Solutions of elastic medium with surface stress effects

Abstract

This dissertation presents a theoretical study of an isotropic elastic material with the consideration of surface stress effects by adopting complete Gurtin-Murdoch continuum theory of elastic material surfaces. The fundamental solutions of an isotropic elastic layer under different loading cases, and an elastic medium with dislocations and crack are presented. Fourier and Hankel integral transforms are used to solve appropriate boundary value problems involving non-classical boundary conditions associated with the surface stresses. The analytical solutions are expressed in terms of semi-infinite integrals that can be accurately computed by employing numerical quadrature scheme. Selected numerical results are presented to portray the influence of surface stresses on the bulk elastic field. It is found that surface stresses show a significant influence on elastic fields of an isotropic elastic material especially in the vicinity of the surface. In contrast to classical elasticity, extensive parametric studies observed in numerical results indicate that the response of the bulk material becomes size-dependent with the consideration of surface stresses. Numerical results presented in this study confirm the fact that the influence of surface stresses is significant in the analysis of problems involving nanoscale systems and soft elastic materials where the surface energy effects are not negligible. The fundamental solutions presented in this study can be used in the development of boundary integral equation and other methods to analyze complicated boundary value problems associated with nanoscale structures and soft elastic solids.