The effective conductivity of a periodic lattice of circular inclusions

Abstract

We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. The problem is reduced to the solution of an infinite system of linear equations. The effective conductivity tensor is obtained in the form of the series expansion in terms of the volume fraction of the cylinders whose coefficients are determined exactly. Results are illustrated by examples.