Elastic solution of surface loaded layer with couple and surface stress effects

Abstract

In this study, an elastic solution of an axisymmetrically surface-loaded thin layer resting on a rigid substrate is established by taking the surface stress and material microstructural effects into account. Derived solutions provide not only a means to investigate the size effects on the mechanical response but also a set of fundamental solutions essential for tackling contact problems in a micro/nano scale. In the formulation, the couple stress and surface elasticity theories are adopted to simulate the microstructured bulk layer and the surface material, respectively. A general solution of an elastic field within the bulk layer is obtained first by Hankel transform method and subsequently used together with the surface equations and boundary conditions to form a set of conditions essential for determining all unknown constants. After being fully tested with available benchmark solutions, results are used to study the role of surface and couple stresses on the load transferring mechanism to the substrate and its size-dependent characteristic for a wide range of external length scales relative to the internal length scales.