Extended finite element method for three-dimensional crack modelling

Authors

  • N. Sukumar,

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

  • N. Moës,

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

  • B. Moran,

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

  • T. Belytschko

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


Abstract

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

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