Modeling holes and inclusions by level sets in the extended finite-element method

N. Sukumar*, D. L. Chopp, N. Moës, T. Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

989 Scopus citations


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. Osher, J.A. Sethian, J. Comput. Phys. 79 (1) (1988) 12) to the extended finite-element method (X-FEM) (N. Moës, J. Dolbow, T. Belytschko, Int. J. Numer. Methods Engrg. 46 (1) (1999) 131). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of holes and material interfaces, and in addition, the level set function is used to develop the local enrichment for material interfaces. Numerical examples in two-dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique.

Original languageEnglish (US)
Pages (from-to)6183-6200
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Issue number46-47
StatePublished - Sep 14 2001


  • Elastic inclusion
  • Extended finite-element method
  • Level set method
  • Material interface
  • Voids

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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