Asymptotic solutions for axisymmetric contact of a thin, transversely isotropic elastic layer

The problem of a rigid sphere in normal contact with a thin, transversely isotropic elastic layer is investigated. The thin elastic layer rests on a rigid foundation and both the limiting cases, wherein the interface is either ideally bonded or unbonded and frictionless, are considered. Approximate analytical solutions for the contact pressure beneath the spherical indenter and for the contact patch radius are presented. By comparing these with those predicted by the finite element method, the accuracy of the solution methods is determined.