Explicit cross-property correlations for anisotropic two-phase composite materials

Abstract

Explicit correlations between two groups of anisotropic effective properties—conductivity and elasticity—are established for two-phase composite materials with anisotropic microstructures (non-randomly oriented inclusions of non-spherical shapes). The correlations are derived in the framework of the non-interaction approximation. The elasticity tensor is expressed in terms of the conductivity tensor in closed form. Applications to realistic microstructures, containing mixtures of diverse inclusion shapes are given. Compliance/stiffness contribution tensors of an inclusion, that characterize the inclusion's contribution to the overall elastic response, are derived in the course of analysis; these results are of interest on their own.