Multipolar viscous fluids
Authors:
J. Nečas and M. Šilhavý
Journal:
Quart. Appl. Math. 49 (1991), 247-265
MSC:
Primary 76A05; Secondary 73B05, 73B25
DOI:
https://doi.org/10.1090/qam/1106391
MathSciNet review:
MR1106391
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Abstract: The purpose of the paper is to develop a thermodynamic theory of constitutive equations of multipolar viscous fluids. The restrictions which the principle of material frame-indifference and the Clausius-Duhem inequality place on the constitutive equations are derived. Explicit forms of the viscous stresses are obtained for linear viscous fluids.
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J. Nečas and M. Růžička, Global solution to the incompressible viscous-multipolar material, to appear
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I. Samohýl, Symmetry groups in the mass conserving, second grade materials, Arch. Mech. 33, 983–987 (1981)
- Morton E. Gurtin, Maurizio Vianello, and William O. Williams, On fluids of grade $n$, Meccanica–J. Italian Assoc. Theoret. Appl. Mech. 21 (1986), no. 4, 179–183. MR 885639, DOI https://doi.org/10.1007/BF01556483
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C. Truesdell, A First Course in Rational Continuum Mechanics, The Johns Hopkins University, Baltimore, 1972
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A. J. M. Spencer, Theory of invariants, Continuum Physics, vol. I (ed. by A. C. Eringen), Academic Press, New York, 1971
J. Nečas, A. Novotný, and M. Šilhavý, Global solution to the ideal compressible heat conductive multipolar fluid, Comment. Math. Univ. Carolinae 30, 551–564 (1989)
J. Nečas and M. Růžička, Global solution to the incompressible viscous-multipolar material, to appear
A. E. Green and R. S. Rivlin, Simple force and stress multipoles, Arch. Rational Mech. Anal. 16, 325–353 (1964)
A. E. Green and R. S. Rivlin, Multipolar continuum mechanics, Arch. Rational Mech. Anal. 17, 113–147 (1964)
K. Bucháček, Thermodynamics of monopolar continuum of grade n, Apl. Mat. 16, 370–383 (1971)
W. Noll, A mathematical theory of behavior of continuous media, Arch. Rational Mech. Anal. 2, 119–226 (1957)
J. J. Cross, Mixtures of fluids and isotropic solids, Arch. Mech. 25, 1025–1039 (1973)
I. Samohýl, Symmetry groups in the mass conserving, second grade materials, Arch. Mech. 33, 983–987 (1981)
M. E. Gurtin, M. Vianello, and W. O. Williams, On fluids of grade n, Meccanica—J. Ital. Assoc. Theoret. Appl. Mech. 21, 179–181 (1986)
C. Truesdell and W. Noll, The Non-linear Field Theories of Mechanics, Handbuch der Physik III/3 (ed. by S. Flügge), Springer, Berlin-Heidelberg-New York, 1965
C. Truesdell, A First Course in Rational Continuum Mechanics, The Johns Hopkins University, Baltimore, 1972
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178 (1963)
A. J. M. Spencer, Theory of invariants, Continuum Physics, vol. I (ed. by A. C. Eringen), Academic Press, New York, 1971
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Article copyright:
© Copyright 1991
American Mathematical Society