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 de nsity and E is the electric field, is studied theoretically and numeri cally. The nonlinear response of the constituents is assumed to have t he form J = sigma E + chi(\E\(2))(beta/2)E, where beta is arbitrary. A n effective medium approximation (EMA) is proposed for the nonlinear r esponse, which is valid for arbitrary beta and for the whole concentra tion range. Previous results for the cases of cubic nonlinearity and/o r low concentrations are recovered as special cases of the present app roximation. The results are compared with numerical data obtained by p erforming detailed simulations on random nonlinear resistor networks. The EMA gives reasonable description of the numerical data and capture s the basic features near the percolation threshold of the system. Pre dictions of the EMA at concentrations near the percolation threshold a re discussed.