PERTURBATION EXPANSION METHOD AND EFFECTIVE-MEDIUM APPROXIMATION FOR EFFECTIVE CONDUCTIVITY OF NONLINEAR COMPOSITE MEDIA

In this paper, we establish an effective medium approximation (EMA) fo r effective conductivity of nonlinear composite media. As an example, we consider a two-dimensional composite medium with a cylindrical incl usion embedded in a homogeneous host, both the host and the inclusion having nonlinear current-voltage constitutive relations, and apply the perturbation expansion method to derive its analytic series solution. Using the nonlinear EMA we derive the formulae of the first-, the thi rd- and the fifth-order effective conductivities, which are valid for nonlinear composite media with middle concentration of inclusion.