Modelling & Simulation


Multiscale modeling and computational simulation of short fiber reinforced composite materials and structures

Jithender J. Timothy, Structural Mechanics/Ruhr University Bochum, Bochum, Germany
Yijian Zhan, Structural Mechanics/Ruhr University Bochum, Bochum, Germany
Günther Meschke, Structural Mechanics/Ruhr University Bochum, Bochum, Germany

We propose a multiscale model for short fiber reinforced composites (SFRC) based upon a combination of semi-analytical and computational sub-models specified at multiple scales. The model architecture allows to follow the influence of design variables at lower scales, such as the fiber type, fiber density and orientation, on the macroscopic behaviour of structures made of SFRC and, consequently, enables the optimization of the material design w.r.t strength, stiffness and ductility. At the scale of the single fiber, a semi-analytical model is developed that characterizes the microslip behaviour at the interface between the matrix and the fiber in terms of the bond characteristics, fiber geometry and the composite stresses. The influence of fiber bundles on microcrack bridging and arrest is taken into account within the framework of linear elastic fracture mechanics. Upscaling to the macroscopic level is achieved using continuum micromechanics [3].

Selected numerical experiments provide insight into the role of the interface property, resulting – on the macroscopic level - in a brittle, softening behaviour in case of weak bond and a rather ductile, hardening behaviour in case of a relatively strong interface bond that is completely described by simple microslip laws. For the finite element analyses of failure behaviour at the structural level, the so-called 'interface solid element' (ISE) is used to represent the cracking process. The softening behaviour of ISE is governed by the crack bridging law obtained above [2]. An implicit-explicit integration scheme is implemented to enhance the robustness of computation. The performance of the model is demonstrated by means of selected validation analyses of benchmark tests.

[1] Timothy, J. J. & Meschke, G., A Continuum Micromechanics-LEFM model for Fiber Reinforced Concrete. Computational Modelling of Concrete and Concrete Structures (EURO-C 2014). CRC Press, 327-333, 2014.
[2] Zhan, Y. & Meschke, G., Analytical model for the pullout behavior of straight and hooked-end steel fibers. J. Eng. Mech., (ASCE), 140(12):04014091(1-13), 2014.
[3] Pichler, B., Hellmich, C. & Mang, H. A., A combined fracture micromechanics model for tensile strain-softeningin brittle materials, based on propagation of interacting microcracks. Int. J. Anal. Num. Meth. Geomech., 31: 111- 132, 2007.

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