Abstract
We propose an approximate general method for calculating the effective dielectric function of a random composite in which there is a weakly nonlinear relation between electric displacement and electric field of the form , where and are position dependent. In a two-phase composite, to first order in the nonlinear coefficients and , the effective nonlinear dielectric susceptibility is found to be , where is the effective dielectric constant in the linear limit () and and are the dielectric function and volume fraction of the ith component. The approximation is applied to a calculation of in the Maxwell-Garnett approximation (MGA) and the effective-medium approximation. For low concentrations of nonlinear inclusions in a linear host medium, our MGA reduces to the results of Stroud and Hui. An exact calculation of is carried out for the Hashin-Shtrikman microgeometry and compared to our MG approximation.
- Received 6 July 1988
DOI:https://doi.org/10.1103/PhysRevB.38.10970
©1988 American Physical Society