A rigid elliptic inclusion in an elastic medium with a slipping interface

When an elastic medium containing an elliptic inclusion with a sliding interface is subjected to a remote pure shear, it was found that the inclusion behaves like a cavity. Since a circle is a special case of an ellipse, the solution should be applicable to a circular inclusion as well. However, it breaks down when the ellipse degenerates into a circle. This implies that the solution is questionable. In this paper the problem is examined by considering a rigid elliptic inclusion in an elastic medium with sliding interface between them. By taking account of a large rotation of the inclusion instead of a small rotation, we obtain a uniformly valid solution applicable to a circular inclusion as well as to an elliptic inclusion. The solution reveals a remarkable snapping behavior of the inclusion under a critical load. A simple condition for its occurrence is derived.