Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity

Miroslav Šilhavý

Applications of Mathematics (1992)

  • Volume: 37, Issue: 5, page 383-400
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Šilhavý, Miroslav. "Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity." Applications of Mathematics 37.5 (1992): 383-400. <http://eudml.org/doc/15723>.

@article{Šilhavý1992,
abstract = {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.},
author = {Šilhavý, Miroslav},
journal = {Applications of Mathematics},
keywords = {multipolar materials; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry},
language = {eng},
number = {5},
pages = {383-400},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity},
url = {http://eudml.org/doc/15723},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Šilhavý, Miroslav
TI - Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 5
SP - 383
EP - 400
AB - 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.
LA - eng
KW - multipolar materials; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry
UR - http://eudml.org/doc/15723
ER -

References

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  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, 10.1016/0020-7225(67)90041-9, Int. J. Engng. Sci. 5 (1967), 323-340. (1967) DOI10.1016/0020-7225(67)90041-9
  3. K. Bucháček, Thermodynamics of monopolar continuum of grade n, Apl. Mat. 16 (1971), 370-383. (1971) MR0290662
  4. B. D. Coleman W. Noll, 10.1007/BF00276168, Arch. Rational Mech. Anal. 6 (1960), 355-370. (1960) MR0119598DOI10.1007/BF00276168
  5. A. E. Green R. S. Rivlin, 10.1007/BF00281725, Arch. Rational Mech. Anal. 16 (1964), 325-354. (1964) MR0182191DOI10.1007/BF00281725
  6. A. E. Green R. S. Rivlin, 10.1007/BF00253051, Arch. Rational Mech. Anal. 17 (1964), 113-147. (1964) MR0182192DOI10.1007/BF00253051
  7. S. R. de Groot P. Mazur, Non-Equilibrium Thermodynamics, North-Holland, Amsterodam, 1962. (1962) 
  8. M. E. Gurtin W. J. Hrusa, 10.1090/qam/1096233, Quart. Appl. Math. 49 (1991), 67-85. (1991) MR1096233DOI10.1090/qam/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. (1989) MR1031872
  10. J. Nečas A. Novotný, M, Šilhavý, 10.1016/0022-247X(91)90189-7, J. Math. Anal. Appl. 162 (1991), 223-241. (1991) MR1135273DOI10.1016/0022-247X(91)90189-7
  11. J. Nečas M. Růžička, Global solution to the incompressible viscous-multipolar material, to appear. 
  12. J. Nečas M. Šilhavý, 10.1090/qam/1106391, Quart. Appl. Math. 49 (1991), 247-265. (1991) MR1106391DOI10.1090/qam/1106391
  13. A. Novotný, Viscous multipolar fluids-physical background and mathematical theory, Progress in Physics 39 (1991). (1991) MR1184232
  14. M. Šilhavý, A note on Onsager's relations, to appear Quart. Appl. Math. Zbl0809.73014MR1292198

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