Stability of a quasi-static evolution of a visco-elastic, visco-plastic or elastic-plastic solid

Farid Abed-Meraim (1) , Quoc Son Nguyen (2)

1 LMT - Laboratoire de Mécanique et Technologie
2 LMS - Laboratoire de mécanique des solides

The problem of stability of a quasi-static evolution of a solid is discussed in the framework of standard plasticity and visco-plasticity. General results concerning the criterion of second variation of energy are presented. Two different approaches are considered to discuss this problem for visco-elastic, visco-plastic or elastic-plastic solids. The first approach is based upon the linearization method and gives the asymptotic stability of the evolution of a visco-elastic solid when the associated dissipation potential is quadratic and positive-definite. The second approach introduces a direct analysis of the evolution in a nonsmooth but convex framework of plasticity and visco-plasticity.

Domaines: Sciences de l'ingénieur [physics]

Farid Abed-Meraim, Quoc Son Nguyen. Stability of a quasi-static evolution of a visco-elastic, visco-plastic or elastic-plastic solid. Nonsmooth/Nonconvex Mechanics, Kluwer Academic Publications, pp.1-14, 2001, ⟨10.1007/978-1-4613-0275-9_1⟩. ⟨hal-00112285⟩