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Stability of a Quasi-Static Evolution of a Visco-Elastic, Visco-Plastic or Elastic-Plastic Solid

  • F. Abed-Meraim
  • Q. S. Nguyen
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 50)

Abstract

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.

Keywords

Asymptotic Stability Tangent Modulus Elastic Domain Dissipation Potential Kinematic Hardening Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • F. Abed-Meraim
    • 1
  • Q. S. Nguyen
    • 2
  1. 1.Laboratoire de Mecanique et TechnologieENS-CachanCachanFrance
  2. 2.Laboratoire de Mecanique des Solides, CNRS-Umr 7649Ecole PolytechniquePalaiseauFrance

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