Indentation of an incompressible inhomogeneous layer by a rigid circular indenter

This work deals with an incompressible inhomogeneous layer bonded to a rigid substrate and indented without friction by a rigid circular indenter. The corresponding mixed boundary-value problem of elasticity is reduced to equivalent dual integral equations. It is shown that the pliability function in these equations may be found from a system of nonlinear differential equations and that its behaviour is peculiar when the elastic medium is incompressible. A novel technique taking into account this peculiarity is developed in order to reduce the dual integral equations to Fredholm integral equations of the second kind with symmetric strictly coercive operators. For a homogeneous layer and a flat indenter, the structure of the Fredholm integral equations permits an approximate analytical solution which is very accurate for any layer thickness. For an indenter of three-dimensional profile, leading asymptotic terms of the solution are derived in the case of a thin inhomogeneous layer.