FIRST-PRINCIPLES APPROACH TO CONDUCTIVITY OF A NONLINEAR COMPOSITE

The Rayleigh method is extended to study the effective response in wea kly nonlinear composites within a perturbative approach. The Rayleigh identity is used to obtain a set of equations for zeroth-order and hig her-order potentials, with the latter resulted from the presence of no nlinearity in the problem. The formalism is applied to study the effec tive response in an array of cylinders embedded in a host. Results are compared with those obtained by other approximations previously propo sed in the literature. Results from the present approach show that whi le the previous approach of applying the Rayleigh identity to determin e the zeroth-order potential and neglecting the induced fields due to the higher-order potentials is valid for a wide range of nonlinear com posites, the effects of induced fields due to the higher-order potenti als are important in composites with high concentrations of inclusions , and in systems with a low value for the ratio of the Linear conducti vities and a high value of the ratio of the third-order nonlinear cond uctivities. The present approach, thus, provides a general formalism f or treating nonlinear composites and establishes the range of validity of previous approximations.