Abstract
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.
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© 2002 Springer-Verlag Wien
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de Saxcé, G., Tritsch, JB. (2002). Shakedown with Non Associated Flow Rule. In: Weichert, D., Maier, G. (eds) Inelastic Behaviour of Structures under Variable Repeated Loads. International Centre for Mechanical Sciences, vol 432. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2558-8_5
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DOI: https://doi.org/10.1007/978-3-7091-2558-8_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83687-3
Online ISBN: 978-3-7091-2558-8
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