Acta Mechanica Solida Sinica

, Volume 25, Issue 4, pp 393–403 | Cite as

Enriched Goal-Oriented Error Estimation Applied to Fracture Mechanics Problems Solved by XFEM

  • Zhijia Lin
  • Zhuo Zhuang
  • Xiaochuan You
  • Heng Wang
  • Dandan Xu


Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method (XFEM), which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.

Key words

goal-oriented error estimation extended finite element method fracture mechanics error bounds 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  • Zhijia Lin
    • 1
  • Zhuo Zhuang
    • 1
  • Xiaochuan You
    • 1
  • Heng Wang
    • 1
  • Dandan Xu
    • 1
  1. 1.Applied Mechanics Lab., School of AerospaceTsinghua UniversityBeijingChina

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