Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity

Abstract

In traditional continuum mechanics, the effect of surface energy is ignored as it is small compared to the bulk energy. For nanoscale materials and structures, however, the surface effects become significant due to the high surface/volume ratio. In this paper, two-dimensional elastic field of a nanoscale elliptical inhomogeneity embedded in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin–Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. By using the complex variable technique of Muskhelishvili, the analytic potential functions are obtained in the form of an infinite series. Selected numerical results are presented to study the size-dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. It is found that the elastic field of an elliptic inhomogeneity under uniform eigenstrain is no longer uniform when the interfacial stress effects are taken into account.