Effective response in nonlinear random composites

A self-consistent mean field theory is presented for the effective response in random mixtures consisting of components with power law J-E relations of the form J = χ|E|βE, where J is the current density and E is the electric field. The nonlinear conductors are treated as conductors with a field-dependent conductivity. The mean field theory assumes a uniform local field in each component. The local field is then determined self-consistently. Results are compared with numerical data obtained by simulations on nonlinear random resistor networks. Results for random mixtures consisting of linear and strongly nonlinear components, and of two strongly nonlinear components are presented. The theory also gives a generalization of the Maxwell-Garnett approximation to the case of dilute strongly nonlinear random composites.