Abstract:The application of element-free Galerkin(EFG) method to problems in three-dimensional fracture problems is presented. The EFG method is based on moving least square(MLS) approximations,and only a set of nodal points and a description of the body are employed to formulate the discrete model. In the EFG method,displacement boundary conditions are not included directly,so along the orientation of displacement known on boundary or surface,a set of springs to implement the essential boundary conditions are assumed. One side of the spring links together with the boundary or surface known displacement,and the other one is fixed. The mistake between calculating displacement and known displacement is regarded as transmutation of spring. The spring is a part of the body,so the potential energy is a part of strain energy of body. The crack causes discontinuity of the body. It has isolation effect on nodal points. The isolation effect of cracks on domain of influence for Gauss points is dealt by the application of visibility criterion. A simple and efficient scheme is proposed to define the variable domain of nodal points influence. The scheme deems that the number of nodal points is constant and visible from each domain of influence. This method significantly increases the efficiency of computing approximate functions by limiting the size of the least-square problem. Three-dimensional discontinuous displacement method is used to evaluate stress intensity factors along the 3D crack front. Applications of the method to the determination of stress intensity factors along single edge planar cracks and single through edge planar crack in 3D finite bodies are presented. The obtained stress intensity factors for both problems are found to be in good agreement with SIF values reported in previous studies. It can guarantee the success for trace propagation of three-dimensional crack.