Effective nonlinear response in random nonlinear granular materials

The effective nonlinear response of random composites in which one or more components with nonlinear J−E response, where J is the current density and E is the electric field, is studied theoretically and numerically. The nonlinear response of the constituents is assumed to have the form J = σE + ξ(E2)β/2E, where β is arbitrary. An effective medium approximation (E is proposed for the nonlinear response, which is valid for arbitrary β and for the whole concentration range. Previous results for the cases of cubic nonlinearity and/or low concentrations are recovered as special cases of the present approximation. The results are compared with numerical data obtained by performing detailed simulations on random nonlinear resistor networks. The EMA gives reasonable description of the numerical data and captures the basic features near the percolation threshold of the system. Predictions of the EMA at concentrations near the percolation threshold are discussed.