Effective conductivity of nonlinear composites. II. Effective-medium approximation

The effective-medium approximation (EMA) is developed to compute the effective nonlinear conductivity of a random composite material characterized by a weakly nonlinear relation between the current density J and the electric field E of the form J=σE+χ‖E ${\mathrm{\Vert }}^2$ E+η‖E ${\mathrm{\Vert }}^4$ E, where σ, χ, and η take on different values in the inclusion and in the host. As an example, we apply the EMA to deal with a spherical inclusion in a host, of either linear or nonlinear J-E relations, and obtain the effective nonlinear conductivity. While the EMA is valid for arbitrary inclusion concentration, we show that the EMA nonlinear conductivity reduces to the Maxwell-Garnett form at low inclusion concentration. Possible applications of the method will be discussed.