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Journal Articles Journal of the Mechanics and Physics of Solids Year : 2014

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

Michaël Peigney

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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Dates and versions

hal-01055869 , version 1 (13-08-2014)

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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, 2014, 71, pp.112-131. ⟨10.1016/j.jmps.2014.06.008⟩. ⟨hal-01055869⟩
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