Effects of surface tension in a perforated anisotropic structure

Abstract

Surface tension proves to be one of the main factors in affecting the mechanical behaviour of materials and structures at small scales. In this paper, we revisit the plane deformation of an anisotropic medium containing an initially elliptical hole endowed with surface tension, and particularly focus on the influence of surface tension on the local elastic response of the medium to an external load. To this end, we formulate, in the context of the complex variable formalism of plane anisotropic elasticity, the boundary value problem incorporating first-order changes in the normal direction and curvature of the boundary of the hole after deformation, and obtain a series solution for the incremental elastic field in the entire medium generated by an arbitrary uniform in-plane far-field load. Numerical results are presented to validate the current solution and to clarify the role of surface tension in corresponding mechanical analysis. We show that for typical anisotropic materials with a small-scale elliptical hole, the presence of surface tension contributes significantly to the local stress concentration (caused by the far-field load) only when the hole is slender (in the case of near-circular plump holes surface tension is negligible in determining the local incremental stress field). In particular, we identify that surface tension plays a role of shifting the location of the maximum stress concentration point on the boundary of the hole for certain combinations of the material anisotropy and the direction of far-field load.