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*

No abstract

No abstract

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.

No abstract

A new model for homogeneous nucleation of structural phase transformations, which can span the range of nucleation from classical to nonclassical, is presented. This model is extended from the classical nucleation theory by introducing driving-force dependencies into the interfacial free energy, the misfit strain energy, and the nucleus chemical free-energy change in order to capture the nonclassical nucleation phenomena. The driving-force dependencies are determined by matching the asymptotic solutions of the new model for the nucleus size and the nucleation energy barrier to the corresponding asymptotic solutions of the Landau-Ginzburg model for nucleation of solid-state phase transformations in the vicinity of lattice instability. Thus, no additional material parameters other than those of the classical nucleation theory and the Landau-Ginzburg model are required, and nonclassical nucleation behavior can be easily predicted based on the well-developed analytical solutions of the classical nucleation model. A comparison of the new model to the Landau-Ginzburg model for homogeneous nucleation of a dilatational transformation is presented as a benchmark example. An application to homogeneous nucleation of a cubic-to-tetragonal transformation is presented to illustrate the capability of this model. The nonclassical homogeneous nucleation behavior of the experimentally studied fcc → bcc transformation in the Fe-Co system is examined by the new model, which predicts a 20 pct reduction in the critical driving force for homogeneous nucleation.

No abstract

No abstract