A multiscale finite-element method for solving rough-surface elastic-contact problems

A novel multiscale finite-element method to investigate the elastic contact of two-dimensional rough surfaces is presented. The aim of the method is to find the microscopic curve that describes the deformed shape of a solid with a smooth boundary surface in frictionless contact with a rigid rough surface. In addition, the real contact area is studied through the surface deformation. The contact traction on the contact surface and the maximum shear stress around the contact region are analyzed. This method is based on the variational inequality approach for solving the elastic frictionless contact problem. The strategy is to separate a small slice within the contact region and solve it as an independent system. Then the contact traction is obtained through iterations between the solution of the independent small slice and the solution of the total solid body. We observe a much higher pressure than the result of Hertz theory around the asperities. The main conclusions are (1) the actual contact area and surface traction are dependent on the wavelength and amplitude of the surface roughness, (2) there is a much higher pressure around the asperities than predicted by Hertz theory, and (3) the location of maximum shear stress tends to be shifted toward the surface as compared with the case of smooth-surface contact. The method has the potential to be extended to solve three-dimensional rough contact problems.