Thermoelasticity without energy dissipation. (English) Zbl 0784.73009

Summary: This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.


74A15 Thermodynamics in solid mechanics
74B99 Elastic materials
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] L. Brun, Methodes énergétiques dans les systémes évolutifs linéare-I. Séparation des energies et II. Théorèmes d’uniclté. J. Mécanique 8 (1969) 125–192.
[2] D.E. Carlson, Linear thermoelasticity. In: C. Truesdell (ed.) S. Flügge’s Handbuch der Physik, Vol. VIa/2. Springer-Verlag (1972) pp. 297–345.
[3] A.E. Green, P.M. Naghdi, On thermodynamies and the nature of the second law. Proc. Roy. Soc. Lond. A 357 (1977) 253–270. · doi:10.1098/rspa.1977.0166
[4] A.E. Green and P.M. Naghdi, A note on invariance under superposed rigid body motions. J. Elasticity 9 (1979) 1–8. · Zbl 0408.70002 · doi:10.1007/BF00040975
[5] A.E. Green and P.M. Naghdi, Aspects of the second law of thermodynamics in the presence of electromagnetic effects. Quart. J. Mech. Appl. Math. 37 (1984) 179–193. · Zbl 0543.73131 · doi:10.1093/qjmam/37.2.179
[6] A.E. Green and P.M. Naghdi, A re-examination of the basic postulates of thermomechanics. Proc. Roy. Soc. Lond. A 432 (1991) 171–194. · Zbl 0726.73004 · doi:10.1098/rspa.1991.0012
[7] A.E. Green and P.M. Naghdi, A demonstration of consistency of an entropy balance with balance of energy. J. Appl. Math. Phys. (ZAMP) 42 (1991) 159–168. · Zbl 0725.73017 · doi:10.1007/BF00945790
[8] D.D. Joseph and L. Preziosi, Heat waves. Revs. Mod. Phys. 61 (1989) 41–73 and addendum 62 (1990) 375–391. · Zbl 1129.80300 · doi:10.1103/RevModPhys.61.41
[9] P.M. Naghdi and J.A. Trapp, A uniqueness theorem in the theory of Cosserat surface. J. Elasticity 2 (1972) 9–20. · doi:10.1007/BF00045690
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