Error of the network approximation for densely packed composites with irregular geometry

Abstract

We apply a discrete network approximation to the problem of the effective conductivity of the high contrast, highly packed composites. The inclusions are irregularly (randomly) distributed in the hosting medium, so that a significant fraction of them may not participate in the conducting spanning cluster. For this class of inclusion distributions we derive a discrete network approximation and obtain an a priori error estimate for this approximation in which all the constants are explicitly computed. Explicit dependence on the irregular geometry of the inclusions' array is obtained. We use variational techniques to provide rigorous mathematical justification for the approximation and its error estimate.