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 fibers directions.
The research has been funded by the Walloon Region under the agreement SIMUCOMP n° 1017232 (CT-EUC 2010-10-12) in the context of the ERA-NET +, Matera + framework.
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