Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

Ted Belytschko, Hao Chen, Jingxiao Xu, Goangseup Zi

Research output: Contribution to journalArticlepeer-review

457 Citations (Scopus)


A methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial differential equation loses hyperbolicity. The approach is limited to rate-independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extended finite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks.

Original languageEnglish
Pages (from-to)1873-1905
Number of pages33
JournalInternational Journal for Numerical Methods in Engineering
Issue number12
Publication statusPublished - 2003 Nov 28
Externally publishedYes


  • Cohesive crack model
  • Dynamic fracture
  • Extended finite element method
  • Finite element method
  • Fracture mechanics
  • Loss of hyperbolicity

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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