  • 2012 • 46 Elastic properties of face-centred cubic Fe-Mn-C studied by nanoindentation and ab initio calculations
    Reeh, S. and Music, D. and Gebhardt, T. and Kasprzak, M. and Jäpel, T. and Zaefferer, S. and Raabe, D. and Richter, S. and Schwedt, A. and Mayer, J. and Wietbrock, B. and Hirt, G. and Schneider, J.M.
    Acta Materialia 60 6025-6032 (2012)
    We have studied experimentally and theoretically the influence of C and Mn content on the Young's modulus of Fe-Mn-C alloys. Combinatorial thin film and bulk samples were characterized regarding their structure, texture and Young's modulus. The following chemical composition range was investigated: 1.5-3.0 at.% C, 28.0-37.5 at.% Mn and 60.6-69.8 at.% Fe. The experimental lattice parameters change marginally within 3.597-3.614 Å with the addition of C and are consistent with ab initio calculations. The Young's modulus data are in the range of 185 ± 12-251 ± 59 GPa for the bulk samples and the thin film, respectively. C has no significant effect on the Young's modulus of these alloys within the composition range studied here. The ab initio calculations are 15-22% larger than the average Young's modulus values of the as-deposited and polished thin film at 3 at.% C. The comparison of thin film and bulk samples results reveals similar elastic properties for equivalent compositions, indicating that the applied research strategy consisting of the combinatorial thin film approach in conjunction with ab initio calculations is useful to study the composition dependence of the structure and elastic properties of Fe-Mn-C alloys. The very good agreement between the presented calculations and the experimentally determined lattice parameters and Young's modulus values implies that the here-adopted simulation strategy yields a reliable description of carbon in Fe-Mn alloys, important for future alloy design. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2012.07.038
  • 2012 • 45 Strong dipole coupling in nonpolar nitride quantum dots due to Coulomb effects
    Schuh, K. and Barthel, S. and Marquardt, O. and Hickel, T. and Neugebauer, J. and Czycholl, G. and Jahnke, F.
    Applied Physics Letters 100 (2012)
    Optical properties of polar and nonpolar nitride quantum dots (QDs) are determined on the basis of a microscopic theory which combines a continuum elasticity approach to the polarization potential, a tight-binding model for the electronic energies and wavefunctions, and a many-body theory for the optical properties. For nonpolar nitride quantum dots, we find that optical absorption and emission spectra exhibit a weak ground-state oscillator strength in a single-particle calculation whereas the Coulomb configuration interaction strongly enhances the ground-state transitions. This finding sheds new light on existing discrepancies between previous theoretical and experimental results for these systems, as a weak ground state transition was predicted because of the spatial separation of the corresponding electron and hole state due to intrinsic fields whereas experimentally fast optical transitions have been observed. © 2012 American Institute of Physics.
    view abstractdoi: 10.1063/1.3688900
  • 2012 • 44 Unilateral interactions in granular packings: A model for the anisotropy modulus
    Shaebani, M.R. and Boberski, J. and Wolf, D.E.
    Granular Matter 14 265-270 (2012)
    Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results. © Springer-Verlag 2012.
    view abstractdoi: 10.1007/s10035-012-0329-0
  • 2012 • 43 Dispersions of silica nanoparticles in ionic liquids investigated with advanced rheology
    Wittmar, A. and Ruiz-Abad, D. and Ulbricht, M.
    Journal of Nanoparticle Research 14 (2012)
    The colloidal stabilities of dispersions of unmodified and surface-functionalized SiO 2 nanoparticles in hydrophobic and hydrophilic imidazolium-based ionic liquids were studied with advanced rheology at three temperatures (25, 100, and 200 °C). The rheological behavior of the dispersions was strongly affected by the ionic liquids hydrophilicity, by the nanoparticles surface, by the concentration of the nanoparticles in the dispersion as well as by the temperature. The unmodified hydrophilic nanoparticles showed a better compatibility with the hydrophilic ionic liquid. The SiO 2 surface functionalization with hydrophobic groups clearly improved the colloidal stability of the dispersions in the hydrophobic ionic liquid. The temperature increase was found to lead to a destabilization in all studied systems, especially at higher concentrations. The results of this study imply that ionic liquids with tailored properties could be used in absorbers directly after reactors for gas-phase synthesis of nanoparticles or/and as solvents for their further surface functionalization without agglomeration or aggregation. © Springer Science+Business Media B.V. 2012.
    view abstractdoi: 10.1007/s11051-011-0651-1
  • 2012 • 42 Nanoindentation of pseudoelastic NiTi containing Ni4Ti 3 precipitates
    Young, M.L. and Frotscher, M. and Bei, H. and Simon, T. and George, E.P. and Eggeler, G.
    International Journal of Materials Research 103 1434-1439 (2012)
    Depending on the processing method, pseudoelastic NiTi alloys can have small, lenticular Ni4Ti3 precipitates; however, the mechanical properties of these precipitates are not well understood. By performing nanoindentation with a spherical indenter, Ni4Ti 3 precipitates within a pseudoelastic NiTi alloy were examined. Scanning electron microscopy was used to examine the indents after nanoindentation. After unloading, the hardness and remnant depth ratios of the indents in the Ni4Ti3 precipitates, the NiTi matrix, and the "average" NiTi alloy were compared. To decouple the effects of elasticity from those of pseudoelasticity, similar nanoindentation experiments were performed on an NiAl sample and compared with results from the NiTi sample. © 2012 Carl Hanser Verlag GmbH & Co. KG.
    view abstractdoi: 10.3139/146.110792
  • 2012 • 41 First-principles study of the thermodynamic and elastic properties of eutectic Fe-Ti alloys
    Zhu, L.-F. and Friák, M. and Dick, A. and Grabowski, B. and Hickel, T. and Liot, F. and Holec, D. and Schlieter, A. and Kühn, U. and Eckert, J. and Ebrahimi, Z. and Emmerich, H. and Neugebauer, J.
