Transport properties of finite and infinite composite materials and Rayleigh's sum

Abstract

The transport properties of a regular array of cylinders embedded in a homogeneous matrix material have been studied by the following method. Let us bound a part of the infinite material by a closed curve γ. Knowing the transport properties of this finite amount of material, we can evaluate the transport properties of the infinite material when γ tends to infinity. This method allows us to justify the method of Lord RAYLEIGH [1] for rectangular arrays of cylinders. Moreover, it is shown that in order to improve the Clausius-Mossotti approximation for a rectangular array, it is necessary to evaluate Rayleigh's sum.