Elastic field of a nano-film subjected to tangential surface load: Asymmetric problem

Surface energy effects can play a significant role in the case of nanoscale materials and structures due to their high surface to volume ratio. In this paper, the general three-dimensional asymmetric problem for an elastic layer of nanoscale thickness that is bonded to a rigid substrate and subjected to tangential loading at the surface is considered. Mukiʹs integral transforms method for classical elasticity is extended to investigate the influence of surface energy effects on the elastic field based on the Gurtin–Murdoch continuum model. Hankel integral transforms are used to solve the non-classical boundary value problems related to a tangential concentrated load and a uniformly distributed tangential circular patch load. Explicit analytical solutions are obtained for the corresponding boundary-value problems. Selected numerical results are presented to illustrate the influence of surface energy effects and layer thickness on the elastic field.