Arbitrary branched and intersecting cracks with the extended finite element method

Authors

  • Christophe Daux,

    1. Department of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A.
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    • Research Assistant, Ecole Normale Superieure de Cachan, France

  • Nicolas Moës,

    Corresponding author
    1. Department of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A.
    • Department of Mechanical Engineering, Northwestern University, 215 Sheridan Road, Evanston, IL 60208, U.S.A.
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    • Research Associate, Department of Mechanical Engineering

  • John Dolbow,

    1. Department of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A.
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    • Assistant Professor, Department of Civil & Environmental Engineering, Duke University

  • Natarajan Sukumar,

    1. Department of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A.
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    • Post-Doctoral Research Fellow, Department of Civil Engineering

  • Ted Belytschko

    1. Department of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A.
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    • Walter P. Murphy, Professor of Mechanical Engineering


Abstract

Extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended finite element method (X-FEM) allows the representation of crack discontinuities and voids independently of the mesh. A standard displacement-based approximation is enriched by incorporating discontinuous fields through a partition of unity method. A methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed. Computation of the stress intensity factors (SIF) in different examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique. Copyright © 2000 John Wiley & Sons, Ltd.

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