Bifurcation of equilibrium solutions and defects nucleation

Abstract

The purpose of this article is to revise some concepts on defects nucleation based on bifurcation of equilibrium solutions. Equilibrium solutions are obtained on a homogeneous body and on a body with an infinitesimal defect such as cavity under the same prescribed dead load. First void formation and growth in non linear mechanics are examined. A branch of radial transformation bifurcates from the undeformed configuration in presence of a small cavity. Two cases of behaviour are examined. One case is the growth of the cavity by only the deformation of the shell. In another modelling the cavity evolves like a damaged zone, the transition between the sound part and the damaged one is governed by a local criterium. Each configuration leads to the definition of a nucleation criterion based on a presence of a bifurcation state, common state of the homogeneous body and a body with an infinitesimal defect.