On the effective medium approximations for the properties of isotropic multicomponent matrix-based composites

From our three-point correlation bounds, which are based on minimum energy principles and Hashin–Shtrikman polarization trial fields, the polarization approximations for the effective conductivity and elastic moduli of isotropic multicomponent suspension of particles in a continuous matrix, generally in d-dimensions, have been deduced, which account for near distance inclusion-matrix interaction, but not the details of far distance inter-particle ones. The approximations, always obeying Hashin–Shtrikman bounds for isotropic multicomponent materials, are compared favourably with other approximations and finite element results.