Contact problem of cylindrical indenter and graded media with account of adhesion forces between two contacted bodies is considered. Analytical solution of the problem for the case of graded media with power-law dependence of elastic modulus on normal coordinate have been found. The case of uncompressible media with Poisson ratio 1/2 was considered in details. It is shown, that in this case the behavior of system can be qualitatively different from the case of homogeneous media. Influence of roughness of the surface is considered. Surface roughness is presented as axially symmetric “waviness”. The contact of parabolic indenter and a gradient media was considered. Differences from the case of a cylinder is shown.
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