Self-similar crack expansion method for three-dimensional crack analysis

Yonglin Xu, B. Moran, T. Belytschko

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The self-similar crack expansion method is developed to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique. With this method, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface, and the crack expansion rate, which is related to the crack energy release rate, is estimated by using a technique based on self similar (virtual) crack extension. For elements on the crack surface, regular integrals and singular integrals are evaluated based on closed-form expressions, which improves the accu- racy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than one percent as compared with exact solutions. The stress intensity factors of subsurface cracks are in good agreement with other numerical solutions.

Original languageEnglish (US)
Pages (from-to)729-737
Number of pages9
JournalJournal of Applied Mechanics, Transactions ASME
Issue number4
StatePublished - Dec 1997
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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