Use of M integral for rubbery material problems containing multiple defects

Jui Hung Chang, Deh Jun Peng

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20 Scopus citations


An energy parameter based on the concept of the M integral is proposed for describing the fracture behavior of a two-dimensional multidefect rubbery mechanical system under the action of large deformation. To this end, we first define a problem-invariant parameter Mc by suitably choosing a closed contour and taking the integration with respect to the geometric center of all the enclosed defects. Attention is then addressed to discussion of the physical meaning of Mc, which is shown to be related to the surface energy corresponding to formation of the defects. Also, the integration appears to be path independent so that the complicated singular stress field in the near-tip areas need not be involved in the calculation. Based on the above characteristics, it is suggested that Mc may be possibly used as a fracture parameter for describing the degradation of material and/or structural integrity caused by irreversible evolution of defects in rubbery media.

Original languageEnglish
Pages (from-to)589-598
Number of pages10
JournalJournal of Engineering Mechanics
Issue number5
StatePublished - May 2004


  • Defects
  • Finite element method
  • Fracture mechanics
  • Integrals
  • Rubber
  • Surface energy


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