Numerical solution of smooth and rough contact problems

A general procedure for the numerical solution of three-dimensional normal and tangential contact problems for non-conforming bodies of arbitrary shape is presented. The proposed procedure is based on the interpolation of known analytical solutions relating surface displacements of an elastic half-space subjected to pyramidal distributions of normal and tangential surface tractions. These formulas are used to interpolate unknown pressure distributions on the contact zone of two elastic bodies in contact. The proposed interpolation significantly reduces the computational burden of the numerical procedure required to interpolate the actual pressure distribution and to determine the initially unknown contact region. It amounts to expressing the contact pressure as a function of the elastic parameters of the two bodies, the distance between their surfaces and the relative displacement between two far-points pertaining to the bodies in contact. The procedure has been validated by comparison with classical contact problems and the results show excellent agreement with existing analytical and numerical solutions.