Homogenized response of composite materials subjected to mixed mode loading conditions

The aim of this paper is to study the effects of damage initiation and evolution due to micro-cracking along an a-priori unknown path on the homogenized constitutive properties of elastic composite materials. A micro-mechanical approach based on homogenization techniques and fracture mechanics concepts is presented. The crack propagation process is driven by the maximum energy release rate criterion, which is used to predict incremental changes in crack path, whereas a coupled stress energy criterion is adopted to predict crack initiation within originally undamaged microconstituents or at bi-material interfaces. To this aim a novel strategy for quasi-automatic simulation of propagation of arbitrary cracks in 2D finite element models has been implemented by taking advantage of a generalized J-integral formulation, accounting for material non-homogeneity and crack propagation under mixed mode loading conditions. Numerical simulations are carried out for two typical 2D composite micro-structures: a porous composite material with initial edge cracks and a particle reinforced composite material with an initially undamaged inclusion/matrix interface. Results highlight the capability of the proposed approach to provide the nonlinear macroscopic response of composite materials for different prescribed macro-strain path directions.