Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method

Nsu Sukumar*, D. L. Chopp, E. Béchet, N. Moës

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


A numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method (X-FEM) and the fast marching method (FMM). In crack modeling using X-FEM, the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields. The initial crack geometry is represented by two level set functions, and subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation. Crack modeling is performed without the need to mesh the crack, and crack propagation is simulated without remeshing. Crack growth is conducted using FMM; unlike a level set formulation for interface capturing, no iterations nor any time step restrictions are imposed in the FMM. Planar and non-planar quasi-static crack growth simulations are presented to demonstrate the robustness and versatility of the proposed technique.

Original languageEnglish (US)
Pages (from-to)727-748
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - 2008


  • Crack propagation
  • Enrichment function
  • Fast marching method
  • Level sets
  • Partition of uniity
  • Signed distance function
  • Stress intensity factor

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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