Influence of surface effect of the edge of a half-plane on the stress concentration around a nearby nanosized hole of arbitrary shape

In the problem of a half-plane containing a nearby nanosized hole, it is customary to assume that the edge of the half-plane is traction free. In the context of nanomechanics, however, the more realistic scenario is to incorporate surface effects not only on the edge of the hole but also on the edge of the half-plane. Our results indicate that the incorporation of surface effects on the edge of the half-plane indeed plays a significant role, in particular as the distance between the hole and the half-plane decreases. In fact, we show that the absence of the corresponding surface effect on the edge of the half-plane induces a significant error in the stress concentration around an arbitrary-shaped hole when the distance between the hole and the edge reaches a critical value. We illustrate our results with a variety of examples including circular, elliptical, triangular and square-shaped holes.