Boundary Element Method for Mixed Mode Fracture Analysis

Denda and Marante [1] have developed the boundary element method for the mixed mode fracture analysis of multiple curvilinear cracks in the general anisotropic solids in two dimensions for which in-plane Mode I, II, and out-of-plane Mode III, of fracture are coupled. They have developed the crack tip singular element (CTSE) to model any curvilinear cracks, including center and edge cracks. The CTSE is one of the best performers among the existing 2-D crack modeling strategies introduce so far. The Green’s function by Snyder and Cruse [2] is limited to the single crack. The quarter-point traction and displacement crack tip elements by Tan and Gao [3] have used analytical expressions for the stress intensity factors. The dual boundary element method of Sollero and Aliabadi [4] has used the J-integral and the dislocation dipole approach of Denda [5, 6] has adopted the conservation integral developed by Chen and Shield [7] to calculate SIFs, respectively; the post-processing requirement is an extra burden for the multiple cracks problems. The numerical Green’s function by Denda and Mattingly [8], which uses the whole crack singular element (WCSE) does not require the post-processing but is limited to straight multiple cracks. The CTSE, first proposed by Denda and Dong [9] for isotropic multiple cracks, is a small WCSE element embedded at each crack tip, to extend the capability of the WCSE to multiple curvilinear cracks. It inherits the advantages of the WCSE which does not require post-processing for the SIF calculation.