Perturbation Expansion Method and Effective Medium Approximation for Effective Conductivity of Nonlinear Composite Media

In this paper, we establish an effective medium approximation (EMA) for effective conductivity of nonlinear composite media. As an example, we consider a two-dimensional composite medium with a cylindrical inclusion 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 third and the fifth-order effective conductivities, which are valid for nonlinear composite media with middle concentration of inclusion.