Stress concentration around a pressurized elliptical hole in a soft elastic solid: Modified results and nonlinear effects

Abstract

Solutions for the elastic field in a perforated structure induced by internal loadings play an essential role in a variety of branches of engineering and applied sciences including pressure vessels and mechanics of biological tissues. In this paper, we reconsider the plane deformation problem of an elastic medium containing an elliptical hole under internal pressure. In contrast to the classical solution for this problem in which the local stress field around the elliptical hole is independent of the stiffness of the surrounding medium, we present a modified closed-form solution incorporating the ratio of the internal pressure to the modulus of the medium by taking into account the directional change of the internal pressure during deformation. We show via large deformation-based finite element simulations of a hyperelastic solid with a pressurized elliptical hole that the modified solution is indeed more accurate than the classical counterpart in predicting the local elastic field and is capable of capturing, to some extent, the nonlinear elastic response of the perforated solid to the internal pressure. In particular, we attain a stiffness-dependent stress intensity factor at the tips of the hole when it tends to a slender crack. Numerical examples are also presented to illustrate the detailed differences between the modified and classical solutions relative to the aspect ratio of the elliptical hole.