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

The clement-free Galerkin (EFG) method belongs to the class of mesh-free me thods, 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 dist ance around a point of discontinuity, such as a crack tip; (2) the transpar ency method, which gradually severs the domains of influence near crack tip s; and (3) the "see-through" method, or continuous line criterion. Two tech niques for enriching the EFG approximations near the tip of a linear elasti c crack are also summarized and compared. extrinsic enrichment, in which sp ecial functions are added to the trial function: and intrinsic enrichment, in which the EFG basis is expanded by special functions. A contact algorith m based on a penalty method is also introduced for enforcing crack contact in overall compressive fields. Several problems involving arbitrary crack p ropagation are solved to illustrate the effectiveness of EFG for this class of problems. (C) 1999 Elsevier Science Ltd. All rights reserved.