Non-local damage-enhanced MFH for multiscale simulations of composites

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way.
Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient computational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions.