| Title:
|
Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity (English) |
| Author:
|
Šilhavý, Miroslav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
5 |
| Year:
|
1992 |
| Pages:
|
383-400 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The integral constitutive equations of a multipolar viscoelastic material are analyzed from the thermodynamic point of view. They are shown to be approximated by those of the differential-type viscous materials when the processes are slow. As a consequence of the thermodynamic compatibility of the viscoelastic model, the coefficients of viscosity of the approximate viscous model are shown to have an Onsager-type symmetry. This symmetry was employed earlier in the proof of the existence of solutions for the corresponding equations. (English) |
| Keyword:
|
multipolar materials |
| Keyword:
|
hereditary laws |
| Keyword:
|
Onsager's relations |
| Keyword:
|
integral constitutive equations |
| Keyword:
|
differential-type viscous materials |
| Keyword:
|
thermodynamic compatibility |
| Keyword:
|
Onsager-type symmetry |
| MSC:
|
73B05 |
| MSC:
|
73B25 |
| MSC:
|
73B30 |
| MSC:
|
73F99 |
| MSC:
|
74A15 |
| MSC:
|
74A20 |
| MSC:
|
74D99 |
| MSC:
|
76A10 |
| idZBL:
|
Zbl 0770.73031 |
| idMR:
|
MR1175932 |
| DOI:
|
10.21136/AM.1992.104518 |
| . |
| Date available:
|
2008-05-20T18:44:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104518 |
| . |
| Reference:
|
[1] H. Bellout F. Bloom C. Gupta: Existence and stability of velocity profiles for Couette flow of a bipolar fluid.to appear. |
| Reference:
|
[2] J. L. Bleustein A. E. Green: Dipolar fluids.Int. J. Engng. Sci. 5 (1967), 323-340. 10.1016/0020-7225(67)90041-9 |
| Reference:
|
[3] K. Bucháček: Thermodynamics of monopolar continuum of grade n.Apl. Mat. 16 (1971), 370-383. MR 0290662 |
| Reference:
|
[4] B. D. Coleman W. Noll: An approximation theorem for functionals, with applications toin continuum mechanics.Arch. Rational Mech. Anal. 6 (1960), 355-370. MR 0119598, 10.1007/BF00276168 |
| Reference:
|
[5] A. E. Green R. S. Rivlin: Simple force and stress multipoles.Arch. Rational Mech. Anal. 16 (1964), 325-354. MR 0182191, 10.1007/BF00281725 |
| Reference:
|
[6] A. E. Green R. S. Rivlin: Multipolar continuum mechanics.Arch. Rational Mech. Anal. 17 (1964), 113-147. MR 0182192, 10.1007/BF00253051 |
| Reference:
|
[7] S. R. de Groot P. Mazur: Non-Equilibrium Thermodynamics.North-Holland, Amsterodam, 1962. |
| Reference:
|
[8] M. E. Gurtin W. J. Hrusa: On the thermodynamics of viscoelastic materials of single-integral type.Quart. Appl. Math. 49 (1991), 67-85. MR 1096233, 10.1090/qam/1096233 |
| Reference:
|
[9] J. Nečas A. Novotný M. Šilhavý: Global solution to the ideal compressible heat conductive multipolar fluid..Comment. Math. Univ. Carolinae 30 (1989), 551-564. MR 1031872 |
| Reference:
|
[10] J. Nečas A. Novotný, M, Šilhavý: Global solution to the compressible isothermal multipolar fluid.J. Math. Anal. Appl. 162 (1991), 223-241. MR 1135273, 10.1016/0022-247X(91)90189-7 |
| Reference:
|
[11] J. Nečas M. Růžička: Global solution to the incompressible viscous-multipolar material.to appear. |
| Reference:
|
[12] J. Nečas M. Šilhavý: Multipolar viscous fluids.Quart. Appl. Math. 49 (1991), 247-265. MR 1106391, 10.1090/qam/1106391 |
| Reference:
|
[13] A. Novotný: Viscous multipolar fluids-physical background and mathematical theory.Progress in Physics 39 (1991). MR 1184232 |
| Reference:
|
[14] M. Šilhavý: A note on Onsager's relations.to appear Quart. Appl. Math. Zbl 0809.73014, MR 1292198 |
| . |
