Using the gradients of temperature and internal parameters in Continuum Thermodynamics

Peter Ireman; Quoc-Son Nguyen

doi:10.1016/j.crme.2004.01.012

Using the gradients of temperature and internal parameters in Continuum Thermodynamics
[Introduction des gradients de température et de paramètres internes en Thermodynamique des Milieux Continus]

Présenté par : André Zaoui

Peter Ireman ¹ ; Quoc-Son Nguyen ²

¹ Department of Mechanical Engineering, Linkoping University, Sweden
² Laboratoire de mécanique des solides, CNRS(umr7649), École polytechnique, Palaiseau, France

Comptes Rendus. Mécanique, Volume 332 (2004) no. 4, pp. 249-255.

Résumé
Abstract

On étudie dans cette note la possibilité d'introduire les gradients de la température et des paramètres internes comme des variables d'état supplémentaires en Thermodynamique des Milieux Continus. A partir d'une expression appropriée de la production interne d'entropie, on donne les énoncés des deux principes et l'expression associée de l'inégalité de Clausius–Duhem. Plusieurs formulations sont proposées et comparées aux résultats existants de la littérature.

In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature.

Reçu le : 2004-01-08
Accepté le : 2004-01-30
Publié le : 2004-03-18

DOI : 10.1016/j.crme.2004.01.012

Keywords: Continuum mechanics, Continuum thermodynamics, State variable, Temperature gradient, Internal parameter gradient
Mot clés : Milieux continus, Thermodynamique des milieux continus, Variable d'état, Gradient thermique, Gradient de paramètre interne

Affiliations des auteurs :

Peter Ireman ¹ ; Quoc-Son Nguyen ²

¹ Department of Mechanical Engineering, Linkoping University, Sweden
² Laboratoire de mécanique des solides, CNRS(umr7649), École polytechnique, Palaiseau, France

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     title = {Using the gradients of temperature and internal parameters {in~Continuum} {Thermodynamics}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {249--255},
     publisher = {Elsevier},
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     number = {4},
     year = {2004},
     doi = {10.1016/j.crme.2004.01.012},
     language = {en},
}

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Peter Ireman; Quoc-Son Nguyen. Using the gradients of temperature and internal parameters in Continuum Thermodynamics. Comptes Rendus. Mécanique, Volume 332 (2004) no. 4, pp. 249-255. doi : 10.1016/j.crme.2004.01.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.01.012/

Bibliographie
Cité par

[1] B. Coleman; M. Gurtin Thermodynamics with internal variables, J. Chem. Phys., Volume 47 (1967), pp. 597-613

[2] I. Gyarmati Non-Equilibrium Thermodynamics, Springer-Verlag, New York, 1970

[3] P. Germain Cours de mécanique des milieux continus, Masson, Paris, 1973

[4] J. Mandel Plasticité classique et viscoplasticité, Cours CISM, Springer-Verlag, Wien, 1971

[5] P. Germain; Q.-S. Nguyen; P. Suquet Continuum thermodynamics, J. Appl. Mech., Volume 50 (1983), pp. 1010-1020

[6] Q.-S. Nguyen Stability and Nonlinear Solid Mechanics, Wiley, Chichester, 2000

[7] M. Frémond Contact unilatéral avec adhérence, une théorie du premier gradient (G. Del Piero; F. Maceri, eds.), Unilateral Problems in Structural Analysis, CISM Courses and Lectures, vol. 304, Springer-Verlag, Wien, 1985, pp. 117-137

[8] G.A. Maugin Internal variables and dissipative structures, J. Non-Equilibrium Thermodynam., Volume 15 (1990), pp. 173-192

[9] T. Svedberg; K. Runesson A thermodynamically consistent theory of gradient-regularized plasticity coupled to damage, Int. J. Plasticity, Volume 13 (1997), pp. 669-696

[10] P. Ireman; A. Klarbring; S. Stromberg A model of damage coupled to wear, Int. J. Solids and Structures, Volume 40 (2003), pp. 2957-2974

[11] S. Forest; R. Sievert Elastoviscoplastic constitutive frameworks for generalized continua, Acta Mech., Volume 160 (2003), pp. 71-111

[12] S. Andrieux, P. de Bonniers, Including thermal gradients into thermo-elastic damaging constitutive laws, Rapport EDF, HI-74:049–0, 1994

[13] J.M. Cardona; S. Forest; R. Sievert Towards a theory of second grade thermoelasticity, Extracta Math., Volume 14 (1999), pp. 127-140

[14] M. Frémond; B. Nedjar Damage, gradient of damage and principle of virtual power, Int. J. Solids and Structures, Volume 33 (1996), pp. 1083-1103

[15] P. Ireman, Continuum models and numerical methods for tribological systems, Thesis, Linkoping University, Sweden, 2003

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