Eshelby Tensor for an Elastic Inclusion With Slightly Weakened Interface

Abstract

The Eshelby tensor for an ellipsoidal inclusion in an elastic matrix of infinite extent is considered in this paper. Instead of assuming perfect bonding between the inclusion and the matrix, the interface between the inclusion and the matrix is modeled by a spring layer of vanishing thickness. The inclusion- matrix interface is said to be slightly weakened if the compliance of the spring layer is much smaller than that of the matrix material. By virtue of the Betti-Rayleigh reciprocal identity in linear elasticity, an integral representation for the displacement field due to an elastic inclusion with a spring layer interface is derived. Explicit expressions of the Eshelby tensor for an ellipsoidal inclusion with slightly weakened interface are obtained through an iteration procedure developed from the integral representation.