Bounds on the Electromagnetic, Elastic, and Other Properties of Two-Component Composites

Abstract

A simple relation between three-point correlation functions is derived for two-component materials. This relation enables one to find concise expressions for the Beran, Molyneux, and McCoy bounds on transport and elastic coefficients in terms of the volume fraction, $f_1$, and two fundamental geometric parameters, ${\zeta }_1$ and ${\eta }_1$. The parameter ${\zeta }_1$ also determines bounds on the complex electrical permittivity. No simple interpretation of ${\zeta }_1$ and ${\eta }_1$ has been found.