Elastic perfectly plastic structures with temperature dependent elastic coefficients

Halphen, Bernard

doi:10.1016/j.crme.2005.07.018

Cited by 22 publications

(23 citation statements)

References 2 publications

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“…. The uniqueness of the stress rateρ has been proved by Halphen (2005) using variational principles for the differential inclusion (11).…”

Section: Evolution Equation For the Stress Fieldmentioning

confidence: 99%

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

Peigney

2014

Journal of the Mechanics and Physics of Solids

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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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“…. The uniqueness of the stress rateρ has been proved by Halphen (2005) using variational principles for the differential inclusion (11).…”

Section: Evolution Equation For the Stress Fieldmentioning

confidence: 99%

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

Peigney

2014

Journal of the Mechanics and Physics of Solids

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“…Le cadre théorique qui a permis le développement des modèles de monocristal a été construit dans les années 70 [1][2][3][4][5][6], et les premières applications ont suivi quelques années plus tard [7,8]. L'histoire de la plasticité cristalline est donc bien connue, elle peutêtre consultée dans quelques livres de référence, comme [9,10].…”

Section: Introductionunclassified

Une introduction à la plasticité cristalline interactions avec l'environnement

Cailletaud

2009

PlastOx 2007 - Mécanismes Et Mécanique Des Interactions Plasticité - Environnement

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Résumé. Cette partie est une introduction aux modèles phénoménologiques de plasticité cristalline. On discute leurs propriétés, et leurs utilisations dans le cadre de modélisations de microstructures. Les versions plastiques et viscoplastiques sont citées. Les applications portent sur des monocristaux ou des polycristaux. Dans ce dernier cas, on a privilégié les modèles éléments finis, qui permettent de véritables calculs de microstructures. L'exposé se conclut par quelques exemples dans lesquels l'environnement jour un rle important.

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“…Replacing (22)(23)(24)(25)(26) in (19) and observing by periodicity that γ(a, a + T ) = γ(0, T ), Eq. (19) is obtained.…”

Section: Variation Of the Elastic Energymentioning

confidence: 99%

“…Starting from a given initial state ρ(t = 0), the evolution of the stress field in H is governed by the ordinary differential equation (9). The uniqueness of the stress rateρ has been proved in [23].…”

Section: Evolution Equation For the Stress Fieldmentioning

confidence: 99%

On Shakedown of Elastic-Plastic Bodies With Temperature Dependent Properties

Peigney¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. For elastic-perfectly plastic structures under prescribed loading histories, the wellknown Melan's theorem gives a sufficient condition for shakedown to occur, i.e. for the evolution to become elastic in the large-time limit. The original Melan's theorem rests on the assumption that the material properties remain constant in time, independently on the applied loading. This communication addresses the long standing issue of extending Melan's theorem to temperaturedependent (or time-dependent) elastic moduli. The main motivation is to extend the range of applications of Melan's theorem to thermomechanical loading histories with large temperature fluctuations: In such case, the variation of the elastic properties with the temperature cannot be neglected. Some recent results obtained in perfect plasticity and viscoplasticity are presented and discussed.

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Elastic perfectly plastic structures with temperature dependent elastic coefficients

Cited by 22 publications

References 2 publications

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

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

Une introduction à la plasticité cristalline interactions avec l'environnement

On Shakedown of Elastic-Plastic Bodies With Temperature Dependent Properties

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