Smoothing, enrichment and contact in the element-free Galerkin method

The element-free Galerkin (EFG) method belongs to the class of mesh-free methods, which are well-suited to problems involving crack propagation due to the absence of any predefined element connectivity. However, the original visibility criterion used to model cracks leads to interior discontinuities in the displacements. Three methods for smoothing meshless approximations near nonconvex boundaries such as cracks are reviewed and compared: (1) the diffraction method, which wraps the nodal domain of influence a short distance around a point of discontinuity, such as a crack tip; (2) the transparency method, which gradually severs the domains of influence near crack tips: and (3) the `see-through' method, or continuous line criterion. Two techniques for enriching the EFG approximations near the tip of a linear elastic crack are also summarized and compared: extrinsic enrichment, in which special functions are added to the trial function; and intrinsic enrichment, in which the EFG basis is expanded by special functions. A contact algorithm based on a penalty method is also introduced for enforcing crack contact in overall compressive fields. Several problems involving arbitrary crack propagation are solved to illustrate the effectiveness of EFG for this class of problems.