Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method

D. L. Chopp*, N. Sukumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

113 Scopus citations


A numerical technique for modeling fatigue crack propagation of multiple coplanar cracks is presented. The proposed method couples the extended finite element method (X-FEM) [Int. J. Numer. Meth. Engng. 48 (11) (2000) 1549] to the fast marching method (FMM) [Level Set Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, Cambridge, UK, 1999]. The entire crack geometry, including one or more cracks, is represented by a single signed distance (level set) function. Merging of distinct cracks is handled naturally by the FMM with no collision detection or mesh reconstruction required. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. 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 [Comput. Meth. Appl. Mech. Engng. 139 (1996) 289]. This enables the domain to be modeled by a single fixed finite element mesh with no explicit meshing of the crack surfaces. In an earlier study [Engng. Fract. Mech. 70 (1) (2003) 29], the methodology, algorithm, and implementation for three-dimensional crack propagation of single cracks was introduced. In this paper, simulations for multiple planar cracks are presented, with crack merging and fatigue growth carried out without any user-intervention or remeshing.

Original languageEnglish (US)
Pages (from-to)845-869
Number of pages25
JournalInternational Journal of Engineering Science
Issue number8
StatePublished - May 2003


  • Coplanar cracks in 3-d
  • Extended finite element method
  • Fast marching method
  • Fatigue crack growth
  • Level set method
  • Partition of unity

ASJC Scopus subject areas

  • Materials Science(all)
  • Engineering(all)
  • Mechanics of Materials
  • Mechanical Engineering


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