The Element-Free Galerkin (EFG) method is a meshless method for solving partial differential 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 refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used:(1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields 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. 1997 by John Wiley & Sons, Ltd. " !cos M cos !sin M sin C J !cos M sin #sin M cos C J !sin M cos #cos M sin C J !sin M sin !cos M cos C J * *x*

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A computational methodology for nucleation of phase hansformations in a class of gade 2. non-linearly elastic materials is presented. Nucleation is treated as an energy exbmum problem. The material is assumed to be governed by a non-linear. non-local elastic constitutive relation represented by a Landau-Ginzburg potential. The extremum problem is solved using the element-free Galerkin (m) method and a pembed Lagrangian lechnique. The m method is used because of its abflity to handle continuity of displacement gradients required in the weak form. Applications to homogeneous nucleation in hvo dimensions are presented which illustrate the accurae of the method and its suitability for problems of this Wpe.

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