Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth

L. Chen, T. Rabczuk, S. P.A. Bordas, G. R. Liu, K. Y. Zeng, P. Kerfriden

Research output: Contribution to journalArticlepeer-review

158 Citations (Scopus)

Abstract

This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.

Original languageEnglish
Pages (from-to)250-265
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume209-212
DOIs
Publication statusPublished - 2012 Feb 1

Keywords

  • Convergence rate
  • Edge-based smoothed finite element method
  • Extended finite element method
  • Fracture analysis
  • Numerical method
  • Stress intensity factor

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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