A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

Timon Rabczuk, Stéphane Bordas, Goangseup Zi

Research output: Contribution to journalArticle

255 Citations (Scopus)


This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.

Original languageEnglish
Pages (from-to)473-495
Number of pages23
JournalComputational Mechanics
Issue number3
Publication statusPublished - 2007 Aug 1



  • Cohesive forces
  • Extended element-free Galerkin method (XEFG)
  • Extrinsic partition of unity enrichment
  • Non-linear fracture mechanics
  • Static and dynamic fracture
  • Three-dimensional cracks

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics

Cite this