Extended finite element method for three-dimensional crack modelling

N. Sukumar, N. Moës, B. Moran, T. Belytschko*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1089 Scopus citations


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 (C) 2000 John Wiley and Sons, Ltd.

Original languageEnglish (US)
Pages (from-to)1549-1570
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number11
StatePublished - Aug 2000
Externally publishedYes


  • Elastostatics
  • Extended finite element method
  • Local enrichment
  • Partition of unity
  • Planar three-dimensional cracks

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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