SGBEM–FEM coupling for analysis of cracks in 3D anisotropic media

Abstract

AbstractA weakly singular symmetric Galerkin boundary element method (SGBEM) is coupled with the standard finite element method (FEM) in order to establish an accurate and efficient numerical technique for analysis of fractures in three‐dimensional, anisotropic, linearly elastic media. In the strategy, the weakly singular SGBEM developed by Rungamornrat and Mear (textitInt. J. Solids Struct. 2008; 45:1283–1301; Comput. Methods Appl. Mech. Engrg 2008; 197:4319–4332) is utilized to model a small‐scale region containing the crack while the (possibly large and complex) compliment region is treated by the FEM. The coupled technique exploits the positive features of both methods; the SGBEM proves to be a convenient and highly accurate method for obtaining mixed‐mode stress intensity factors along the crack front, whereas the FEM is very efficient for modeling large‐scale problems in the absence of cracks. An important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the SGBEM and FEM regions is enforced in a weak sense. This allows the two regions (one modeled by the SGBEM and the other by the FEM) to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions, and this flexibility in the discretization process leads to a significant reduction in the modeling effort. To demonstrate the utility and accuracy of the technique, several boundary value problems involving both embedded and surface breaking cracks are treated, and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement. Copyright © 2010 John Wiley & Sons, Ltd.