Elastic analysis for contact problems with surface effects under normal load

Abstract

Based on surface elasticity theory, contact problems with surface effects at the nano-scale are considered in this paper. The complex variable function method is adopted to derive the fundamental solutions for the contact problem. As examples, the deformations induced by uniformly distributed normal pressures and concentrated force are analyzed in detail. The results reveal some interesting characteristics in contact mechanics, which are distinctly different from those in classical elasticity theory. At the nano-scale, the deformation gradient on the deformed surface varies smoothly across the loading boundary as a result of surface effects. In addition, for nano-indentation, the indent depth depends strongly on the surface stress.