CONTACT PROBLEMS WITH SURFACE STRESS EFFECTS

Abstract

This dissertation presents a theoretical study of contact problems with consideration of surface energy effects by adopting a complete Gurtin-Murdoch theory of surface elasticity. The fundamental solution of a layered elastic half-space subjected to axisymmetric surface loading is obtained by using Love’s representation and the Hankel integral transform. The analytical solutions for both displacement and stress fields are expressed in terms of semi-infinite integrals, which can be accurately evaluated by employing a numerical quadrature scheme. The obtained solutions are employed as the required influence functions in the investigation of axisymmetric indentation on a layered elastic medium with frictionless and adhesive contacts. In addition, they are also employed in the analysis of an elastic circular nanoplate under axisymmetric vertical loading resting on an elastic half-space based on a variational formulation. The accuracy of the present solution scheme is confirmed by comparison with relevant existing solutions, and selected numerical results on elastic fields under various contact problems are also presented. It is found that the surface stresses have a significant influence on both displacement and stress fields in the elastic medium especially in the vicinity of the surface. An extensive parametric study confirms that, unlike the classical elasticity solution, the material becomes stiffer and size-dependent with the presence of surface stresses. The present solution can be used as a benchmark solution in the development of numerical techniques such as the finite element and boundary element methods for analysis of more complicated contact problems under the influence of surface energy effects such as nanoscale problems and soft elastic solids.