| The element-free Galerkin (EFG) method is a computational tool for solving solid mechanics problems with an approximation based only on nodes. It is developed here for linear elastic fracture problems. This method, which belongs to the class of meshless methods, is particularly useful for problems involving crack propagation due to the absence of any predefined element connectivity.; Special techniques are presented for enriching the EFG approximations near the tip of a linear elastic crack. In this region, the first term of an asymptotic expansion of the stress is 1/{dollar}sqrt{lcub}r{rcub}{dollar} singular and dominates the stress field. The enrichment is formulated so as to include all or part of the near tip crack field. Two methods are presented for enriching EFG approximations: extrinsic enrichment involves adding the form of the solution to the trial function; for intrinsic enrichment, the EFG basis is expanded to include terms from the near tip crack solution.; Three basic methods of smoothing meshless approximations near nonconvex boundaries are presented. The diffraction method consists of modifying the nodal domain of influence so that it wraps a short distance around a point of discontinuity, such as a crack tip. The transparency method, which is described only for cracks, yields continuous approximations by gradually severing the domains of influence near crack tips. The "see-through" method, or continuous line criterion, does not enforce a discontinuity or crack if the tip is within the domain of influence and has no effect in the presence of smooth boundaries.; A contact algorithm is presented for cracks in sliding contact. The variational principle is modified by placing a penalty on the amount of interpenetration of two surfaces, which enforces contact. A two-surface model is introduced for crack contact in meshless methods. Because cracks are modeled by lines which cut the domains of influence, a two surface crack model is introduced in which pseudosurfaces are introduced along the crack and are used for contact checking.; Several problems involving fatigue and quasi-static crack propagation are solved to illustrate the effectiveness of EFG for this class of problems. |
