Circular Microstructural Volume Elements With Periodic Boundary Conditions for Localization Problems

Abstract

A common choice for multiscale modelling of the mechanical response of composites is to use periodic boundary conditions (PBCs) on square representative volume elements (RVEs). these PBCs over-constrain the response when strain localization takes place in bands that are not compatible with the imposed periodic constraints. PBCs periodicity the mapping matrix-fiber RVEs, of fibers cross edges, the of localization of circular RVEs with PBCs to obtain a micromodel with transversely isotropic response. the original formulation proposed in to the full softening response due to over-constraining when cracks reach the boundary. we propose a modification to the PBCs which allows for cracks to cross the edges.