    Acta Materialia 60 1594-1602 (2012)
    Ti-Fe alloys covering a broad range of Ti concentrations are studied using quantum-mechanical calculations. Employing density functional theory, we correctly reproduce selected key features of the experimental Fe-Ti phase diagram. Analyzing the electronic structure of the stable phases in detail provides an explanation for the thermodynamic stability in terms of the strong correlation between the composition and density of states at the Fermi energy (DOS(EF)). Based on this insight, we extend our study on both single-crystalline and polycrystalline elasticity of various Fe-Ti alloys by computing the compositional dependence of homogenized elastic constants. These quantities and their compositional dependence provide a direct explanation for the origin of the ductility and softness of the β-Ti(Fe) phase. Specifically, we find that this phase has an Fe concentration close to a threshold value connected with the onset of mechanical instability. By interlinking thermodynamic and mechanical stabilities we explain the softness and ductility of the β-Ti(Fe) in terms of a reduced mechanical stability that is connected with an increased DOS(EF) in the β-Ti(Fe). © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2011.11.046
  • 2011 • 40 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 abstractdoi: 10.1088/0031-9155/56/14/004
  • 2011 • 39 Dislocation-vacancy interactions in tungsten
    Chen, Z.M. and Mrovec, M. and Gumbsch, P.
    Modelling and Simulation in Materials Science and Engineering 19 (2011)
    We systematically investigate the interaction between a monovacancy and various lattice dislocations in body-centered cubic (bcc) metal tungsten by means of atomistic simulations. Two models with a different level of sophistication have been employed for the description of interatomic interactions - the empirical Finnis-Sinclair potential, which is a central-force scheme, and the bond-order potential, which is able to describe correctly unsaturated directional covalent bonds that are crucial for the cohesion and structure of bcc transition metals. Our simulation results show that the vacancy-dislocation interaction depends sensitively on the separation distance and orientation of the two defects. A comparison of the simulation results with the predictions of elasticity theory shows excellent agreement between the two approaches when the separation between the vacancy and the dislocation core is above 0.5 nm. Large deviations from the elastic limit are found at close distances, when the vacancy enters the dislocation core. © 2011 IOP Publishing Ltd.
    view abstractdoi: 10.1088/0965-0393/19/7/074002
  • 2011 • 38 Effect of magnetic nanoparticles on the surface rheology of surfactant films at the water surface
    Degen, P. and Wieland, D.C.F. and Leick, S. and Paulus, M. and Rehage, H. and Tolan, M.
    Soft Matter 7 7655-7662 (2011)
    The stability of fluid interfaces is important in many technical fields, e.g. suspensions, emulsions and foams. In this publication we investigated the influence of maghemite nanoparticles (γ-Fe<inf>2</inf>O<inf>3</inf>) on the surface stability of different surfactant films (SDS, CTAB, Brij 35). We investigated the interactions between nanoparticles and surfactant films by means of surface dilatation and surface shear rheological experiments. For further characterizations we used X-ray reflectivity (XRR) measurements, dynamic light scattering (DLS) and zeta (ζ)-potential measurements. For CTAB and more obvious for SDS it was found that at low to moderate surfactant concentrations, the viscoelasticity of the interface was increased drastically in the presence of the iron oxide nanoparticles. For films of Brij 35, however, the nanoparticles did not have any influence on the surface rheology. © The Royal Society of Chemistry 2011.
    view abstractdoi: 10.1039/c1sm05248a
  • 2011 • 37 Determining the elasticity of materials employing quantum-mechanical approaches from the electronic ground state to the limits of materials stability
    Friák, M. and Hickel, T. and Körmann, F. and Udyansky, A. and Dick, A. and Von Pezold, J. and Ma, D. and Kim, O. and Counts, W.A. and Šob, M. and Gebhardt, T. and Music, D. and Schneider, J. and Raabe, D. and Neugebauer, J.
    Steel Research International 82 86-100 (2011)
    Quantum-mechanical (so-called ab initio) calculations have achieved considerable reliability in predicting physical and chemical properties and phenomena. Due to their reliability they are becoming increasingly useful when designing new alloys or revealing the origin of phenomena in existing materials, also because these calculations are able to accurately predict basic material properties without experimental input. Due to the universal validity of fundamental quantum mechanics, not only ground-state properties, but also materials responses to external parameters can reliably be determined. The focus of the present paper is on ab initio approaches to the elasticity of materials. First, the methodology to determine single-crystalline elastic constants and polycrystalline moduli of ordered compounds as well as disordered alloys is introduced. In a second part, the methodology is applied on α-Fe, with a main focus on (i) investigating the influence of magnetism on its elasticity and phase stability and (ii) simulating extreme loading conditions that go up to the theoretical tensile strength limits and beyond. Copyright © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/srin.201000264
  • 2011 • 36 Achieving small structures in thin NiTi sheets for medical applications with water jet and micro machining: A comparison
    Frotscher, M. and Kahleyss, F. and Simon, T. and Biermann, D. and Eggeler, G.
    Journal of Materials Engineering and Performance 20 776-782 (2011)
    NiTi shape memory alloys (SMA) are used for a variety of applications including medical implants and tools as well as actuators, making use of their unique properties. However, due to the hardness and strength, in combination with the high elasticity of the material, the machining of components can be challenging. The most common machining techniques used today are laser cutting and electrical discharge machining (EDM). In this study, we report on the machining of small structures into binary NiTi sheets, applying alternative processing methods being well-established for other metallic materials. Our results indicate that water jet machining and micro milling can be used to machine delicate structures, even in very thin NiTi sheets. Further work is required to optimize the cut quality and the machining speed in order to increase the cost-effectiveness and to make both methods more competitive. © ASM International.
    view abstractdoi: 10.1007/s11665-010-9789-8
  • 2011 • 35 High temperature elastic properties of Mg-cordierite: Experimental studies and atomistic simulations
    Haussühl, E. and Vinograd, V.L. and Krenzel, T.F. and Schreuer, J. and Wilson, D.J. and Ottinger, J.
