Fundamental-solution-based hybrid finite element with singularity control for two-dimensional mixed-mode crack problems

In this work, a fundamental-solution-based hybrid finite element method is presented for modeling mixed-mode cracks in two-dimensional (2D) isotropic elastic media. In the method, a double-variable hybrid functional for each element is formulated to derive element stiffness equation in terms of nodal displacements, which includes line integrals along the element boundary only. The element interior displacement field is approximated using a linear combination of displacement fundamental solutions at different source locations, while the independent element frame displacement field is approximated by one-dimensional shape function interpolation. To correctly model the behavior of crack-tip displacement, the discontinuous quarter-point crack-tip singular hybrid element formulation is developed, so that crack tip stress intensity factors can be easily evaluated by the near-tip displacement method. Three numerical examples of internal cracks in 2D elastic domains are presented to show the efficiency of the proposed method.