A method for growing multiple cracks without remeshing and its application to fatigue crack growth

Goangseup Zi, Jeong Hoon Song, Elisa Budyn, Sang Ho Lee, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

90 Citations (Scopus)


A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

Original languageEnglish
Pages (from-to)901-915
Number of pages15
JournalModelling and Simulation in Materials Science and Engineering
Issue number5
Publication statusPublished - 2004 Sept

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Computer Science Applications


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