ENRICHED ELEMENT-FREE GALERKIN METHODS FOR CRACK TIP FIELDS

The Element-Free Galerkin (EFG) method is a meshless method for solving partial di¤erential equations which uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate reÞnement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial reÞnement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic Þelds to the trial function and (2) augmenting the basis by the asymptotic Þelds. A local mapping of the enriched Þelds for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom.