Computational Mechanics

, Volume 40, Issue 3, pp 473–495 | Cite as

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

  • Timon Rabczuk
  • Stéphane Bordas
  • Goangseup Zi
Original Paper


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.


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


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Copyright information

© Springer Verlag 2007

Authors and Affiliations

  1. 1.Institute for Numerical MechanicsTechnical University of MunichGarching b. MunichGermany
  2. 2.Ecole Polytechnique Fédérale de Lausanne (EPFL) Laboratoire de structures et de mécanique des milieux continusLausanneSwitzerland
  3. 3.Department of Civil and Environmental EngineeringKorea UniversitySeoulSouth Korea

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