Shape effect on weakly nonlinear elliptical composites

The electric field responses of two types of weakly nonlinear dielectric composites consisting of elliptic cylindrical inclusions, one with identical shape and the another with distributed shapes, randomly embedded in the linear host media in the dilute limit are investigated. The dielectric property of the inclusions is that the relation between the displacement (D) and electric (E) fields obey the form D = εE + χ∣E∣βE where β is a nonlinear integer exponent and ε ≫ χ∣E∣β. By using the decoupling approximation, the effective nonlinear susceptibility (χe) is determined and analyzed for varying the aspect ratios and the shape distribution parameters for the composites with identical and distributed inclusion shapes, respectively. In addition, the exact analytic result of χe for the elliptical composites with distributed inclusion shapes for the case of β = 2 is derived in this article.