On the Relevance of Mean Field to Continuum Damage Mechanics
Résumé
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.