Effective nonlinear response in dilute nonlinear granular materials

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Abstract
We consider the nonlinear response of a granular material in which a concentration p of spherical grains of nonlinear material are embedded in a linear host. An approximation, based on the Maxwell–Garnett formula, is proposed for the effective nonlinear susceptibility which is applicable for arbitrary nonlinearity in the dilute limit of embedded grains. The nonlinear susceptibility is found to be χeff=p[3ε0A/(ε0B +2ε0A)]2‖3ε0A/(ε0B +2ε0A)‖βχB, where ε0A is the dielectric constant of the linear host, and the displacement and electric field in the nonlinear grains are related by D=ε0BE+χB‖E‖βE. Previous results on cubic nonlinearity are recovered as a special case of the present approximation.