Stress concentration around an elliptical hole with surface tension based on the original Gurtin–Murdoch model

作者：M. Dai, Hai-Bing Yang, P. Schiavone · 发表于：Mechanics of materials (Print) · 年份：2019 · DOI：10.1016/J.MECHMAT.2019.05.009 · 研究领域：Materials Science

Abstract It is widely appreciated that surface tension plays a central role in the mechanics of soft solids such as gels. The original Gurtin–Murdoch (G–M) surface model incorporated the contribution of surface tension also via the dependence of surface stress on surface deformation. In many subsequent researches, this contribution was neglected presumably to simplify the analysis of the corresponding models of deformation. Here, we restore the original G–M surface model and re-examine the problem of an elliptical hole with a constant surface tension in an elastic infinite plane under a uniform remote in-plane loading. Semi-analytic solutions for the full stress field are derived based on series expansion techniques. Numerical examples are presented to compare the original G–M model with its simplified counterpart (which neglects the deformation-induced change in the configuration of the hole) in predicting the hoop stress around the hole. We show that in the absence of remote loading the use of the simplified G–M model generally overestimates the surface tension-induced residual hoop stress around the hole especially when the hole is slender. In the context of the original G–M model, we find that the presence of surface tension may intensify the remote loading-induced hoop stress concentration significantly at the endpoints of the hole's major axis as the hole becomes slender (for example, in the case of a remote tensile loading perpendicular to the major axis of the hole), ...