The anisotropic elastic solid with an elliptic hole or rigid inclusion

Abstract

The two-dimensional problem of an elliptic hole in a solid of general anisotropy subject to an arbitrarily prescribed traction on the hole surface is studied. Stroh's complex formalism is adopted here but real-form solutions are obtained for the displacement and the hoop stress around the hole. For an arbitrarily prescribed traction, the solutions are in the form of an infinite series. However, through the use of a conjugate function they can be expressed in closed form directly in terms of the applied traction. We also consider an elliptic rigid inclusion subject to a force and a torque. Again, real-form solutions are obtained for the interface stress, the hoop stress around the rigid inclusion and the rotation of the rigid inclusion. When there is no torque applied at the inclusion, the traction vector at the surface of the rigid inclusion is in the direction of the applied force and is a constant when the ellipse is a circle. This is an unexpected result since the material surrounding the rigid inclusion is of general anisotropy.