SUMMARYAn element-free Galerkin method which is applicable to arbitrary shapes but ,requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.

SUMMARYA minimal remeshing ÿnite element method for crack growth is presented. Discontinuous enrichment functions are added to the ÿnite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy.

An improvement of a new technique for modelling cracks in the ÿnite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous ÿelds and the near tip asymptotic ÿelds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique.

An improvement of a new technique for modelling cracks in the ÿnite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous ÿelds and the near tip asymptotic ÿelds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique.

No abstract

A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (S.

Abstract.The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

The extended finite element method allows one to model displacement discontinuities which do not conform to interelement surfaces. This method is applied to modeling growth of arbitrary cohesive cracks. The growth of the cohesive zone is governed by requiring the stress intensity factors at the tip of the cohesive zone to vanish. This energetic approach avoids the evaluation of stresses at the mathematical tip of the crack. The effectiveness of the proposed approach is demonstrated by simulations of cohesive crack growth in concrete.