Theory of effective response in dilute strongly nonlinear random composites

The effective response of random media consisting of two-different kinds of materials, each of which with current density and electric field relation of the form J = chi\E\(2)E, is studied in the dilute concentration limit of one of the components. Based on linearizing the problem in standard mean field treatments and determining the mean fields self-consistently, a simple expression for the effective response is derived which is valid to the first order of the concentration of the dilute component. The result is then generalized to systems of arbitrary spatial dimensions and arbitrary nonlinearity. Our result represents a generalization of the low concentration expression widely used in linear random composites resulted from the Maxwell-Garnett approximation and the effective medium approximation to strongly nonlinear random composites of arbitrary dimensions and nonlinearity. (C) 1996 American Institute of Physics.