Axially symmetric contact of two elastic bodies with friction and adhesion

We consider an axially symmetric problem of the friction contact of two elastic paraboloidal bodies under the condition that the contact zone can be split into a circular zone of adhesion and an annular zone of sliding. Since the contact zone is small, we replace the bodies by elastic half spaces. Furthermore, we pass from the boundary-value problem for two elastic half-spaces to a problem for a single half space and obtain its analytic solution by the generalized Wiener-Hopf method. We also determine the radii of the contact zone and the zone of adhesion, distribution of the contact stresses, and the approach of the bodies.