The topological derivative provides the variation of a response functional when an infinitesimal hole of a particular shape is introduced at a point of the domain. In this fracture mechanics work we use the topological derivative to approximate the energy release rate field associated with a small crack at any boundary location and at any orientation. Our proposed method offers significant computational advantages over current finite element based methods since it requires a single analysis, whereas the others require a distinct analysis for each crack locationorientation combination. Moreover, the proposed method evaluates the topological derivative in the non-cracked domain which eliminates the need for tailored meshes in the crack region.

Original languageEnglish (US)
Pages (from-to)925-939
Number of pages15
JournalJournal of the Mechanics and Physics of Solids
Issue number5
StatePublished - May 2011


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

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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