Semi-empirical formulation of contact with an interphase boundary

Mechanics of an intimate contact between solid bodies is of key importance to a variety of scientific and engineering disciplines. However, currently, we can only quantify shallow elastic contacts between geometrically well-defined homogeneous materials. In this work we expand the classical formulations in Hertzian contact mechanics and derive an analytical description of a contact with an inhomogeneous material that emerges in numerous synthetic, geological and biological systems. The developed expression is successfully validated using static and dynamic nanoindentation-based measurements across a silicon/silicon dioxide interface. The presented experimental, numerical and theoretical framework is a stepping-stone towards establishing an analytical description of contact with complex structures.