Singular p-version finite elements for stress intensity factor computations

Pakal Rahulkumar, Sunil Saigal, Shah Yunus

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The finite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and finite non-singular stress distributions in the crack tip region. The availability of a constant stress term in addition to the singular term in the standard h-version singular finite elements is insufficient to model the finite nonsingular stress zone. A p-version singular finite element capable of modelling the higher-order non-singular stress terms in addition to the singular term and the constant term is presented. The formulation for the displacement substitution technique for computing the stress intensity factors using singular p-version triangular finite elements is developed. Unlike the standard h-version formulation, the stress intensity factors computed using the p-version displacement substitution technique do not depend on the specific arrangement and length of the quarter point elements, and require simple mesh designs as well as fewer number of degrees of freedom. Numerical studies comparing the convergence of the stress intensity factors computed by the p-version method against other available alternatives such as the h-version method and the contour integral method are presented to demonstrate the effectiveness of the present developments.

Original languageEnglish (US)
Pages (from-to)1091-1114
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • F-version
  • Finite element methods
  • Fracture mechanics
  • Mixed mode
  • Singular elements
  • Stress intensity factors


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