Surface effects in the deformation of an anisotropic elastic material with nano-sized elliptical hole

Abstract

We examine the effect of surface energy on an anisotropic elastic material weakened by an elliptical hole. A closed-form, full-field solution is derived using the standard Stroh formalism. In particular, explicit expressions for the hoop stress, normal, in-plane tangential and out-of-plane displacement components along the edge of the hole are obtained. These expressions clearly demonstrate the effect of elastic anisotropy of the bulk material on the corresponding field variables. When the material becomes isotropic, the hoop stress agrees with the well-known result in the literature while both the in-plane tangential and out-of-plane displacements vanish and the normal displacement is constant along the entire boundary of the elliptical hole.