Connectivity of rough contacts in plane and axially symmetric cases

Abstract

It is customary to assume that a contact of rough elastic solids is always multiply connected, i.e. have regions in it where contact surfaces are apart of each other and contact pressure is zero. The issue of the connectivity in rough elastic contacts has both theoretical and practical interest. In this paper we extend the earlier conducted analysis of rough contacts in plane formulation on the case of axially symmetric rough elastic contacts and compare our findings. The main goal of the paper is to obtain an analytical solution of axially symmetric rough elastic contact and analyze its 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 Legendre orthogonal polynomials. In case of a plane contact of rough elastic solids it has been achieved using the solution expansions in Chebyshev orthogonal polynomials. In both axially symmetric and plane cases of rough elastic contacts the ranges of contact parameters for which contacts are singly connected have been determined.