Electric-field fluctuations in random dielectric composites

When a composite is subjected to a constant applied electric, thermal, or stress field, the associated local fields exhibit strong spatial fluctuations. In this paper, we evaluate the distribution of the local electric field (i.e., all moments of the field) for continuum (off-lattice) models of random dielectric composites. The local electric field in the composite is calculated by solving the governing partial differential equations using efficient and accurate integral equation techniques. We consider three different two-dimensional dispersions in which the inclusions are either (i) circular disks, (ii) squares, or (iii) needles. Our results show that in general the probability density function associated with the electric field for disks and squares exhibits a double-peak character. Therefore, the variance or second moment of the field is inadequate in characterizing the field fluctuations in the composite. Moreover, our results suggest that the variances for each phase are generally not equal to each other. In the case of a dilute concentration of needles, the probability density function isa singly peaked one, but the higher-order moments are appreciably larger for needles than for either disks or squares.