New crack-tip elements for XFEM and applications to cohesive cracks

Goangseup Zi, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

473 Citations (Scopus)


An extended finite element method scheme for a static cohesive crack is developed with a new formulation for elements containing crack tips. This method can treat arbitrary cracks independent of the mesh and crack growth without remeshing. All cracked elements are enriched by the sign function so that no blending of the local partition of unity is required. This method is able to treat the entire crack with only one type of enrichment function, including the elements containing the crack tip. This scheme is applied to linear 3-node triangular elements and quadratic 6-node triangular elements. To ensure smooth crack closing of the cohesive crack, the stress projection normal to the crack tip is imposed to be equal to the material strength. The equilibrium equation and the traction condition are solved by the Newton-Raphson method to obtain the nodal displacements and the external load simultaneously. The results obtained by the new extended finite element method are compared to reference solutions and show excellent agreement.

Original languageEnglish
Pages (from-to)2221-2240
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number15
Publication statusPublished - 2003 Aug 21
Externally publishedYes


  • Cohesive crack
  • Crack growth
  • Finite elements
  • Fracture

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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