Computational Mechanics

, Volume 40, Issue 3, pp 473–495

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

Original Paper

DOI: 10.1007/s00466-006-0122-1

Cite this article as:
Rabczuk, T., Bordas, S. & Zi, G. Comput Mech (2007) 40: 473. doi:10.1007/s00466-006-0122-1


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 

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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