MEAN-FIELD THEORY OF STRONGLY NONLINEAR RANDOM COMPOSITES - STRONG POPOWER-LAW NONLINEARITY AND SCALING BEHAVIOR

The effective response of random media consisting of two different kin ds of strongly nonlinear materials with strong power-law nonlinearity is studied. Each component satisfies current density and electric-fiel d relation of the form J=(chi)\E\(beta)E. A simple self-consistent mea n-field theory, which lends to a simple way in determining the average local electric field in each constituent, is introduced. Each compone nt is assumed to have a conductivity depending on the averaged local e lectric field. The averaged local electric field is then determined se lf-consistently. Numerical simulations of the system are carried out o n random nonlinear resistor networks. Theoretical results are compared with simulation data. and excellent agreements are found. Results are also compared with the Hashin-Shtrikman lower bound proposed by Fonts Castaneda ef al. [Phys. Rc v. B 46, 4387 (1992)]. It is found that th e present theory, at small contrasts of (chi) between the two componen ts, gives a result identical to that of Ponte Castaneda er nl. up to s econd order of the contrast. The crossover and scaling behavior of the effective response near the percolation threshold as suggested by the present theory are discussed and demonstrated.