FEM-SGBEM coupling for modeling of mode-I planar cracks in three-dimensional elastic media with residual surface tension effects

Abstract

A computationally efficient numerical technique capable of modeling mode-I planar cracks in three-dimensional linear elastic media by taking the influence of the residual surface tension into account, is presented in this paper. The elastic medium (i.e., the bulk material) is modeled by the classical theory of linear elasticity, whereas the crack surface is treated as a zero-thickness layer perfectly bonded to the bulk material with its behavior governed by the special case of Gurtin–Murdoch surface elasticity model. Governing equations of the bulk material are formulated in terms of weakly singular, weak-form boundary integral equations, whereas those of the surface are cast in a weak form using a weighted residual technique. The solution of the final coupled system of governing equations is subsequently accomplished by using a numerical procedure based primarily on a coupling between standard finite element technique and a weakly singular, symmetric Galerkin boundary element method. Extensive numerical simulations are conducted and the results are compared with available benchmark solutions to verify the formulation and numerical implementation. Applications of the technique to the analysis of nano-crack problems are presented for some selected cases, to study nano-scale influence and size-dependency behavior.