A dynamic XFEM formulation for crack identification

Chao Zhang, Cuixia Wang, Tom Lahmer, Pengfei He, Timon Rabczuk

Research output: Contribution to journalArticle

19 Citations (Scopus)


Nelder–Mead (NM) and Quasi-Newton (QN) optimization methods are used for the numerical solution of crack identification problems in elastodynamics. Fracture is modeled by the eXtended Finite Element Method. The Newmark-β method with Rayleigh damping is employed for the time integration. The effects of various dynamical test loads on the crack identification are investigated. For a time-harmonic excitation with a single frequency and a short-duration signal measured along part of the external boundary, the crack is detected through the solution of an inverse time-dependent problem. Compared to the static load, we show that the dynamic loads are more effective for crack detection problems. Moreover, we tested different dynamic loads and find that NM method works more efficient under the harmonic load than the pounding load while the QN method achieves almost the same results for both load types.

Original languageEnglish
JournalInternational Journal of Mechanics and Materials in Design
Publication statusAccepted/In press - 2015 Jun 3


  • Crack identification
  • Inverse analysis
  • Nelder–Mead method
  • Quasi-Newton method
  • XFEM

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)

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