3D Micromechanics and Effective Moduli for Brittle Composites with Randomly Located Interacting Microcracks and Inclusions

An innovative 3D, statistical micromechanical framework is proposed for brittle composites with interacting microcracks and interacting inclusions based on the concept of the ensemble—volume average and pairwise interactions. To account for the effect of 3D interactions among constituents, an approximate analytical solution of a micromechanical formulation is presented to accommodate all possible first-order and second-order ensemble—volume averaged perturbations due to the existence and interactions of randomly located microcracks and inclusions. In particular, explicit analytical solutions for the interactions between penny-shaped microcracks and spherical inclusions are systematically derived. The proposed pairwise interacting and first-order micromechanical damage models are compared to illustrate the influence of constituent interactions on effective elastic-damage moduli of composites. This framework provides a viable methodology to accommodate statistical, micromechanical, and interacting aspects of randomly distributed microcracks and inclusions.