An iterative coupling between meshless methods to solve embedded crack problems

A truly meshless iterative coupling is presented to solve linear elastic fracture mechanic (LEFM) problems. The global domain of the problem is decomposed into sub-domains, where each one is addressed using an appropriate meshless method. The sub-domain which has embedded cracks is modeled by the method of fundamental solutions (MFS) with the help of the numerical Greens function (NGF) approach and the sub-domain without cracks is modeled by the meshless local Petrov–Galerkin (MLPG) procedure. By using the NGF approach the representation of the crack is automatically included. The specific computations of each meshless method are performed independently, coupled with an iterative renewal of variables procedure, restricted to interface unknowns, to achieve the final convergence. The iterative solution procedure presented yields good results as compared with the boundary element method and analytical solutions for stress intensity factor computations.