Numerical method for solving contact problems under partial slip conditions

An elastic contact model for three-dimensional similar and dissimilar materials under coupled normal load and tangential load in the contact plane, with consideration of partial slip effects, is studied. When two surfaces in static contacts are subjected to normal load and tangential load, even only applying a normal load for dissimilar materials, microscopic slip will take place at certain areas of the contact region even though the contacting bodies remain still without macroscopic movement. The semi-analytical method is used to solve the partial contact problems, in which analytical solutions of displacements due to unit pressure or shear tractions are based on green function. The contact pressure and shear tractions are solved by a numerical procedure based on conjugate gradient method and fast Fourier transform technique. The meshes are applied to the positions just in the contact areas of interest, which saves the computing time. The good agreement with the results from Cattaneo-Mindlin's solution validates the numerical method. The analysis is extended to the sinusoidal wave contact to provide a further demonstration for the pressure distributions, shear stress distributions and stick regions. The results show that the stick regions are located at several disconnected areas due to the roughness effects. With the increase of tangential force, the pressure distribution inclines along the opposite direction of tangential force, the value of shear stress τx becomes positive and the stick zones shrink and move opposite to the direction of tangential force. © 2010 Journal of Mechanical Engineering.