On the path independency of the point-wise J integral in three-dimensions

Netta Omer, Zohar Yosibash*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


The asymptotic solution in the vicinity of a crack front in a three-dimensional (3-D) elastic domain is provided explicitly following the general framework in M. Costabel, M. Dauge and Z. Yosibash, 2004, SIAM Journal of Mathematical Analysis, 35(5), 1177-1202. Using it, we show analyticall y for several fully 3-D displacement fields (which are neither plane strain nor plane stress) that the pointwise path-area JX1-integral in 3-D is path-independent. We then demonstrate by numerical examples, employing p-finite element methods, that good numerical approximations of the path-area JX1-integral may be achieved which indeed show path independency. We also show that computation of the path part of the JX1 on a plane perpendicular to the crack front is path dependent. However, one may still use this path integral computed at several radii, followed by the application of Richardson's extrapolation technique (as R → 0) to obtain a good estimate for JX1-integral.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalInternational Journal of Fracture
Issue number1-4
StatePublished - Nov 2005
Externally publishedYes


  • Edge stress intensity functions
  • High order finite elements
  • J -integral


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