Shakedown with Non Associated Flow Rule

  • Géry de Saxcé
  • Jean-Bernard Tritsch
Part of the International Centre for Mechanical Sciences book series (CISM, volume 432)


First, we present the concept of bifunctional which allows to extend the calculus of variation in case of a material admitting a bipotential. Next, the bound theorems of the shakedown analysis are generalized for this class of plastic materials. The key of the proof is that the normality rule is conserved but in an implicit form. The theory is illustrated by the problem of a thin walled tube under constant tension and alternating cyclic torsion. We recover the value of the shakedown factor given by Lemaitre and Chaboche and we prove that it is the exact one.


Back Stress Residual Stress Field Thin Walled Tube Constant Tension Associate Flow Rule 


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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Géry de Saxcé
    • 1
  • Jean-Bernard Tritsch
    • 1
  1. 1.University of LilleLilleFrance

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