Indentation of a rigid sphere into an elastic half-space in the direction orthogonal to the axis of material symmetry

In this work a contact problem for a transversely isotropic half-space indented by a rigid sphere is considered. The axis of symmetry of the half-space is orthogonal to the axis of the applied contact load, which makes the problem fully three-dimensional. An exact solution to this contact problem is constructed. Stresses and strains are obtained in the form of contour integrals in the complex plane with explicitly determined dimensionless integrands. As an illustrative application of the constructed solution, failure beneath the indenter in a unidirectional composite is analyzed.