Formulation and implementation of a high-order 3-D domain integral method for the extraction of energy release rates

H. Ozer, C. A. Duarte, I. L. Al-Qadi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This article presents a three dimensional (3-D) formulation and implementation of a high-order domain integral method for the computation of energy release rate. The method is derived using surface and domain formulations of the J-integral and the weighted residual method. The J-integral along 3-D crack fronts is approximated by highorder Legendre polynomials. The proposed implementation is tailored for the Generalized/eXtended Finite Element Method and can handle discontinuities arbitrarily located within a finite element mesh. The domain integral calculations are based on the same integration elements used for the computation of the stiffness matrix. Discontinuities of the integrands across crack surfaces and across computational element boundaries are fully accounted for. The proposed method is able to deliver smooth approximations and to capture the boundary layer behavior of the J-integral using tetrahedral meshes. Numerical simulations of mode-I and mixed mode benchmark fracture mechanics examples verify expected convergence rates for the computed energy release rates. The results are also in good agreement with other numerical solutions available in the literature.

Original languageEnglish (US)
Pages (from-to)459-476
Number of pages18
JournalComputational Mechanics
Issue number4
StatePublished - Apr 2012
Externally publishedYes


  • Extended finite element method
  • Fracture
  • Generalized finite element method
  • J-Integral

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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