Efficient graph-based tensile strength simulations of random fiber structures

In this paper, we propose a model-simulation framework for virtual tensile strength testing of random fiber structures, such as those in nonwoven materials. The focus is on efficient handling of the problem-inherent multi-scales and randomness. In particular, the interplay between random microstructure and deterministic structural production-related features on the macro-scale makes classical homogenization-based approaches computationally complex and costly. In our approach we model the fiber structure as graph-based and of truss-type, equipped with a nonlinear elastic material law. The tensile strength test is described by a sequence of force equilibria with varied boundary conditions. Its embedding into a singularly perturbed dynamical system is advantageous with respect to statements on solution theory and convergence of numerical methods. A problem-tailored data reduction provides additional speed-up, while Monte-Carlo simulations account for randomness. This work serves as a proof of concept and opens the field for optimization.