M- and Mc-integrals for multicracked problems in three dimensions

J. H. Chang, Y. C. Kang, L. G. Chung

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Aproblem-invariantMc-integral is proposed as an energy parameter for describing the degradation of structural integrity caused by irreversible evolution of multiple cracks in three-dimensional (3D) elastic solids. The physical meaning for 3DMc, which is related to the surface energy corresponding to creation of the cracks, does not hold in the same manner as that for two-dimensional (2D)Mc and needs to be properly reformulated. Also, the 3D integration is shown to be surface-independent in a modified sense. With this property, by choosing a closed surface remote from the crack fronts, the 3D Mc can then be accurately evaluated with finite-element (FE) solutions even when the near-front areas are not simulated with very fine grids.

Original languageEnglish
Pages (from-to)1874-1880
Number of pages7
JournalJournal of Engineering Mechanics
Issue number12
StatePublished - 2013


  • M-integral
  • M-integral
  • Modified surface-independence
  • Multiple cracks
  • Surface energy
  • Three dimensions


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