A nonlocal surface theory for surface–bulk interactions and its application to mechanics of nanobeams

Abstract

A nonlocal surface theory is proposed for interactions between surface and bulk media of nanostructures. The nonlocal elasticity theory is generalized to account for nonlocal contribution and reception of surface, dividing the whole landscape of nonlocal interactions into four parts of contributions: bulk-to-bulk, surface-to-surface, surface-to-bulk, and bulk-to-surface, in the viewpoint of contributors and receivers. The thickness is restored for an originally two-dimensionally modeled surface by curvature-dependence of surface energy, and thus the commonly-used surface theories can be applied in conjunction with three-dimensional nonlocal elasticity. With application of the theory to a nanobeam, it is shown that the surface-to-bulk nonlocal interactions have the same order of magnitude as the bulk-to-bulk one and thus cannot be neglected. Furthermore, the ratio of the nonlocal characteristic length to surface thickness characterizes the ratio of surface-to-bulk nonlocal contributions to surface’s own rigidity.