The effective conductivity of three-phase composite materials with circular cylindrical inclusions

摘要

We extend the Rayleigh method for the calculation of the effective conductivity to three-phase composite materials. The materials under study consist of two types of circular cylinders in a periodic arrangement embedded in a matrix. Highly accurate values for lattice sums were obtained using algorithms which have been recently developed. A series of explicit formulations, which are used to facilitate the calculation of the effective conductivity of the composites under study, are reported. We also perform a series of numerical calculations to study the behaviour of these composites. [References: 21]