Effective response of a non-linear composite in external AC electric field

Abstract

A general effective response is proposed for nonlinear composite media, which obey a current–field relation of the form J= σE+ χ| E| 2 E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency ω, the effective constitutive relation between the current density and electric field can be defined as, 〈 J( x, ω, t)〉= σ e 〈 E( x, ω, t)〉+ χ e 〈| E( x, ω, t)| 2 E( x, ω, t)〉+⋯, where σ e and χ e are the general effective linear and nonlinear conductive responses, respectively. The angled brackets 〈⋯〉 denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response.