Inhomogeneity problem with a sliding interface under remote shearing stress

The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to remote uniform shearing stress. Both the elastic inclusion and matrix are considered isotropic with a separate elastic modulus. Based on Lur’e’s approach to solving ellipsoidal cavity problems through Lame functions, several harmonic functions are introduced for Papkovich-Neuber displacement potentials. The displacement fields inside and outside the ellipsoidal inclusion are obtained explicitly, and the stress field in the whole domain is consequently determined.