Failure zone homogenization for modeling damage- and debonding-induced softening in composites including gradient-extended damage at finite strains

Abstract

Within multiscale modeling strategies for composite materials, standard Hill averaging is widely used for homogenization of repeating unit cells (RUCs). However, Hill’s homogenization approach reaches its limitations at the presence of strain softening, because in the standard averaging sense the representativeness of the considered micro-scale volume is lost. Hence, in order to overcome these limitations, we propose a new failure zone averaging scheme at finite strains, which is also applicable in the softening regime. First, starting from Hill’s assumption of equal virtual work densities on different scales, a novel homogenization approach is derived analytically. Then, the analytical results are verified by numerical simulations evaluating different RUC sizes and accounting for varying geometric realizations in a statistical manner. It is shown that the proposed homogenization scheme yields size-independent stress–strain relations even after localized damage has occurred leading to strain softening within the RUCs. In addition, the material model for the epoxy bulk is valid for the description of damage progression at large deformations using a gradient-enhanced damage model. It turns out that the micromorphic power density – related to the gradient enhancement – of the failure zone gives significant values during the formation of localization while the overall work density is small. Thus, it can be concluded that for accurate failure zone homogenization, the contribution of gradient terms has to be considered. Further, cohesive zone elements are incorporated to consider the decohesion between fibers and matrix. As a result, the stress–strain curves show a lower peak stress and a higher scatter in the stress response compared to samples with perfect interfaces. In contrast, the work density plots show a higher dissipation for the RUC with damaging interfaces.