Energy release rate approximation for edge cracks using higher-order topological derivatives

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Topological derivatives provide the variation of a functional when an infinitesimal hole is introduced into the domain. In Silva et al. (J Mech Phys Solids 59(5):925–939, 2011), the authors developed a first-order approximation of the energy release rate associated with a small crack at any boundary location and at any orientation using a first-order topological derivative. This approach offers significant computational advantages over other methods because (i) it requires only a single analysis while other methods require an analysis for each crack size-location-direction combination, and (ii) it is performed on the non-cracked domain, removing the need to create very fine meshes in the vicinity of the crack. In the present study, higher-precision approximations of the energy release rate are developed using higher-order topological derivatives which allow the analyst to accurately treat longer cracks and determine the crack lengths for which the first-order approximation is accurate.

Original languageEnglish (US)
Pages (from-to)187-205
Number of pages19
JournalInternational Journal of Fracture
Issue number1-2
StatePublished - Mar 1 2018


  • Asymptotic analysis
  • Edge cracks
  • Energy release rate
  • Topological derivative

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


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