Indentation of a Plate on a Thin Transversely Isotropic Elastic Layer

This work investigates the indentation response of an elastic plate resting upon a thin, transversely isotropic elastic layer supported by a rigid substrate. Such a scenario is encountered across a range of length scales from piezoresistive tests on graphite nanoflakes to the bending of floating ice shelves atop seabed, where the elastic layer commonly exhibits certain anisotropy. We first develop an approximate model to describe the elastic response of a transversely isotropic layer by exploiting the slenderness of the layer. We show that this approximate model can be reduced to the classic compressible Winkler foundation model as the elastic constants of the layer are set isotropic. We then investigate the combined response of an elastic plate on the transversely isotropic elastic layer. Facilitated by the simplicity of our proposed approximate model, we can derive simple analytical solutions for the cases of small and large indenter radii. The analytical results agree well with numerical calculations obtained via finite element methods, as long as the system is sufficiently slender in a mechanical sense. These results offer quantitative insights into the mechanical behavior of numerous semiconductor materials characterized by transverse isotropy and employed with slender geometries in various practical applications where the thin layer works as conductive and functional layers.