Variational bounds on some bulk properties of a two-phase composite material

Abstract

A variational principle due to Hashin and Shtrikman is used to obtain theoretical upper and lower bounds on the effective bulk dielectric constant ${\epsilon }_e$ (or an analogous property such as magnetic permeability, electrical or thermal conductivity, or a diffusivity) of a two-phase macroscopically homogeneous composite material from information about another similar effective bulk property. For the case of a composite whose macroscopic symmetry under rotations is either isotropic or cubic, we obtain a new and rather simple pair of bounds that are usually considerably better than any of those that are presently obtainable under these conditions.