Small-scale indentation of an elastic coated half-space: The effect of compliant substrate

Under consideration in this paper is the axisymmetric problem of unilateral frictionless indentation of a thin stiff film bonded to a compliant substrate, which is assumed to be a homogeneous isotropic elastic half-space. The previously developed first-order asymptotic model for the small-scale indentation, when the contact radius is small compared to the film thickness, is compared with approximate solutions based on the Kirchhoff thin plate theory with satisfactory results.