Reciprocal theorem for a linear elastic Cosserat interphase with general geometry

Abstract

Interphases in heterogeneous media are typically thin regions, such as coatings on inclusions bonded to matrixes. These interphases are modeled with approximate equations that connect fields on both surfaces of the interphase. The theory of a Cosserat surface is a special continuum theory that models the response of thin structures. Cosserat interphase models based on this theory provide unified equations that are valid for the entire range of material parameters of the inclusion, interphase and matrix. Since the balance laws for these Cosserat interphases are global integral equations, the theory inherits many of the fundamental properties of the exact three-dimensional theory. Here, it is shown that the Cosserat interphase model for linear elasticity also satisfies a global form of the reciprocal theorem.