[Thermomécanique avec gradients dʼentropie et de température : Dissipation, inégalité de la conduction et équation de la chaleur]
Une approche alternative et cohérente, ne faisant pas appel au principe des puissances virtuelles et à la procédure de Coleman–Noll, est utilisée pour obtenir les lois de comportement avec gradients de température ou dʼentropie, ainsi que les équations dʼévolution en thermomécanique. En partant du bilan dʼénergie, une analyse de la dissipation conduit naturellement à la définition de la température et de lʼentropie par des dérivées variationnelles. Tout en préservant les formes classiques des équations, lʼapproche permet dʼétablir les formes cohérentes de lʼinégalité de lʼentropie (second principe) et de la conduction dont une nouvelle forme est proposée. Le formalisme standard généralisé offre ensuite un moyen commode dʼétablir des lois admissibles. La méthodologie est appliquée en prenant dʼabord lʼentropie et son gradient comme variables dʼétat (énergie interne comme potentiel), et ensuite la température et son gradient (énergie libre comme potentiel).
An alternative and consistent approach, not appealing to the principle of virtual power and to Coleman–Noll procedure, is used to derive constitutive and governing equations involving temperature or entropy gradients, in thermomechanics of materials. Using the balance of energy, an analysis of the dissipation naturally leads to the definition of the temperature and the entropy as variational derivatives. The approach preserves the classical forms of the equations and yields to consistent form of the second law and heat conduction inequality. The framework of generalized standard materials is then suitable for deriving admissible constitutive laws. The methodology is applied, first using entropy and its gradient as state variables (with internal energy as thermodynamic potential), and second using temperature and its gradient (starting from the free energy).
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Mot clés : Milieux continus, Thermodynamique des milieux continus, Gradient dʼentropie, Gradient de température, Second principe, Inégalité de la conduction de la chaleur, Équation de la conduction
@article{CRMECA_2012__340_6_434_0,
author = {Mahaman-Habibou Maitournam},
title = {Entropy and temperature gradients thermomechanics: {Dissipation,} heat conduction inequality and heat equation},
journal = {Comptes Rendus. M\'ecanique},
pages = {434--443},
publisher = {Elsevier},
volume = {340},
number = {6},
year = {2012},
doi = {10.1016/j.crme.2012.04.001},
language = {en},
}
TY - JOUR AU - Mahaman-Habibou Maitournam TI - Entropy and temperature gradients thermomechanics: Dissipation, heat conduction inequality and heat equation JO - Comptes Rendus. Mécanique PY - 2012 SP - 434 EP - 443 VL - 340 IS - 6 PB - Elsevier DO - 10.1016/j.crme.2012.04.001 LA - en ID - CRMECA_2012__340_6_434_0 ER -
Mahaman-Habibou Maitournam. Entropy and temperature gradients thermomechanics: Dissipation, heat conduction inequality and heat equation. Comptes Rendus. Mécanique, Volume 340 (2012) no. 6, pp. 434-443. doi : 10.1016/j.crme.2012.04.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.04.001/
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