An element-free Galerkin method for three-dimensional fracture mechanics

The application of a coupled finite element± element-free Galerkin (EFG) method to problems in threedimensional fracture is presented. The EFG method is based on moving least square (MLS) approximations and uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. The EFG method is coupled with the finite element method which allows for the use of the EFG method in the crack region and the finite element method to model the remainder of the problem. Domain integral methods are used to evaluate stress intensity factors along the 3D crack front. Both planar and volume representations of the domain integrals are considered. The former require derivatives of stress and strain which are readily obtainable in the EFG method due to the C¹ continuity of the MLS approximations used here. Applications of the method to the determination of stress intensity factors along planar cracks in 3D are presented