Connectivity in a rough plane and axially symmetric contacts with a special coating

There is some evidence that in certain cases a contact of rough elastic solids is multiply connected, i.e. have regions in it where contact surfaces are apart from each other and the contact pressure is zero. The issue of the connectivity in rough elastic contacts has both theoretical and practical interest, especially for seals. In this paper, we extend the earlier conducted analysis of rough contacts without coatings in plane and axially symmetric formulations on the cases of plane and axially symmetric rough elastic contacts with special coatings and compare our findings. The main goal of the paper is to obtain the exact analytical solutions of plane and axially symmetric rough elastic contacts with a special coating and analyze their properties such as contact connectivity and contact pressure smoothness compared to the smoothness of the surface roughness profile. This goal is achieved by using solution expansions in Chebyshev and Legendre orthogonal polynomials. A range of contact parameters has been determined for which the contacts are connected individually.