Stress field around an arbitrarily shaped nanosized hole with surface tension

Surface tension plays an important role in nanosized materials. In this paper, the stress field induced by surface tension around an arbitrarily shaped nanosized hole is investigated through complex variable-method using truncated series, with an emphasis on the relationship between the hoop stress and the curvature of the hole's boundary curve. Our numerical results for various shapes of holes show that maximum hoop stress always appears nearby, but not exactly at the point of maximum curvature on the hole's boundary. Surprisingly, for elliptical holes with certain aspect ratios and typical non-elliptical holes (such as triangular, square and rectangular holes), our results show that hoop stress can even attain a local minimum (not a local maximum) or even the overall minimum at the point of maximum curvature. In particular, surface tension-induced hoop stress can be very large around nanosized holes. On the other hand, the surface tension-induced stress field is always localized for nanosized holes of arbitrary shapes and fades away with increasing distance from the hole.