Adhesion between a rigid indenter and an elastic half-space for incompressible gradient media with a high gradientness index

The contact problem of a cylindrical indenter and gradient medium is considered with allowance for adhesion forces between surfaces of contacting bodies. An analytical solution of the problem is found for the case of a gradient medium with a power dependence of the elastic modulus on the normal coordinate. The case of incompressible media with a Poisson ratio of 1/2 is described in detail. It is shown that the behavior of the system in this case can qualitatively differ from the case of homogeneous media. The influence of the surface roughness, which is modeled in the form of axisymmetric waviness is considered. Special attention is paid to the contact between a parabolic indenter and a gradient medium; the differences from the case of a cylinder are shown.