On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

Stéphane P.A. Bordas, Sundararajan Natarajan, Pierre Kerfriden, Charles Edward Augarde, D. Roy Mahapatra, Timon Rabczuk, Stefano Dal Pont

Research output: Contribution to journalArticlepeer-review

136 Citations (Scopus)


By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25:137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6):859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM).

Original languageEnglish
Pages (from-to)637-666
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Issue number4-5
Publication statusPublished - 2011 Apr 29


  • Boundary integration
  • EXtended finite element method
  • Linear elastic fracture mechanics
  • Smoothed finite element method
  • Strain smoothing

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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