Extended meshfree methods without branch enrichment for cohesive cracks

Goangseup Zi, Timon Rabczuk, Wolfgang Wall

Research output: Contribution to journalArticlepeer-review

161 Citations (Scopus)


An extended meshless method for both static and dynamic cohesive cracks is proposed. This new method does not need any crack tip enrichment to guarantee that the crack closes at the tip. All cracked domains of influence are enriched by only the sign function. The domain of influence which includes a crack tip is modified so that the crack tip is always positioned at its edge. The modification is only applied for the discontinuous displacement field and the continuous field is kept unchanged. In addition to the new method, the use of Lagrange multiplier is explored to achieve the same goal. The crack is extended beyond the actual crack tip so that the domains of influence containing the crack tip are completely cut. It is enforced that the crack opening displacement vanishes along the extension of the crack. These methods are successfully applied to several well-known static and dynamic problems.

Original languageEnglish
Pages (from-to)367-382
Number of pages16
JournalComputational Mechanics
Issue number2
Publication statusPublished - 2007 Jul


  • Cohesive cracks
  • Extended element free Galerkin method (XEFG)
  • Local partition of unity
  • Static and dynamic fractures

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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