EFFECTIVE NONLINEAR RESPONSE IN DILUTE NONLINEAR GRANULAR-MATERIALS

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[3ε0 A/(ε0B +2ε0 A)]2∥3ε0A/(ε 0B +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=ε0 BE+χB∥E∥βE. Previous results on cubic nonlinearity are recovered as a special case of the present approximation.