Homogenization techniques for linear dielectric random composite materials in stationary conditions

Abstract

In this paper, homogenized dielectric constitutive equations for heterogeneous materials characterized by a random arrangement of the inclusions are obtained. The homogenization problem is formulated by using the Hashin and Shtrikman variational principle and by considering macroscopic charge density. The solution of the homogenization problem is obtained both in the Fourier and in the space domain. Explicit expressions of homogenized constitutive equations are presented for statistically homogeneous two-phase composites in terms of the two point correlation functions of the inclusions. These functions are deduced for a special class of heterogeneous materials reinforced by square or rectangular fibres whose arrangement is generated from the probability density function (p.d.f.) of the centres of the inclusions. At this aim, an efficient procedure to obtain the two-point correlation functions from the p.d.f. of the centres is proposed. Finally, several examples of overall constitutive equations are developed both for periodic and for random composites and comparisons with exact results for laminates are presented.