NONLINEAR ELECTRICAL-CONDUCTIVITY IN HETEROGENEOUS MEDIA

A new method is proposed for estimating the effective behaviour of str ongly nonlinear composite materials. The central idea is to write down second-order Taylor expansions for the constituent phase energy funct ions, about appropriately chosen reference fields. This allows the res tatement of the problem for the nonlinear composite in terms of a corr esponding problem for a fictitious linear composite with anisotropic c onstituents, subjected to a given distribution of polarization fields. The procedure thus permits the straightforward conversion of well-kno wn estimates for linear composites, such as the Maxwell-Garnett and ef fective-medium approximations, into corresponding estimates for nonlin ear composites. The resulting nonlinear Maxwell-Garnett and effective- medium estimates are exact to second order in the contrast.