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)


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.


Asymptotic Stability Tangent Modulus Elastic Domain Dissipation Potential Kinematic Hardening Model 
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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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