    Zeitschrift fur Kristallographie 226 236-253 (2011)
    The temperature dependence of the elastic stiffness coefficients of natural orthorhombic Mg-cordierite was studied between 295 K and 1573 K using resonant ultrasound spectroscopy. The measurements revealed a continuous decrease of all the elastic constants with increasing temperature. The bulk modulus softens from about 129(2) GPa at 295 K to 110(2) GPa at 1473 K. Irreversible anomalies in the temperature evolution of the resonance frequencies of certain eigenmodes were observed above 920 K due to the escape of volatiles and the occurrence of microcracks. However, the dehydrated samples still showed integrity on the macroscopic scale. Therefore, despite the occurrence of the micro-cracks, a reasonable quantitative analysis of the high-temperature RUS data of cordierite samples was still feasible. The thermal expansion was studied between 100 K and 1570 K using dilatometry. The new data are consistent with earlier experimental results and confirm the expansion of the a and b unit cell parameters and the contraction of the c parameter with increasing temperature. Possible contributions of the Al/Si disorder to the elastic properties of Mg-cordierite were estimated on the basis of force-field and quantum mechanical calculations. The behaviour of individual elastic stiffness coefficients was followed across the order/disorder transition by Monte Carlo simulations. The simulations predicted a decrease in the bulk modulus with increasing Al/Si disorder. However, this effect is much smaller than that observed experimentally. The measured decrease in the elastic stiffness coefficients is mainly due to phonon softening effects. © by Oldenbourg Wissenschaftsverlag, München.
    view abstractdoi: 10.1524/zkri.2011.1307
  • 2011 • 34 Mechanistic studies of Fc-PNA(·DNA) surface dynamics based on the kinetics of electron-transfer processes
    Hüsken, N. and Gȩbala, M. and La Mantia, F. and Schuhmann, W. and Metzler-Nolte, N.
    Chemistry - A European Journal 17 9678-9690 (2011)
    N-Terminally ferrocenylated and C-terminally gold-surface-grafted peptide nucleic acid (PNA) strands were exploited as unique tools for the electrochemical investigation of the strand dynamics of short PNA(·DNA) duplexes. On the basis of the quantitative analysis of the kinetics and the diffusional characteristics of the electron-transfer process, a nanoscopic view of the Fc-PNA(·DNA) surface dynamics was obtained. Loosely packed, surface-confined Fc-PNA single strands were found to render the charge-transfer process of the tethered Fc moiety diffusion-limited, whereas surfaces modified with Fc-PNA·DNA duplexes exhibited a charge-transfer process with characteristics between the two extremes of diffusion and surface limitation. The interplay between the inherent strand elasticity and effects exerted by the electric field are supposed to dictate the probability of a sufficient approach of the Fc head group to the electrode surface, as reflected in the measured values of the electron-transfer rate constant, k 0. An in-depth understanding of the dynamics of surface-bound PNA and PNA·DNA strands is of utmost importance for the development of DNA biosensors using (Fc-)PNA recognition layers. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/chem.201003764
  • 2011 • 33 FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
    Klawonn, A. and Neff, P. and Rheinbach, O. and Vanis, S.
    ESAIM: Mathematical Modelling and Numerical Analysis 45 563-602 (2011)
    We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP:= sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is formulated and a convergence estimate is provided for the special case that P-T = ∇ψ is a gradient. It is shown that the condition number depends only quadratic-logarithmically on the number of unknowns of each subdomain. The dependence of the constants of the bound on P is highlighted. Numerical examples confirm our theoretical findings. Promising results are also obtained for settings which are not covered by our theoretical estimates. © EDP Sciences, SMAI, 2010.
    view abstractdoi: 10.1051/m2an/2010067
  • 2011 • 32 Rheological properties of capsule membranes
    Leick, S. and Degen, P. and Rehage, H.
    Chemie-Ingenieur-Technik 83 1300-1304 (2011)
    By using the spinning- and squeezing-capsule method it is possible to characterize the rheological properties of capsule membranes. On the basis of a capsule model system, it could be shown that the incorporation of solid particles in the gel membrane of liquid filled capsules leads to a significant increase of the mechanical stability as well as the two dimensional Young modulus. A combination of both methods enabled the calculation of the two dimensional Poisson ratio of the membrane material. © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/cite.201100043
  • 2011 • 31 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 abstractdoi: 10.1109/TMI.2011.2139222
  • 2011 • 30 A flexible, plane-wave-based formulation of continuum elasticity and multiband k·p models
    Marquardt, O. and Schulz, S. and O'Reilly, E.P. and Freysoldt, C. and Boeck, S. and Hickel, T. and Neugebauer, J.
    Proceedings of the International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 111-112 (2011)
    We present a highly flexible, plane-wave based formulation of continuum elasticity and multiband k·p-formalism to study the elastic and electronic properties of semiconductor nanostructures. This approach has been implemented in the framework of the density functional theory (DFT) software library S/Phi/nX [1] and allows the investigation of arbitrary-shaped nanostructures such as quantum wells, wires and dots consisting of various materials. Moreover, our approach grants the flexibility to employ user-generated k·p Hamiltonians suited to the requirements of the study regarding accuracy and computational costs. © 2011 IEEE.
    view abstractdoi: 10.1109/NUSOD.2011.6041165
  • 2011 • 29 Growth process, characterization, and modeling of electronic properties of coupled InAsSbP nanostructures
    Marquardt, O. and Hickel, T. and Neugebauer, J. and Gambaryan, K.M. and Aroutiounian, V.M.
    Journal of Applied Physics 110 (2011)
    Quaternary III-V InAsSbP quantum dots (QDs) have been grown in the form of cooperative InAsSb/InAsP structures using a modified version of the liquid phase epitaxy. High resolution scanning electron microscopy, atomic force microscopy, and Fourier-transform infrared spectrometry were used to investigate these so-called nano-camomiles, mainly consisting of a central InAsSb QD surrounded by six InAsP-QDs, that shall be referred to as leaves in the following. The observed QDs average density ranges from 0.8 to 2 × 109 cm -2, with heights and widths dimensions from 2 to 20 nm and 5 to 45 nm, respectively. The average density of the leaves is equal to (6-10) × 109 cm-2 with dimensions of approx. 5 to 40 nm in width and depth. To achieve a first basic understanding of the electronic properties, we have modeled these novel nanostructures using second-order continuum elasticity theory and an eight-band k p model to calculate the electronic structure. Our calculations found a clear localization of hole states in the central InAsSb dot. The localization of electron states, however, was found to be weak and might thus be easily influenced by external electric fields or strain. © 2011 American Institute of Physics.
    view abstractdoi: 10.1063/1.3624621
  • 2011 • 28 A thermodynamically and variationally consistent class of damage-type cohesive models
    Mosler, J. and Scheider, I.
