Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity
Šilhavý, Miroslav
Applications of Mathematics, Tome 37 (1992), p. 383-400 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1992-01-01
Classification:  73B05,  73B25,  73B30,  73F99,  74A15,  74A20,  74D99,  76A10 
@article{104518,
     author = {Miroslav \v Silhav\'y},
     title = {Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity},
     journal = {Applications of Mathematics},
     volume = {37},
     year = {1992},
     pages = {383-400},
     zbl = {0770.73031},
     mrnumber = {1175932},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104518}
}

Šilhavý, Miroslav. Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity. Applications of Mathematics, Tome 37 (1992) pp. 383-400. http://gdmltest.u-ga.fr/item/104518/

H. Bellout F. Bloom C. Gupta Existence and stability of velocity profiles for Couette flow of a bipolar fluid, to appear.

J. L. Bleustein A. E. Green Dipolar fluids, Int. J. Engng. Sci. 5 (1967), 323-340. (1967)

K. Bucháček Thermodynamics of monopolar continuum of grade n, Apl. Mat. 16 (1971), 370-383. (1971) | MR 0290662

B. D. Coleman W. Noll An approximation theorem for functionals, with applications toin continuum mechanics, Arch. Rational Mech. Anal. 6 (1960), 355-370. (1960) | MR 0119598

A. E. Green R. S. Rivlin Simple force and stress multipoles, Arch. Rational Mech. Anal. 16 (1964), 325-354. (1964) | MR 0182191

A. E. Green R. S. Rivlin Multipolar continuum mechanics, Arch. Rational Mech. Anal. 17 (1964), 113-147. (1964) | MR 0182192

S. R. De Groot P. Mazur Non-Equilibrium Thermodynamics, North-Holland, Amsterodam, 1962. (1962)

M. E. Gurtin W. J. Hrusa On the thermodynamics of viscoelastic materials of single-integral type, Quart. Appl. Math. 49 (1991), 67-85. (1991) | MR 1096233

J. Nečas A. Novotný M. Šilhavý Global solution to the ideal compressible heat conductive multipolar fluid., Comment. Math. Univ. Carolinae 30 (1989), 551-564. (1989) | MR 1031872

J. Nečas A. Novotný; M; Šilhavý Global solution to the compressible isothermal multipolar fluid, J. Math. Anal. Appl. 162 (1991), 223-241. (1991) | Article | MR 1135273

J. Nečas M. Růžička Global solution to the incompressible viscous-multipolar material, to appear.

J. Nečas M. Šilhavý Multipolar viscous fluids, Quart. Appl. Math. 49 (1991), 247-265. (1991) | MR 1106391

A. Novotný Viscous multipolar fluids-physical background and mathematical theory, Progress in Physics 39 (1991). (1991) | MR 1184232

M. Šilhavý A note on Onsager's relations, to appear Quart. Appl. Math. | MR 1292198 | Zbl 0809.73014