Contact Analysis Using Surface Green’s Functions for Isotropic Materials With Surface Stress and Surface Elasticity

Abstract

Surface stress and surface elasticity are related to an organization of surface pattern and reconstruction of surface atoms. When the size of material reduces to a nanometer level, a ratio of surface to volume increases. Then, surface stress and surface elasticity influence on mechanical response near surface for an external force on the surface. Stroh formalism is very useful for analyzing the stress and displacement in anisotropic materials. When the Stroh’s formalism is applied to isotropic materials, the eigen matrix derived from equilibrium equation yields a triple root of i (i: imaginary unit), and then an independent eigen vector corresponding to the eigen value can not be determined. In this paper, surface Green function for isotropic materials is derived using Stroh’s formalism. The derived Green function considering neither surface stress nor surface elasticity agrees with the solution of Boussinesq. The surface Green’s function considering surface stress and surface elasticity is used for analyzing the displacement fields in amorphous silicon. It was found that the displacements obtained from the Green’s function were less than those from Boussinesq’s solution. Furthermore, the derived surface Green’s function is applied to a contact analysis for isotropic materials such as amorphous silicon. It is found that an apparent Young’s modulus determined from a force-indentation depth curve increases when surface stress and elasticity is taken into account in the analysis.