    Journal of the Mechanics and Physics of Solids 59 1647-1668 (2011)
    A novel class of cohesive constitutive models suitable for the analysis of material separation such as that related to cracks, shear bands or delamination processes is presented. The proposed framework is based on a geometrically exact description (finite deformation) and it naturally accounts for material anisotropies. For that purpose, a Helmholtz energy depending on evolving structural tensors is introduced. In sharp contrast to previously published anisotropic cohesive models with finite strain kinematics based on a spatial description, all models belonging to the advocated class are thermodynamically consistent, i.e., they are rigorously derived by applying the Coleman and Noll procedure. Although this procedure seems nowadays to be standard for stressstrain-type constitutive laws, this is not the case for cohesive models at finite strains. An interesting new finding from the Coleman and Noll procedure is the striking analogy between cohesive models and boundary potential energies. This analogy gives rise to the introduction of additional stress tensors which can be interpreted as deformational surface shear. To the best knowledge of the authors, those stresses which are required for thermodynamical consistency at finite strains, have not been taken into account in existing models yet. Furthermore, the additional stress tensors can result in an effective traction-separation law showing a non-trivial stress-free configuration consistent with the underlying Helmholtz energy. This configuration is not predicted by previous models. Finally, the analogy between cohesive models and boundary potential energies leads to a unique definition of the controversially discussed fictitious intermediate configuration. More precisely, traction continuity requires that the interface geometry with respect to the deformed configuration has to be taken as the average of both sides. It will be shown that the novel class of interface models does not only fulfill the second law of thermodynamics, but also it shows an even stronger variational structure, i.e., the admissible states implied by the novel model can be interpreted as stable energy minimizers. This variational structure is used for deriving a variationally consistent numerical implementation. © 2011 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.jmps.2011.04.012
  • 2011 • 27 Robustness and optimal use of design principles of arthropod exoskeletons studied by ab initio-based multiscale simulations
    Nikolov, S. and Fabritius, H. and Petrov, M. and Friák, M. and Lymperakis, L. and Sachs, C. and Raabe, D. and Neugebauer, J.
    Journal of the Mechanical Behavior of Biomedical Materials 4 129-145 (2011)
    Recently, we proposed a hierarchical model for the elastic properties of mineralized lobster cuticle using (i) ab initio calculations for the chitin properties and (ii) hierarchical homogenization performed in a bottom-up order through all length scales. It has been found that the cuticle possesses nearly extremal, excellent mechanical properties in terms of stiffness that strongly depend on the overall mineral content and the specific microstructure of the mineral-protein matrix. In this study, we investigated how the overall cuticle properties changed when there are significant variations in the properties of the constituents (chitin, amorphous calcium carbonate (ACC), proteins), and the volume fractions of key structural elements such as chitin-protein fibers. It was found that the cuticle performance is very robust with respect to variations in the elastic properties of chitin and fiber proteins at a lower hierarchy level. At higher structural levels, variations of design parameters such as the volume fraction of the chitin-protein fibers have a significant influence on the cuticle performance. Furthermore, we observed that among the possible variations in the cuticle ingredients and volume fractions, the experimental data reflect an optimal use of the structural variations regarding the best possible performance for a given composition due to the smart hierarchical organization of the cuticle design. © 2010 Elsevier Ltd.
    view abstractdoi: 10.1016/j.jmbbm.2010.09.015
  • 2011 • 26 Ab initio study of the modification of elastic properties of α-iron by hydrostatic strain and by hydrogen interstitials
    Psiachos, D. and Hammerschmidt, T. and Drautz, R.
    Acta Materialia 59 4255-4263 (2011)
    The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of α-iron is investigated using ab initio density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic shear moduli. For the key slip planes in α-iron, [11̄0] and [112̄], we find a shear modulus reduction of approximately 1.6% per at.% H. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2011.03.041
  • 2011 • 25 Structure and mechanical properties of TiAlN-WNx thin films
    Reeswinkel, T. and Sangiovanni, D.G. and Chirita, V. and Hultman, L. and Schneider, J.M.
    Surface and Coatings Technology 205 4821-4827 (2011)
    A combinatorial method was employed to grow TiAlN-WNx films by DC sputtering as well as by High Power Pulsed Magnetron Sputtering (HPPMS) where the W concentration was varied between 10-52. at.% and 7-54. at.%, respectively. Experiments were paired with ab initio calculations to investigate the correlation between composition, structure, and mechanical properties. During all depositions the time averaged power was kept constant. As the W concentration was increased, the lattice parameter of cubic TiAlN-WNx films first increased and then decreased for W concentrations above ≈. 29. at.% (DCMS) and ≈. 27. at.% (HPPMS) as the N concentration decreased. Calculations helped to attribute the increase to the substitution of Ti and Al by W and the decrease to the presence of N vacancies. Young's modulus and hardness were around 385-400. GPa and 29-31. GPa for DCMS and 430-480. GPa and 34-38. GPa for HPPMS, respectively, showing no significant trend as the W concentration was increased, whereas calculations showed a continuous decrease in Young's modulus from 440 to 325. GPa as the W concentration was increased from 0 to 37.5. at.%. The presence of N vacancies was shown to increase the calculated Young's modulus. Hence, the relatively constant values measured may be understood based on N vacancy formation as the W concentration was increased. HPPMS-deposited films exceed DCMS films in Young's modulus and hardness, which may be a consequence of the larger degree of ionization in the HPPMS plasma. It is reasonable to assume that especially the ionized film forming species may contribute towards film densification and N vacancy formation. © 2011 Elsevier B.V.
    view abstractdoi: 10.1016/j.surfcoat.2011.04.066
  • 2011 • 24 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 abstractdoi: 10.1007/s11665-010-9797-8
  • 2011 • 23 Studies on the cycling, processing and programming of an industrially applicable shape memory polymer Tecoflex® (or TFX EG 72D)
    Schmidt, C. and Chowdhury, A.M.S. and Neuking, K. and Eggeler, G.
