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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.