The classical thermomechanics of solids is extended to incorporate a non-trivial dependence of the internal energy density function on the gradient of entropy. A generalized heat equation is derived for rigid heat conductors. The theory is shown to differ from existing models including gradient of temperature effects in the free energy.
Une extension de la thermomécanique classique des milieux continus est proposée afin d'incorporer des effets de gradient d'entropie dans la fonction densité d'énergie interne. On en déduit une équation de la chaleur généralisée pour les conducteurs rigides. La théorie proposée s'avère distincte d'une formulation basée sur l'introduction du gradient de température dans la densité d'énergie libre du milieu.
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Mots-clés : Milieux continus, Thermomécanique des milieux continus, Gradient d'entropie, Gradient de température, Équation de la chaleur généralisée
Samuel Forest 1; Michel Amestoy 1
@article{CRMECA_2008__336_4_347_0,
author = {Samuel Forest and Michel Amestoy},
title = {Hypertemperature in thermoelastic solids},
journal = {Comptes Rendus. M\'ecanique},
pages = {347--353},
publisher = {Elsevier},
volume = {336},
number = {4},
year = {2008},
doi = {10.1016/j.crme.2008.01.007},
language = {en},
}
Samuel Forest; Michel Amestoy. Hypertemperature in thermoelastic solids. Comptes Rendus. Mécanique, Volume 336 (2008) no. 4, pp. 347-353. doi : 10.1016/j.crme.2008.01.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.01.007/
[1] The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Ration. Mech. Anal., Volume 13 (1963), pp. 167-178
[2] Thermodynamics and departures from Fourier's law of heat conduction, Arch. Ration. Mech. Anal., Volume 13 (1963), pp. 245-261
[3] Sur la forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée, C. R. Acad. Sci. Paris, Volume 247 (1958), pp. 431-433
[4] Extended Thermodynamics, Springer Tracts in Natural Philosophy, vol. 37, 1993
[5] Microstructural influence on heat-conduction, Int. J. Heat Mass Transfer, Volume 38 (1995), pp. 3181-3195
[6] Thermoelasticity of second-grade media (G.A. Maugin; R. Drouot; F. Sidoroff, eds.), Continuum Thermomechanics, The Art and Science of Modelling Material Behaviour, Paul Germain's Anniversary Volume, Kluwer Academic Publishers, 2000, pp. 163-176
[7] Towards a theory of second grade thermoelasticity, Extracta Math., Volume 14 (1999) no. 2, pp. 127-140
[8] Using the gradients of temperature and internal parameters in continuum mechanics, C. R. Mecanique, Volume 332 (2004), pp. 249-255
[9] The non-local generalized standard approach: a consistent gradient theory, C. R. Mecanique, Volume 333 (2005), pp. 139-145
[10] Thermodynamical frameworks for higher grade material theories with internal variables or additional degrees of freedom, J. Non-Equilib. Thermodynam., Volume 31 (2006), pp. 319-353
[11] Damage, gradient of damage and principle of virtual power, Int. J. Solids Structures, Volume 33 (1996), pp. 1083-1103
[12] Generalized Ginzburg–Landau and Cahn–Hilliard equations based on a microforce balance, Physica D, Volume 92 (1996), pp. 178-192
[13] Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys., Volume 28 (1958), pp. 258-267
[14] Mixture of fluids involving entropy gradients and acceleration waves in interfacial layers, Eur. J. Mech. B Fluids, Volume 24 (2005), pp. 596-613
[15] La méthode des puissances virtuelles en mécanique des milieux continus, première partie : théorie du second gradient, J. Mécanique, Volume 12 (1973), pp. 235-274
[16] Internal variables and dissipative structures, J. Non-Equilib. Thermodyn., Volume 15 (1990), pp. 173-192
[17] On the thermomechanics of continuous media with diffusion and/or weak nonlocality, Arch. Appl. Mech., Volume 75 (2006), pp. 723-738
[18] On the thermodynamics of thermoelastic materials with additional scalar degrees of freedom, Continuum Mech. Thermodynam., Volume 4 (1999), pp. 247-262
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