    High Performance Polymers 23 300-307 (2011)
    The present investigations were undertaken to find out whether and how often cycling, processing and programming can be repeated, whether repeated programming affects the one way effect and how much irreversible strain the shape memory polymeric material accumulates at a particular temperature. The effect was investigated in dependence of different stress levels, and the effect of both recovery temperature and recovery time was considered. As a model material the commercially and industrially applicable amorphous shape memory polymer Tecoflex® was examined and subjected to 50 programming cycles. Tecoflex® is characterized by a glass transition temperature, Tg, of 74 °C, above which it looses all its strength. During tensile testing at 20 °C (T < Tg), stresses a steady increase to 26 MPa as strains approached the rupture strain of 25%. It is observed that at 60 °C (T < Tg, but near Tg) the material can be strained to more than 2500% before rupture occurs while stresses slowly increase to values less than 0.3 MPa. It turns out that programming, cooling, unloading and heating to trigger the one way effect causes an increase of irreversible strain that is associated with a corresponding decrease of the intensity of the one way effect during the first thermomechanical cycles. © The Author(s) 2011.
    view abstractdoi: 10.1177/0954008311405245
  • 2011 • 22 A new mixed finite element based on different approximations of the minors of deformation tensors
    Schröder, J. and Wriggers, P. and Balzani, D.
    Computer Methods in Applied Mechanics and Engineering 200 3583-3600 (2011)
    Finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking-free behavior for incompressible materials, a good bending performance and accurate solutions for coarse meshes need still attention. Therefore, the main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible finite elasticity. Based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line-, area- and volume elements, as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed. Due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form. Examples show the performance and robustness of the element. © 2011 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2011.08.009
  • 2011 • 21 Wetting morphologies and their transitions in grooved substrates
    Seemann, R. and Brinkmann, M. and Herminghaus, S. and Khare, K. and Law, B.M. and McBride, S. and Kostourou, K. and Gurevich, E. and Bommer, S. and Herrmann, C. and Michler, D.
    Journal of Physics Condensed Matter 23 (2011)
    When exposed to a partially wetting liquid, many natural and artificial surfaces equipped with complex topographies display a rich variety of liquid interfacial morphologies. In the present article, we focus on a few simple paradigmatic surface topographies and elaborate on the statics and dynamics of the resulting wetting morphologies. It is demonstrated that the spectrum of wetting morphologies increases with increasing complexity of the groove structure. On elastically deformable substrates, additional structures in the liquid morphologies can be observed, which are caused by deformations of the groove geometry in the presence of capillary forces. The emergence of certain liquid morphologies in grooves can be actively controlled by changes in wettability and geometry. For electrically conducting solid substrates, the apparent contact angle can be varied by electrowetting. This allows, depending on groove geometry, a reversible or irreversible transport of liquid along surface grooves. In the case of irreversible liquid transport in triangular grooves, the dynamics of the emerging instability is sensitive to the apparent hydrodynamic slip at the substrate. On elastic substrates, the geometry can be varied in a straightforward manner by stretching or relaxing the sample. The imbibition velocity in deformable grooves is significantly reduced compared to solid grooves, which is a result of the microscopic deformation of the elastic groove material close to the three phase contact line. © 2011 IOP Publishing Ltd.
    view abstractdoi: 10.1088/0953-8984/23/18/184108
  • 2011 • 20 Analysis of a modified first-order system least squares method for linear elasticity with improved momentum balance
    Starke, G. and Schwarz, A. and Schröder, J.
    SIAM Journal on Numerical Analysis 49 1006-1022 (2011)
    A modified first-order system least squares formulation for linear elasticity, obtained by adding the antisymmetric displacement gradient in the test space, is analyzed. This approach leads to surprisingly small momentum balance error compared to standard least squares approaches. It is shown that the modified least squares formulation is well posed and its performance is illustrated by adaptive finite element computation based on using a closely related least squares functional as a posteriori error estimator. The results of our numerical computations show that, for the modified least squares approach, the momentum balance error converges at a much faster rate than the overall error. We prove that this is due to a strong connection of the stress approximation to that obtained from a mixed formulation based on the Hellinger-Reissner principle (with exact local momentum balance). The practical significance is that our proposed approach is almost momentum-conservative at a smaller number of degrees of freedom than mixed approximations with exact local momentum balance. © 2011 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/100799149
  • 2011 • 19 Efficient solvers for mixed finite element discretizations of nonlinear problems in solid mechanics
    Starke, G.
    Lecture Notes in Applied and Computational Mechanics 57 201-209 (2011)
    A common goal of our projects in the three phases of GRK 615 was, among other issues, the development of efficient solvers for different mixed finite element approaches to nonlinear problems in solid mechanics. In the first phase, the PEERS ('plane elasticity element with reduced symmetry') was studied for elastoplastic deformationmodels. The nonlinear algebraic systems were solved with a fixed point iteration leading to a linear elasticity problem in each step which was treated by suitable constraint preconditioners.The treatment of elastoplastic deformations by least squaresmixed finite elementmethodswas the subject of the project in the second phase. In particular, appropriate regularizations for the non-smoothness of the nonlinear problems were investigated. In the third phase, the least squares finite element formulation of contact problems was studied. For the Signorini problem, the quadratic minimization problems under affine constraints were treated by an active set strategy. Preconditioned conjugate gradient iterations for a null space formulation were used for the systems arising in each step. © 2011 Springer-Verlag Berlin Heidelberg.
    view abstractdoi: 10.1007/978-3-642-20490-6-8
  • 2011 • 18 Pollen characterization and identification by elastically scattered light
    Surbek, M. and Esen, C. and Schweiger, G. and Ostendorf, A.
    Journal of Biophotonics 4 49-56 (2011)
    The authors recorded the elastic light-scattering pattern of pollen over a large spatial angle range to investigate the potential light scattering for pollen identification. The scattering from elm, hazel, birch, chestnut, willow, sunflower, ragweed and pine was measured. The scattering patterns show distinct differences that can be used for the classification of pollen with simple algorithms. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/jbio.200900088
  • 2011 • 17 High-throughput characterization of mechanical properties of Ti-Ni-Cu shape memory thin films at elevated temperature
    Zarnetta, R. and Kneip, S. and Somsen, C. and Ludwig, Al.
