Effects of inclusion shapes on electric responses of nonlinear dielectric composites

Abstract

The electric field reponses of two types of nonlinear dielectric composites consisting of elliptic cylindrical inclusions, one with an identical shape and another with distributed shapes, randomly embedded in the host media in the dilute limit are investigated. The dielectric property of the inclusions is that the relation between the displacement field (D) and electric field (E) satisfies a more general form D = ƐE + X | [superscript β]E, where β is a nonlinear integer exponent and ε≫χ | [superscript β] for weakly nonlinear composites. For strongly nonlinear composites, the dielectric property of both inclusion and medium satisfyingD=χ |[superscript 2] E is considered. By using the simple decoupling approximation, the effective nonlinear coefficients (X[subscript e]) are determined and the efforts of inclusion shapes on X[subscript e] are reported in terms of the aspect ratio (M), and the shape distribution paremeter (Δ) for the former and the latter types of composites, respectively. For weakly nonlinear composites with identical inclusion shape, the results show the rapid increase in X[subscript e] with increasing M within the range of lower values of M. However, within the range of higher values of M, increasing M affects the increasing of X[subscript e] very slightly. The similar behavior is also observed for strongly nonlinear composites. For composites with distributed inclusion shapes, the results reveal the rapid increase or decrease in X[subscript e] within increasing Δ, especially, when Δ near 1. Furthermore, the exact analytic rusult of X[subscript e] for weakly nonlinear ellitical composites with distributed inclusion shapes for the case of β = 2 is also determined and this is consistent with the numerical result.