Bifurcation of equilibrium solutions and defects nucleation

Claude Stolz (1)

1 LMS - Laboratoire de mécanique des solides

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 prescirbed 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 is examined. One case is the growth of cavity by only the deformation of the matrix. 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 criterium based on a presence of a bifurcation state, comman state of the homogeneous boby and a body with an infinitesimal defect.

Mots clés: Bifurcation; Nucleation of defects; Hyperelasticity; Local damage; Composite sphere

Domaines: Mécanique des matériaux [physics.class-ph]; Physique mathématique [math-ph]

Claude Stolz. Bifurcation of equilibrium solutions and defects nucleation. International Journal of Fracture, 2007, 147, pp.103-107. ⟨10.1007/s10704-007-9147-5⟩. ⟨hal-00154127⟩