    Materials Science and Engineering A 528 6552-6557 (2011)
    Hardness and Young's moduli values for TixNi90-xCu10 (37at.%< x< 67at.%) thin films from a continuous composition spread type materials library, annealed at 500°C for 1h, were determined at room temperature (martensitic state) and 80°C (austenitic state) using high-throughput nanoindentation experiments. These values are found to increase as the compositions deviate from Ti contents close to 50at.%. The increases in hardness is correlated to the presence of Ti-rich and (Ni,Cu)-rich precipitates resulting in precipitate hardening and grain size refinement (Hall-Petch effect). The increase of the Young's moduli is rationalized by considering the significantly higher Young's moduli of the different precipitate phases and applying the rule of mixtures. The contributions of the precipitate phases and the matrix to the combined Young's modulus were estimated by evaluating the load-displacement curves in detail. The obtained results are in good agreement with the Young's moduli determined from thin film curvature measurements [R. Zarnetta et al., Smart Mater. Struct. 19 (2010) 65032]. Thus, the experimental restrictions for nanoindentation experiments at elevated temperatures are concluded to not adversely affect the validity of the results. © 2011 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2011.05.006
  • 2010 • 16 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 abstractdoi: 10.1007/s00419-009-0379-x
  • 2010 • 15 Al-matrix composite materials reinforced by Al-Cu-Fe particles
    Bonneville, J. and Laplanche, G. and Joulain, A. and Gauthier-Brunet, V. and Dubois, S.
    Journal of Physics: Conference Series 240 (2010)
    Al-matrix material composites were produced using hot isostatic pressing technique, starting with pure Al and icosahedral (i) Al-Cu-Fe powders. Depending on the processing temperature, the final reinforcement particles are either still of the initial i-phase or transformed into the tetragonal ω-Al0 0.70Cu0.20Fe0.10 crystalline phase. Compression tests performed in the temperature range 293K - 823K on the two types of composite, i.e. Al/i and Al/ω, indicate that the flow stress of both composites is strongly temperature dependent and exhibit distinct regimes with increasing temperature. Differences exist between the two composites, in particul ar in yield stress values. In the low temperatureregime (T ≤ 570K), the yield stress of the Al/ω composite is nearly 75% higher than that of the Al/i composite, while for T &gt; 570K both composites exhibit similar yield stress values. The results are interpreted in terms of load transfer contribution between the matrix and the reinforcement particles and elementary dislocation mechanisms in the Al matrix. © 2010 IOP Publishing Ltd.
    view abstractdoi: 10.1088/1742-6596/240/1/012013
  • 2010 • 14 Influence of heat treatment and microstructure on the tensile pseudoelastic response of an Ni-rich NiTi shape memory alloy
    Bujoreanu, L.-G. and Young, M.L. and Gollerthan, S. and Somsen, C. and Eggeler, G.
    International Journal of Materials Research 101 623-630 (2010)
    The influence of microstructure on the stress-strain behavior of an Ni-rich NiTi shape memory alloy is examined. Specimens cut from a large-diameter bar of Ni50.7Ti49.3 shape memory alloy were analyzed in two states: (i) annealed and (ii) annealed and aged. The annealed state shows a fully austenitic structure with no precipitates and no distortions caused by residual stresses. The annealed and aged state has coherent Ni 4Ti3 particles precipitated in the proximity of the austenite grain boundaries. The size of the precipitates increases moving away from the grain boundaries toward the grain interiors. The evolution of the two states in the stress-strain-temperature space has been analyzed using tensile specimens with special geometry. Due to the complex effects of the coherent precipitates, the specimens in the aged state exhibited lower stress plateaus in the tensile loading-unloading curves, which enabled the occurrence of transformation pseudoelasticity from room temperature to 333 K. © 2010 Carl Hanser Verlag.
    view abstractdoi: 10.3139/146.110317
  • 2010 • 13 Using Ab initio calculations in designing bcc MgLi-X alloys for ultra-lightweight applications
    Counts, W.A. and Friák, M. and Raabe, D. and Neugebauer, J.
    Advanced Engineering Materials 12 1198-1205 (2010)
    Body centered cubic (bcc) Mg-Li-based alloys are a promising light-weight structural material. In order to tailor the Mg-Li composition with respect to specific industrial requirements, systematic materials-design concepts need to be developed and applied. Quantum-mechanical calculations are increasingly employed when designing new alloys as they accurately predict basic thermodynamic, structural, and functional properties using only the atomic composition as input. We have therefore performed a quantum-mechanical study using density functional theory (DFT) to systematically explore fundamental physical properties of a broad set of bcc MgLi-based compounds. These DFT-determined properties are used to calculate engineering parameters such as (i) the specific Young's modulus (Y/ρ) or (ii) the bulk over shear modulus ratio (B/G) which allow differentiating between brittle and ductile behavior. As we have recently shown, it is not possible to increase both specific Young's modulus, as a measure of strength, and B/G ratio, as a proxy for ductility, by changing only the composition in the binary bcc Mg-Li system. In an attempt to bypass such fundamental materials-design limitations, a large set of MgLi-X substitutional ternaries derived from stoichiometric MgLi with CsCl structure are studied. Motivated by the fact that for Mg-Li alloys (i) 3rd row Si and Al and (ii) 4th row Zn are industrially used as alloying elements, we probe the alloying performance of the 3rd (Na, Al, Si, P, S, Cl) and 4th row transition metal (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) elements. The studied solutes offer a variety of properties but none is able to simultaneously improve both specific Young's modulus and ductility. Therefore, in order to explore the alloying performance of yet a broader set of solutes, we predict the bulk modulus of MgX and LiX B2-compounds running over 40 different elements. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA.
    view abstractdoi: 10.1002/adem.201000225
  • 2010 • 12 Ab Initio guided design of bcc ternary Mg-Li-X (X=Ca, Al, Si, Zn, Cu) alloys for ultra-lightweight applications
    Counts, W.A. and Friák, M. and Raabe, D. and Neugebauer, J.
