Extended finite element method and fast marching method for three-dimensional fatigue crack propagation

N. Sukumar, D. L. Chopp, B. Moran

Research output: Contribution to journalArticlepeer-review

253 Scopus citations


A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, 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 modeled by finite elements with no explicit meshing of the crack surfaces. The initial crack geometry is represented by level set functions, and subsequently signed distance functions are used to compute the enrichment functions that appear in the displacement-based finite element approximation. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. Stress intensity factors for planar three-dimensional cracks are computed, and fatigue crack growth simulations for planar cracks are presented. Good agreement between the numerical results and theory is realized.

Original languageEnglish (US)
Pages (from-to)29-48
Number of pages20
JournalEngineering Fracture Mechanics
Issue number1
StatePublished - Jan 2003
Externally publishedYes


  • Crack propagation
  • Extended finite element method
  • Fast marching method
  • Level set method
  • Stress intensity factor

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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