Improved implementation and robustness study of the X-FEM for stress analysis around cracks

Authors

  • E. Béchet,

    1. Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 6183, Ecole Centrale de Nantes, B.P. 92101, 44321 Nantes Cedex 3, France
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  • H. Minnebo,

    1. Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 6183, Ecole Centrale de Nantes, B.P. 92101, 44321 Nantes Cedex 3, France
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  • N. Moës,

    Corresponding author
    1. Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 6183, Ecole Centrale de Nantes, B.P. 92101, 44321 Nantes Cedex 3, France
    • Institut de Recherche en Génie Civil et Mécanique, Ecole Centrale de Nantes, B.P. 92101, 1 rue de la Noë, 44321 Nantes Cedex 3, France
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  • B. Burgardt

    1. SNECMA Moteurs, Rond Point René Ravaud—Réau, 77550 Moissy-Cramayel, France
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Abstract

Numerical crack propagation schemes were augmented in an elegant manner by the X-FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh, which is of industrial interest, especially when a numerical model for crack propagation is desired. This paper improves the implementation of the X-FEM method for stress analysis around cracks in three ways. First, the enrichment strategy is revisited. The conventional approach uses a ‘topological’ enrichment (only the elements touching the front are enriched). We suggest a ‘geometrical’ enrichment in which a given domain size is enriched. The improvements obtained with this enrichment are discussed. Second, the conditioning of the X-FEM both for topological and geometrical enrichments is studied. A preconditioner is introduced so that ‘off the shelf’ iterative solver packages can be used and perform as well on X-FEM matrices as on standard FEM matrices. The preconditioner uses a local (nodal) Cholesky based decomposition. Third, the numerical integration scheme to build the X-FEM stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme. A 2D benchmark problem is designed to show the improvements and the robustness. Copyright © 2005 John Wiley & Sons, Ltd.

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