Enriched element-free galerkin methods for crack tip fields

M. Fleming*, Y. A. Chu, B. Moran, T. Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

638 Scopus citations


The Element-Free Galerkin (EFG) method is a meshless method for solving partial differential equations which uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom.

Original languageEnglish (US)
Pages (from-to)1483-1504
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
StatePublished - 1997
Externally publishedYes


  • Crack propagation
  • Elastostatic fracture
  • Enriched approximations
  • Meshless methods
  • Stress intensity factor

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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