Explicit expressions for energy release rates using virtual crack extensions

Robert B. Haber, Hyun M. Koh

Research output: Contribution to journalArticlepeer-review


A new finite element technique for calculating energy release rates is presented. An explicit expression for energy changes due to virtual crack extensions is formulated based on a variation of isoparametric element mappings. Energy release rates are calculated directly from integral expressions evaluated over singular quarter‐point isoparametric elements surrounding the crack tip. Since the energy release rates are expressed in variational form, there is no need for the analyst to select a small finite crack extension to simulate a virtual crack extension. The method is shown to produce very accurate solutions even with fairly coarse element meshes. A similar technique for mixed‐mode fracture based on mutual potential energy release rates is described.

Original languageEnglish (US)
Pages (from-to)301-315
Number of pages15
JournalInternational Journal for Numerical Methods in Engineering
Issue number2
StatePublished - Feb 1985

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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