Models of thin interphases and the effective medium approximation in composite media with curvilinearly anisotropic coated inclusions

Abstract

Two models of three-dimensional thin interphases are formulated in the setting of steady thermal conduction and general curvilinear anisotropy. The models make possible to determine the fields in the media adjacent to the interphase without the need to solve for fields within the interphase itself. They facilitate the implementation of methods that are aimed at the determination of the effective moduli of heterogeneous media which contain thin interphases. A formulation of the so-called Effective Medium Approximation (EMA) in composite media is given in which we incorporate the developed interphase models. The implementation of the constructed general framework is illustrated for the special case of a composite material which consists of coated spherical particles that possess spherical transverse isotropy, and are embedded in an isotropic matrix.