Clausius-Mossotti approximation for a family of nonlinear composites

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Abstract
A generalization of the Clausius-Mossotti approximation is proposed to describe the bulk effective dielectric constant, or electric conductivity, of a family of nonlinear composite media. These composites are composed of nonlinear spherical or ellipsoidal inclusions embedded in a uniform linear matrix. The nonlinearity of the inclusions may be of arbitrary form. Explicit results are obtained for strong and weak power-law nonlinearities. Our approach is also extended to random resistor networks made of a uniform linear network in which nonlinear resistors are randomly distributed.