Explicit cross-property correlations for porous materials with anisotropic microstructures

Abstract

Explicit correlations between two groups of anisotropic effective properties—conductivity and elasticity—are established for porous materials with anisotropic microstructures (non-randomly oriented pores of non-spherical shapes). In the present work, the correlations are derived in the framework of the non-interaction approximation. The elasticity tensor is expressed in terms of the conductivity tensor in the closed form. These results are based on the possibility to represent, with good accuracy, the fourth rank tensor of elastic compliances in terms of a certain second rank symmetric tensor and a unit tensor. Applications to realistic microstructures, containing mixtures of diverse pore shapes are discussed.