Effects of surface stresses on contact problems at nanoscale

Based on the surface elasticity theory, we examined the effects of surface stresses on nanosized contact problems. The Fourier integral transform method is adopted to derive the general solution for the contact problem under pressure. As two examples, the deformations induced, respectively, by a uniform distributed pressure and a concentrated force are analyzed in detail. The results indicate some interesting characteristics in contact mechanics, which are distinctly different from those in classical elasticity theory. Both the contact normal stress and the deformation gradient on the deformed surface vary smoothly across the loading boundary as a result of surface stress. In addition, the indent depth and the maximum normal contact stress depend strongly on the surface stress for nanoindentation.