An Effective Medium Approximation of Nonlinear Compositeswith Spherical Particle

Abstract

We have proposed a nonlinear effective medium approximation (EMA) method toestimate the bulk effective conductivities of weakly nonlinear compositemedia, which obey a current-field relation of the form J = σE + χ|E|2E. As an example in three dimensions, we apply the EMAmethod to deal with a spherical inclusion in a host and derive theapproximate analytic formulae of nonlinear effective response, which aresuitable for the larger volume fraction of spherical inclusion. From ourresults, we can exactly obtain the generalized Landau formulae in the dilutelimit.