In-plane stress analysis of two nanoscale holes under surface tension

Studied in this paper is the surface tension-induced stress field around two nanoscale holes in an infinite, elastic matrix. The complex variable method is adopted to describe the assumed plane-strain deformation of the structure. The stress boundary conditions at the surfaces of the holes are formulated via the integral-type Gurtin–Murdoch model. The stress field is finally obtained with the aid of conformal mapping and series expansion methods. Numerical examples are demonstrated for the case of one approximately triangular, smooth hole and one approximately square, smooth hole. A detailed discussion is carried out about the influence of the distance between the two holes on the stress field.