Transport Coefficients of Composite Materials

Abstract

The problem of the effective conductivity of a composite material whose local conductivity is a function of position is treated. Using the analogy between this problem and the diffusion of ions in a periodic potential, previously obtained variational results are used to obtain upper and lower bounds for the effective conductivity. These bounds are shown to be the conductivities obtained in certain commonly used equivalent circuit approximations. Although the discussion in the paper is in terms of the electrical conductivity, the theory is equally applicable to other transport coefficients, such as the heat conductivity and the diffusion constant, as well as to a class of response functions such as the magnetic permeability and dielectric constant.