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Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli

Michaël Peigney 1
1 msa - Matériaux et Structures Architecturés
navier umr 8205 - Laboratoire Navier
Abstract : For elastic-perfectly plastic materials with constant properties, the well-known Melan's theorem gives a sufficient condition for shakedown to occur, independently on the initial state. It has been conjectured that Melan's theorem could be extended to temperature-dependent (or time-dependent) elastic moduli, but no theoretical result is available. This paper aims at providing results in that direction, with a special emphasis on time-periodic variations. If Melan's condition is satisfied, we show that shakedown indeed occurs provided the time fluctuations of the elastic moduli satisfy a certain condition (which in particular is fulfilled if the time fluctuations are not too large). We provide a counterexample which shows that setting such a constraint on the elastic moduli is necessary to reach path-independent theorems as proposed. A simple mechanical system is studied as an illustrative example.
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Soumis le : mercredi 13 août 2014 - 16:07:54
Dernière modification le : vendredi 17 juillet 2020 - 17:09:09
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Michaël Peigney. Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli. Journal of the Mechanics and Physics of Solids, Elsevier, 2014, 71, pp.112-131. ⟨10.1016/j.jmps.2014.06.008⟩. ⟨hal-01055869⟩

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