A three-dimensional large deformation meshfree method for arbitrary evolving cracks

T. Rabczuk, T. Belytschko

Research output: Contribution to journalArticlepeer-review

840 Citations (Scopus)


A new approach for modelling discrete cracks in meshfree particle methods in three dimensions is described. The cracks can be arbitrarily oriented, but their growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centered at the particles. The method is formulated for large deformations and arbitrary nonlinear and rate-dependent materials; cohesive laws govern the traction-crack opening relations. To reduce computational cost and since more accuracy around the crack tip is needed to obtain adequate results, h-adaptivity is incorporated in the method. The model is applied to several three-dimensional problems, some of which are compared to experimental data.

Original languageEnglish
Pages (from-to)2777-2799
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
Issue number29-30
Publication statusPublished - 2007 May 15


  • Cohesive crack model
  • Dynamic fracture
  • Meshfree methods

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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