Article
MSC:
73B05,
73B25,
73B30,
73F99,
74A15,
74A20,
74D99,
76A10 | MR 1175932 | Zbl 0770.73031 | DOI: 10.21136/AM.1992.104518
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Keywords:
multipolar materials; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry
multipolar materials; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry
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.
References:
[1] H. Bellout F. Bloom C. Gupta: Existence and stability of velocity profiles for Couette flow of a bipolar fluid. to appear.
[2] J. L. Bleustein A. E. Green: Dipolar fluids. Int. J. Engng. Sci. 5 (1967), 323-340. DOI 10.1016/0020-7225(67)90041-9
[3] K. Bucháček: Thermodynamics of monopolar continuum of grade n. Apl. Mat. 16 (1971), 370-383. MR 0290662
[4] B. D. Coleman W. Noll: An approximation theorem for functionals, with applications toin continuum mechanics. Arch. Rational Mech. Anal. 6 (1960), 355-370. DOI 10.1007/BF00276168 | MR 0119598
[5] A. E. Green R. S. Rivlin: Simple force and stress multipoles. Arch. Rational Mech. Anal. 16 (1964), 325-354. DOI 10.1007/BF00281725 | MR 0182191
[6] A. E. Green R. S. Rivlin: Multipolar continuum mechanics. Arch. Rational Mech. Anal. 17 (1964), 113-147. DOI 10.1007/BF00253051 | MR 0182192
[7] S. R. de Groot P. Mazur: Non-Equilibrium Thermodynamics. North-Holland, Amsterodam, 1962.
[8] M. E. Gurtin W. J. Hrusa: On the thermodynamics of viscoelastic materials of single-integral type. Quart. Appl. Math. 49 (1991), 67-85. DOI 10.1090/qam/1096233 | MR 1096233
[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
[10] J. Nečas A. Novotný, M, Šilhavý: Global solution to the compressible isothermal multipolar fluid. J. Math. Anal. Appl. 162 (1991), 223-241. DOI 10.1016/0022-247X(91)90189-7 | MR 1135273
[11] J. Nečas M. Růžička: Global solution to the incompressible viscous-multipolar material. to appear.
[12] J. Nečas M. Šilhavý: Multipolar viscous fluids. Quart. Appl. Math. 49 (1991), 247-265. DOI 10.1090/qam/1106391 | MR 1106391
[13] A. Novotný: Viscous multipolar fluids-physical background and mathematical theory. Progress in Physics 39 (1991). MR 1184232
[14] M. Šilhavý: A note on Onsager's relations. to appear Quart. Appl. Math. MR 1292198 | Zbl 0809.73014
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