An elliptic inclusion with imperfect interface in anti-plane shear

A semi-analytic solution is developed for the problem associated with an elliptic inclusion embedded within an in®nite matrix in anti-plane shear. The bonding at the inclusion-matrix interface is assumed to be homogeneously imperfect. The interface is modeled as a spring (interphase) layer with vanishing thickness. The behaviour of this interphase layer is based on the assumption that tractions are continuous but displacements are discontinuous across the interface. Complex variable techniques are used to obtain in®nite series representations of the stresses induced within the inclusion. The results obtained demonstrate how the (non-uniform) stress ®eld and the average stresses inside the inclusion vary with the aspect ratio of the inclusion and the parameter describing the imperfect interface. In addition, it is shown that, in some cases (depending on the aspect ratio of the ellipse), it is possible to identify speci®c values of the interface parameter which correspond to maximum peak stress along the interface. 7