The rotation of a rigid spheroidal inclusion embedded in a transversely isotropic medium

The exact three-dimensional elasticity solutions are given for two problems related to a rigid spheroidal inclusion embedded in bonded contact with an infinite transversely isotropic elastic medium. The first is of axisymmetric nature in which the inclusion is given a constant rotation about its axis of revolution which coincides with the axis of symmetry of the material. The second problem is asymmetric where the spheroidal inclusion is given a constant rotation about a direction that is perpendicular to the axis of elastic symmetry of the material. The displacement potential representation for the equilibrium of three-dimensional transversely isotropic bodies is used to solve the problem. In both cases, the moment-rotation relationship for the spheroidal inclusion and its limiting configurations are obtained in closed form. Numerical results are presented to show the effect of the aspect ratio of the spheroid on the rotational stiffness.