Depth-sensing indentation of a transversely isotropic elastic layer: Second-order asymptotic models for canonical indenters

Simple analytical approximations to the frictionless indentation problem for a transversely isotropic layer are obtained for spherical, conical, and pyramidal indenters as well as for axisymmetric indenters of power-low profile and self-similar non-axisymmetric indenters. These approximations are asymptotically exact in the small-contact limit. The results obtained are validated in the case of an isotropic layer for spherical and conical indenters.