Surface effect on deformation around an elliptical hole by surface energy density theory

Abstract

The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.