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.

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.

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.

A technique for modelling arbitrary discontinuities in finite elements is presented. Both discontinuities in the function and its derivatives are considered. Methods for intersecting and branching discontinuities are given. In all cases, the discontinuous approximation is constructed in terms of a signed distance functions, so level sets can be used to update the position of the discontinuities. A standard displacement Galerkin method is used for developing the discrete equations. Examples of the following applications are given: crack growth, a journal bearing, a non‐bonded circular inclusion and a jointed rock mass. Copyright © 2001 John Wiley & Sons, Ltd.