 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| P.A. Belov and S.A. Lurie, "Ideal Nonsymmetric 4D-Medium as a Model of Invertible Dynamic Thermoelasticity," Mech. Solids. 47 (5), 580-590 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
5 |
Pages |
580-590 |
| DOI |
10.3103/S0025654412050123 |
| Title |
Ideal Nonsymmetric 4D-Medium as a Model of Invertible Dynamic Thermoelasticity |
| Author(s) |
P.A. Belov (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, pbelov@yandex.ru)
S.A. Lurie (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, lurie@ccas.ru) |
| Abstract |
The space-time continuum (4D-medium) is considered, and a generalized model of reversible dynamic thermoelasticity is constructed as a theory of elasticity of an ideal (defect-free) nonsymmetric 4D-medium that is transversally-isotropic with respect to the time coordinate. The definitions of stresses and strains for the space-time continuum are introduced. The constitutive equations of the medium model relating the components of nonsymmetric stress and distortion 4D-tensors are stated. Physical interpretations of all tensor components of the thermomechanical properties are given. The Lagrangian of the generalized model of coupled dynamic thermoelasticity is presented, and the Euler equations are analyzed. It is shown that the three Euler equations are generalized equations of motion of the dynamic classical thermoelasticity, and the last, fourth, equation is a generalized heat equation which allows one to predict the wave properties of heat. An energy-consistent version of thermoelasticity is constructed where the Duhamel-Neumann and Maxwell-Cattaneo laws (a nonclassical generalization of the Fourier law for the heat flow) are direct consequences of the constitutive equations. |
| Keywords |
extended thermodynamics, thermal conductivity, dynamic thermoelasticity, wave properties of temperature |
| References |
| 1. | S. A. Lurie and P. A. Belov,
Mathematical Models of Continuum Mechanics and Physical Fields
(Izd-vo VTs, Moscow, 2000)
[in Russian]. |
| 2. | S. A. Lurie, P. A. Belov, and Yu. G. Yanovskii,
"On Simulation of Heat Transmission in Dynamically Deformed Media,"
Mekh. Komp. Mater. Konstr.
6 (3), 436-444 (2000)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 3. | S. A. Lurie and P. A. Belov,
"A Variational Model for Nonholonomic Media,"
Mekh. Komp. Mater. Konstr.
7 (2), 266-276 (2001)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 4. | P. A. Belov, A. G. Gorshkov, and S. A. Lurie,
"Variational Model of Nonholonomic 4D-Media,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 29-46 (2006)
[Mech. Solids (Engl. Transl.)
41 (6), 22-35 (2006)]. |
| 5. | P. A. Belov and S. A. Lurie,
"Models of Deformation of Solids and Their Analogs in Field Theory,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 157-166 (1998)
[Mech. Solids (Engl. Transl.)
43 (3), 128-136 (1998)]. |
| 6. | D. D. Joseph and L. Preziozi,
"Heat Waves,"
Rev. Modern Phys.
61 (1), 41-73 (1989). |
| 7. | S. L. Sobolev, "Transport Processes and Traveling Waves in Systems
with Local Nonequilibrium," Usp. Phys. Nauk 161 (3),
5-29 (1991) [Sov. Phys. Usp. (Engl. Transl.) 34 (3),
217-Ts229 (1991)]. |
| 8. | D. Jou, J. Casas-V'azquez, and G. Lebon,
"Extended Irreversible Thermodynamics Revisited (1988-98),"
Rep. Prog. Phys.
62, 1035-1142 (1999). |
| 9. | V. A. Kovalev and Yu. N. Radaev,
Elements of Field Theory: Variational Symmetries and Geometric Invariants
(Fizmatlit, Moscow, 2009)
[in Russian]. |
| 10. | S. A. Lurie, I. F. Obraztsov, P. A. Belov, and Yu. G. Yanovskii,
"On Some Classes of Models of Thin Structures,"
Izv. Vyssh. Uchebn. Zaved. Estestv. Nauki,
No. 3, 110-118 (2000). |
| 11. | J. C. Maxwell,
"On the Dynamic Theory of Gases,"
Phil. Trans. Roy. Soc. Lon.
157, 49-88 (1866). |
| 12. | M. C. Cattaneo,
"Sur une forme de l'equation de la chaleur eliminant le paradoxe d'une propagation instantanee,"
Copmtes Rendus Hebd. Seances Acad.
247 (4), 431-433 (1958). |
| 13. | W. Nowacki,
Theory of Elasticity
(PWN, Warsaw, 1970; Mir, Moscow, 1975). |
|
| Received |
25 June 2010 |
| Link to Fulltext |
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