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

Abstract

The application of a coupled ®nite 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 ®nite element method which allows for the use of the EFG method in the crack region and the ®nite 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 C 1 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.

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…Moreover, the extension of the diffraction method into three dimensions is complex. Nevertheless, several authors have presented implementations of the diffraction method in 3D [216,217].…”

Derivative recovery and a posteriori error estimate for extended finite elements

“…This gives the method the ability to achieve good accuracy with relatively coarse meshes. Note that partition of unity has also been applied in a so-called meshfree context, through extrinsic enrichment [19,46], intrinsic enrichment [43] or weight function enrichment [18]. One of the most recent examples for fracture of quasi-brittle materials using meshfree methods with extrinsic enrichment is shown here: [33].…”

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…In order to model fractures / discontinuities, the method requires adaptation of the weight functions of the nodes whose domain of influence is cut by the fracture. This can be done either in a sharp / discontinuous way or via a smooth approximation (Sukumar et al, 1997;Krysl and Belytschko, 1999). Ultimately, this implies to carry and update an important data structure and perform special operations to account for fracture efficiently.…”

“…Despite its early attractiveness, the use of EFG for fracture propagation has had limited success (Sukumar et al, 1997). The reasons for its limited success are mostly related to integration procedures (underlying mesh), data structure, and weight functions for handling fracture propagation in a simple and accurate manner.…”