    Advanced Engineering Materials 12 572-576 (2010)
    Ab initio calculations are becoming increasingly important for designing new alloys as these calculations can accurately predict basic structural, mechanical, and functional properties using only the atomic composition as a basis. In this paper, fundamental physical properties (like formation energies and elastic constants) of a set of bcc Mg-Li and Mg-Li-based compounds are calculated using density functional theory (DFT). These DFT-determined properties are in turn used to calculate engineering parameters such as (i) specific Young's modulus (Y/p) or (ii) shear over bulk modulus ratio (G/B) differentiating between brittle and ductile behavior. These parameters are then used to identify those alloys that have optimal mechanical properties for lightweight structural applications. First, in case of the binary Mg-Li system, an Ashby map containing Y/r versus G/B shows that it is not possible to increase Y/r without simultaneously increasing G/B (i.e., brittleness) by changing only the composition of a binary alloy. In an attempt to bypass such a fundamental materials-design limitation, a set of Mg-Li-X ternaries (X=Ca, Al, Si, Cu, Zn) based on stoichiometric Mg-Li with CsCl structure was studied. It is shown that none of the studied ternary solutes is able to simultaneously improve both specific Young's modulus and ductility. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/adem.200900308
  • 2010 • 11 Ab initio study of thermodynamic, structural, and elastic properties of Mg-substituted crystalline calcite
    Elstnerová, P. and Friák, M. and Fabritius, H.O. and Lymperakis, L. and Hickel, T. and Petrov, M. and Nikolov, S. and Raabe, D. and Ziegler, A. and Hild, S. and Neugebauer, J.
    Acta Biomaterialia 6 4506-4512 (2010)
    Arthropoda, which represent nearly 80% of all known animal species, are protected by an exoskeleton formed by their cuticle. The cuticle represents a hierarchically structured multifunctional biocomposite based on chitin and proteins. Some groups, such as Crustacea, reinforce the load-bearing parts of their cuticle with calcite. As the calcite sometimes contains Mg it was speculated that Mg may have a stiffening impact on the mechanical properties of the cuticle (Becker et al., Dalton Trans. (2005) 1814). Motivated by these facts, we present a theoretical parameter-free quantum-mechanical study of the phase stability and structural and elastic properties of Mg-substituted calcite crystals. The Mg-substitutions were chosen as examples of states that occur in complex chemical environments typical for biological systems in which calcite crystals contain impurities, the role of which is still the topic of debate. Density functional theory calculations of bulk (Ca,Mg)CO3 were performed employing 30-atom supercells within the generalized gradient approximation as implemented in the Vienna Ab-initio Simulation Package. Based on the calculated thermodynamic results, low concentrations of Mg atoms are predicted to be stable in calcite crystals in agreement with experimental findings. Examining the structural characteristics, Mg additions nearly linearly reduce the volume of substituted crystals. The predicted elastic bulk modulus results reveal that the Mg substitution nearly linearly stiffens the calcite crystals. Due to the quite large size-mismatch of Mg and Ca atoms, Mg substitution results in local distortions such as off-planar tilting of the CO32- group. © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actbio.2010.07.015
  • 2010 • 10 Combined ab initio and experimental study of structural and elastic properties of Fe3Al-based ternaries
    Friák, M. and Deges, J. and Krein, R. and Frommeyer, G. and Neugebauer, J.
    Intermetallics 18 1310-1315 (2010)
    A combined theoretical and experimental study of thermodynamical, structural, and elastic properties of Fe3Al-based ternary alloys is presented. The theoretical part is based on a scale-bridging, multi-disciplinary combination of (i) thermodynamic aspects of the site preference and (ii) elastic stiffness data for substitutional ternary elements in Fe3Al single crystals, as determined by parameter-free first-principles calculations, and (iii) Hershey's homogenization model for the polycrystalline aggregates within the frame of linear elasticity theory. The approach was employed in order to explore the relation between chemical composition and both structural and elastic properties of Fe3Al ternary alloys containing the selected substituents (Ti, V, W, Cr and Si). The ab initio calculations employ density-functional theory (DFT) and the generalized gradient approximation (GGA). The determined elastic constants are used to calculate the elastic moduli, such as the Young's and bulk modulus. The theoretical results are compared to both literature data and novel impulse excitation measurements. Specifically, for Fe3Al-Ti alloys with low to medium Ti concentrations, an unexpected non-linear compositional dependence of the polycrystalline Young's modulus was found experimentally. The origin of this behavior is analyzed and discussed based on our theoretical results. © 2010 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.intermet.2010.02.025
  • 2010 • 9 Synthesis and characterization of lamellar and fibre-reinforced NiAl-Mo and NiAl-Cr
    Haenschke, T. and Gali, A. and Heilmaier, M. and Krüger, M. and Bei, H. and George, E.P.
    Journal of Physics: Conference Series 240 (2010)
    Directionally solidified (DS) alloys of the eutectic systems NiAl-10Mo and NiAl-34Cr (at.%) are potential candidates for high-temperature structural applications. Here, these alloys were first arc-melted and drop-cast. Thereafter, they were directionally solidified (DS) at growth rates of 20 and 80 mm/h while rotating at a fixed rotation speed of 60 revolutions per minute. Specimens of the DS alloys were tested in three-point-bending and uniaxial compression to obtain mechanical properties, including the ductile to brittle transition temperature (DBTT). For the NiAl-Cr system DBTT was found to be around 300 °C. Microstructural observations revealed that in the section perpendicular to the growth direction a uniform distribution of fibres was observed. The expected decrease of the fibre diameter with increasing growth rate was not observed. Instead, the fibre diameter slightly increased with increasing crystal growth rates. First compression tests were performed to get insights into the creep behaviour of these fibre-reinforced microstructures. © 2010 IOP Publishing Ltd.
    view abstractdoi: 10.1088/1742-6596/240/1/012063
  • 2010 • 8 Development of a method to determine Burgers vectors from atomistic data
    Hua, J. and Hartmaier, A.
