Generalized finite element method enrichment functions for curved singularities in 3D fracture mechanics problems

J. P. Pereira, C. A. Duarte, X. Jiao, D. Guoy

Research output: Contribution to journalArticlepeer-review


This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of curvilinear coordinate systems. A description of the computation of derivatives of enrichment functions and curvilinear base vectors is presented. The coordinate systems are automatically defined using geometrical information provided by an explicit representation of the crack surface. A detailed procedure to accurately evaluate the surface normal, conormal and tangent vectors along curvilinear crack fronts in explicit crack surface representations is also presented. An accurate and robust definition of orthonormal vectors along crack fronts is crucial for the proper definition of enrichment functions. Numerical experiments illustrate the accuracy and robustness of the proposed approaches.

Original languageEnglish (US)
Pages (from-to)73-92
Number of pages20
JournalComputational Mechanics
Issue number1
StatePublished - Jun 2009


  • 3D fracture mechanics
  • Crack front enrichments
  • Generalized/Extended finite element method
  • Partition of unity methods

ASJC Scopus subject areas

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

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