A domain of influence theorem in linear thermo-elasticity with thermal relaxation and internal variable

• Autorzy: Cimmelli V. A. , Rogolino P.
• Języki publikacji: EN

Abstrakty

EN

A domain of influence theorem is proved for a linear thermoelastic solid with a Cattaneo's type heat conduction law and a scalar internal variable. The obtained result is applied to prove the hyperbolicity of a semiempirical heat conduction theory, describing the propagation of thermal waves in crystals at low temperatures.

Słowa kluczowe

EN

linear thermo-elasticity; thermal relaxation; semi-empirical heat conduction model

PL

liniowa termosprężystość; relaksacja termiczna; pół-empiryczny model przenośności ciepła

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2002
• Tom: Vol. 54, nr 1
• Strony: 15--33
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Cimmelli V. A.

• Dept. of Mathematics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza-Italy

autor

Rogolino P.

• Dept. of Mathematics, University of Basilicata, Contrada Macchia Romana, 85100, Potenza-Italy

Bibliografia

• 1. M. E. GURTIN, The. linear theory of elasticity, Handbuch der Physik, band VIa/2, 1-295, Springer-Verlag, Berlin, 1972.
• 2. A. C. ERINGEN and S. SUHUBI, Elastodynamics, 2, Academic Press, New York, 1975.
• 3. C. CATTANEO, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3, 83-101, 1948.
• 4. H. W. LORD and Y. SHULMAN, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 229-309, 1967.
• 5. J. IGNACZAK, Domain of influence theorem in linear thermoelasticity, Int. J. Engng. Sci., 16. 139-145, 1978.
• 6. J. IGNACZAK and J. BIALY, Domain of influence in thermoelasticity with one relaxation time, J. Therm. Stresses, 3, 391-399, 1980.
• 7. B. CARBONARO and R. RUSSO, Energy inequalities and the domain of influence theorem in classical elastodynamics, J. Elast., 14, 163-174, 1984.
• 8. J. IGNACZAK, B. CARBONARO and R. Russo, Domain of influence theorem in thermoelasticity with one relaxation time, J. Therm. Stresses, 9, 79-91, 1986.
• 9. A. MORRO and T. RUGGERI, Second sound and internal energy in solids, Int. J. Non- Lin. Mech., 22, 1, 27-36, 1987.
• 10. V. A. CIMMELLI and W. KOSIŃSKI, Non-equilibrium semi-empirical temperature in materials with thermal relaxation, Arch. Mech., 43, 6, 753-767, 1991.
• 11. G. CAVIGLIA, A. MORRO and B. STRAUGHAN, Thermoelasticity at cryogenic temperatures, Int. J. Non-Lin. Mech., 27, 2, 251-263, 1992.
• 12. V. A. ClMMELLI, Thermodynamics of anisotropic solids near absolute zero, Math. Comput. Modelling, 28,3, 79-89, 1998.
• 13. G. A. KLUITENBERG and V. ClANClO, On linear dynamical equations of state for isotropic media I, Physica, 93A, 273-286, 1978.
• 14. D. S. CHANDRASEKHARAIAH, Hyperbolic thermoelasticity: A review of recent literature, Appl. Mech. Rev., 51, no. 12, part 1, 1998.
• 15. F. BAMPI and A. MORRO, Non-equilibrium thermodynamics: a hidden variable approach; |in:| Recent Developments in Non-Equilibrium Thermodynamics, J. CASAS-VAZQUEZ, D. Jou and G. LEBON [Eds.], 211-232, Springer-Verlag, Berlin 1984.
• 16. F. BAMPI and A. MORRO, Relaxation phenomena in irreversible thermodynamics, Atti Sem. Mat. Fis. Univ. Modena, XXX, 1-15, 1981.
• 17. G. BOILLAT, La propagation des ondes, Traite de physique theorique et de physique mathematique, Gauthier-Villars, Paris, 1965.
• 18. T. RUGGERI, Thermodynamics and symmetric hyperbolic systems, Rend. Sem. Mat. Univ. Pol. Torino, Fascicolo Speciale, 167-183, 1988.
• 19. K. FRISCHMUTH and V. A. CIMMELLI, Coupling in thermomechanical wave propagation in NaF at low temperature, Arch. Mech.. 50, 703-713, 1998.
• 20. D. E. CARLSON, Linear thermoelasticity, Handbuch der Physik, Band VIa/2, 297-345, Springer-Verlag, Berlin, 1972.
• 21. G.A. MAUGIN and W. MUSCHIK, Thermodynamics with internal variables. Part I. General Concepts, J. Non-Equilib. Thermodyn., 19, 217-249, 1994.
• 22. W. MUSCHIK, Non-equilibrium thermodynamics with applications to solids, CISM Courses and Lectures, no. 336, Springer-Verlag, Berlin, 1994.
• 23. M. PITTERI, On the axiomatic foundations of temperature, Appendix G 6 of Rational Thermodynamics, C. TRUESDELL [Ed.|, Springer Verlag, Berlin, 1984.