Stress state of a transversely-isotropic body with elliptical inclusion

We present an exact solution for the problem in elasticity theory of a transversely Isotropic body containing an elliptical inclusion. We assume that the tensile stresses act at a distance sufficiently far away from the inclusion, along the axes of the ellipse and perpendicular to the plane of the ellipse. We find that two fracture mechanisms are possible under the action of the type of force under consideration: detachment of the material from the inclusion, and fracture near the stress concentrator. We obtain formulas for the stress intensity factors for each case.