    Journal of Physics: Conference Series 240 (2010)
    Large-scale molecular dynamics simulations have been widely used to investigate the mechanical behaviour of materials. But complex datasets, involving the positions of millions of atoms, generated during the simulations make quantitative data analysis quite a challenge. This paper presents a novel method to determine not only dislocations in the crystal, but also to quantify their Burgers vectors. This is achieved by combining geometrical methods to determine the atoms lying in the dislocations cores, like for example the common neighbour analysis or the bond angle analysis, with the slip vector analysis. The first methods are used to filter out the atoms lying in undisturbed regions of the crystal; the latter method yields the relative slip of the remaining atoms and thus indicates the Burgers vector of those atoms lying in the dislocation cores. The validity of the method is demonstrated here on a single edge dislocation in a relatively small sample. Furthermore a way will be sketched how this analysis can be used to determine densities of statistically stored and geometrically necessary dislocations, respectively. Hence, this method can be expected to provide valuable input for strain gradient plasticity models. © 2010 IOP Publishing Ltd.
    view abstractdoi: 10.1088/1742-6596/240/1/012010
  • 2010 • 7 Highly scalable parallel domain decomposition methods with an application to biomechanics
    Klawonn, A. and Rheinbach, O.
    ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 90 5-32 (2010)
    Highly scalable parallel domain decomposition methods for elliptic partial differential equations are considered with a special emphasis on problems arising in elasticity. The focus of this survey article is on Finite Element Tearing and Interconnecting (FETI) methods, a family of nonoverlapping domain decomposition methods where the continuity between the subdomains, in principle, is enforced by the use of Lagrange multipliers. Exact onelevel and dual-primal FETI methods as well as related inexact dual-primal variants are described and theoretical convergence estimates are presented together with numerical results confirming the parallel scalability properties of these methods. New aspects such as a hybrid onelevel FETI/FETI-DP approach and the behavior of FETI-DP for anisotropic elasticity problems are presented. Parallel and numerical scalability of the methods for more than 65 000 processor cores of the JUGENE supercomputer is shown. An application of a dual-primal FETI method to a nontrivial biomechanical problem from nonlinear elasticity, modeling arterial wall stress, is given, showing the robustness of our domain decomposition methods for such problems. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/zamm.200900329
  • 2010 • 6 L21-ordered Fe-Al-Ti alloys
    Krein, R. and Friak, M. and Neugebauer, J. and Palm, M. and Heilmaier, M.
    Intermetallics 18 1360-1364 (2010)
    Fe-Al-Ti alloys with the ordered L21-structure (Heusler phase) belong to the few Fe-Al-based alloys which show comparably high-strength at high temperatures, e.g. at 800 °C. However, like many other high-temperature materials based on intermetallics they show limited ductility even at high temperatures. In order to further explore the possibilities in increasing their strength and ductility, alloys with four different microstructures, i.e. single-phase L21, L21 with incoherent precipitates of TiB2 or Laves phase, and coherent L21 + A2, were produced. Also, the influence of alloying with Cr and B has been investigated. The Young's modulus of Fe-25Al-20Ti-4Cr (at.%) in dependence of temperature up to 900 °C has been determined and results of the compressive flow stress, creep strength and brittle-toductile transition temperatures (BDTT) are summarised and compared to those of binary Fe3Al (D03), Fe-Al-Ti-based alloys, and some commercial alloys. © 2010 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.intermet.2009.12.036
  • 2010 • 5 Plane-wave implementation of the real-space k ṡ p formalism and continuum elasticity theory
    Marquardt, O. and Boeck, S. and Freysoldt, C. and Hickel, T. and Neugebauer, J.
    Computer Physics Communications 181 765-771 (2010)
    In this work we demonstrate how second-order continuum elasticity theory and an eight-band k ṡ p model can be implemented in an existing density functional theory (DFT) plane-wave code. The plane-wave formulation of these two formalisms allows for an accurate and efficient description of elastic and electronic properties of semiconductor nanostructures such as quantum dots, wires, and films. Gradient operators that are computationally expensive in a real-space formulation can be calculated much more efficiently in reciprocal space. The accuracy can be directly controlled by the plane-wave cutoff. Furthermore, minimization schemes typically available in plane-wave DFT codes can be applied straightforwardly with only a few modifications to a plane-wave formulation of these continuum models. As an example, the elastic and electronic properties of a III-nitride quantum dot system are calculated. © 2009 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.cpc.2009.12.009
  • 2010 • 4 An in situ tensile tester for studying electrochemical repassivation behavior: Fabrication and challenges
    Neelakantan, L. and Schönberger, B. and Eggeler, G. and Hassel, A.W.
    Review of Scientific Instruments 81 (2010)
    An in situ tensile rig is proposed, which allows performing electrochemical (repassivation) experiments during dynamic mechanical testing of wires. Utilizing the basic components of a conventional tensile tester, a custom-made minitensile rig was designed and fabricated. The maximal force that can be measured by the force sensor is 80 N, with a sensitivity of 0.5 mV/V. The maximum travel range of the crosshead induced by the motor is 10 mm with a minimum step size of 0.5 nm. The functionality of the tensile test rig was validated by investigating Cu and shape memory NiTi wires. Wires of lengths between 40 and 50 mm with varying gauge lengths can be tested. An interface between wire and electrochemical setup (noncontact) with a smart arrangement of electrodes facilitated the electrochemical measurements during tensile loading. Preliminary results on the repassivation behavior of Al wire are reported. © 2010 American Institute of Physics.
    view abstractdoi: 10.1063/1.3292685
  • 2010 • 3 The exoskeleton of the American lobster- From texture to anisotropic properties
    Raue, L. and Klein, H. and Raabe, D.
    Solid State Phenomena 160 287-294 (2010)
    The exoskeleton of the crustacean Homarus americanus, the American lobster, is a biological multiphase composite consisting of a crystalline organic matrix (chitin), crystalline biominerals (calcite), amorphous calcium carbonate and proteins. One special structural aspect is the occurrence of pronounced crystallographic orientations and resulting directional anisotropic mechanical properties. The crystallographic textures of chitin and calcite have been measured by wide-angle Bragg diffraction, calculating the Orientation Distribution Function (ODF) from pole figures by using the series expansion method according to Bunge. A general strong relationship can be established between the crystallographic and the resulting mechanical and physical properties. © (2010) Trans Tech Publications.
    view abstractdoi: 10.4028/
  • 2010 • 2 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 abstractdoi: 10.1002/nme.2692
  • 2010 • 1 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 abstractdoi: 10.1088/1742-6596/240/1/012140