Prediction of effective nonlinear susceptibility of composites

An analytical method is proposed to predict the nonlinear susceptibility of general composite materials. The method was based on the secant permittivities of each phase, and a nonlinear problem was transformed into a series of linear problems. The method is applied to any anisotropic composite and the nonlinearity of the constituents, contrary to the Stroud and Hui method, which is valid for isotropic composites and weak nonlinearity. As for the nonlinear mechanical behavior, it is shown that the proposed method is identical to the Ponte Castaneda variational method when the same method is used for the linear comparison composite. Some numerical computations are provided to illustrate the influence of the microstructure on the overall nonlinear relation between the electric displacement and the electric field.