A finite element homogenization-based approach to analyze anisotropic mechanical properties of chopped fiber composites using realistic microstructural models

This article presents the application of cubic Statistical Volume Elements (SVEs) to homogenize the elasticity tensor of epoxy matrix chopped glass fiber composites using displacement boundary conditions. A virtual microstructure reconstruction algorithm is used to reconstruct three large domains of the composites with different fiber orientation distributions. A non-iterative parallel meshing algorithm, named CISAMR, is then implemented to generate high-fidelity finite element models and simulate the linear elastic response of 1536 SVEs extracted from these domains. While the fiber orientations imply transversely isotropic elasticity stiffness matrices, for the SVE sizes considered, the composite is not quite transversely isotropic. We propose two indices of transverse isotropy to (1) determine the orientation at which a given property most closely matches the transversely isotropic assumption for an SVE, (2) quantify the corresponding transversely isotropic discrepancy, and (3) state the extent of transverse isotropy by measuring the difference between transverse and average normal quantities. The former can be applied to any orientation-dependent quantity such as strength, whereas the latter only applies to the elasticity tensor. We demonstrate the superiority of the latter for elastic properties and use the former to show that a proposed initiation fracture strength is farther away from its transversely isotropic limit compared to the directional elasticity normal stiffness.