Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities

Abstract

Based on the general micromechanical framework proposed in a companion paper, effective elastic moduli of two-phase composites containing randomly dispersedspherical inhomogeneities are investigated in this paper. At variance with existing micromechanical pairwise interaction models (accurate up to the second-order in particle volume fraction ϕ), the proposed approximate, probabilistic pairwise particle interaction formulationcoupled with the general ensemble-volume averaged field equations leads to a novel, higher-order (in ϕ), and accurate method for the prediction of effective elastic moduli of two-phase composites containing randomly located spherical particles. The relevant ensemble integrals in the proposed formulation are absolutely convergent due to a “renormalization” procedure employed in a companion paper. In accordance with the analogy between the effective shear modulus of an incompressible elastic composite with randomly dispersed rigid spheres and the effective shear viscosity of a colloidal dispersion with randomly dispersed rigid spheres (at high shear rates), the proposed ensemble-micromechanical approach is extended to predict effective shear viscosities of colloidal dispersions at the high-shear limit. Comparisons with experimental data, classical variational bounds, improved three-point bounds, the second-order particle interaction model, and other micromechanical models are also presented. It is observed that significant improvement in predictive capability for two-phase composites with randomly dispersed spheres can be achieved by using the proposed method.