Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties

Abstract

A micromechanical analytical framework is presented to predict effective elastic moduli of three-phase composites containing many randomly dispersed and pairwisely interacting spherical particles. Specifically, the two inhomogeneity phases feature distinct elastic properties. A higher-order structure is proposed based on the probabilistic spatial distribution of spherical particles, the pairwise particle interactions, and the ensemble-volume homogenization method. Two non-equivalent formulations are considered in detail to derive effective elastic moduli with heterogeneous inclusions. As a special case, the effective shear modulus for an incompressible matrix containing randomly dispersed and identical rigid spheres is derived. It is demonstrated that a significant improvement in the singular problem and accuracy is achieved by employing the proposed methodology. Comparisons among our theoretical predictions, available experimental data, and other analytical predictions are rendered. Moreover, numerical examples are implemented to illustrate the potential of the present method.