Role of surface effects in the finite deformation of an elastic solid with elliptical hole

We study the finite plane deformations of a particular harmonic material surrounding an elliptical hole whose boundary incorporates the contribution of surface mechanics. We are particularly interested in the distribution of the Piola hoop stress along the edge of the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by the surface effects is identical to that in the corresponding case in a linearly elastic solid. In addition, we show that even in the presence of surface effects, we can nevertheless design a so-called ‘harmonic hole’ where the Piola mean stress remains constant everywhere in the surrounding solid. In this case, however, the hoop stress is no longer constant along the edge of the elliptical hole due to the contribution from surface energy.

► Surface effects in solids subjected to large deformations.
► Design of harmonic holes in a class of non-linearly elastic solids.
► Contribution of surface energy to the stress concentration: large deformations.