An Effective Medium Approximation of Nonlinear Compositeswith Spherical Particle

We have proposed a nonlinear effective medium approximation (EMA) method to estimate the bulk effective conductivities of weakly nonlinear composite media, which obey a current-field relation of the form J = σE+ X|E|² E. As an example in three dimensions, we apply the EMA method to deal with a spherical inclusion in a host and derive the approximate analytic formulas of nonlinear effective response, which are suitable for the larger volume fraction of spherical inclusion. From our results, we can exactly obtain the generalized Landau formulas in the dilute limit.