International Journal of Fracture

, Volume 116, Issue 3, pp 219–229 | Cite as

On the Relevance of Mean Field to Continuum Damage Mechanics

  • Stéphane RouxEmail author
  • François Hild


Damage theory is, by its very essence, a mean-field theory. In this note, we argue that considering the effective interaction kernel between an additional micro-crack, and the effective equivalent damaged matrix, the power-law decay of the influence function (or Green's function) becomes more and more long-ranged as the tangent modulus vanishes. Moreover, the reloaded region becomes a narrower and narrower `cone', so that the damage in this cone becomes closer and closer to the so-called global load sharing rule used, for instance, to study a fiber bundle. This constitutes a formal justification of the relevance of such a mean-field approach as the peak stress is approached.

Continuum Damage Mechanics mode III crack local load sharing global load sharing mean field regime far-field stress 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  1. 1.Laboratoire `Surface du Verre et Interfaces'CNRS UMR 125 / Saint-GobainAubervilliers CedexFrance
  2. 2.LMT-Cachan, ENS de Cachan / CNRS UMR 8535 /Université Paris 6Cachan CedexFrance

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