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On boundary conditions for polar materials

  • R. J. Atkin
  • S. C. Cowin
  • N. Fox
Original Papers

Summary

We discuss some restrictions on boundary conditions in continuum mechanics arising from the requirement that the basic balance laws, invariance conditions and entropy inequality must hold for the material outside of the bounding surface. We illustrate our assertions for polar materials, but the ideas we use are applicable to all continuum theories.

Keywords

Boundary Condition Entropy Mathematical Method Continuum Theory Invariance Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

Es werden einige Einschränkungen für die Randbedingungen in der Kontinuumsmechanik behandelt, die von der Forderung herrühren, dass für die Materie ausserhalb der Grenzfläche die fundamentalen Bilanzgleichungen, die Invarianzbedingungen und die Entropieungleichung gelten sollen. Diese Behauptungen werden für polare Materialien erläutert, jedoch sind die hier eingeführten Begriffe auf Kontinuumstheorien aller Art anwendbar.

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References

  1. [1]
    S. C. Cowin,The Theory of Polar Fluids, Adv. Appl. Mech.14, 279 (1974).Google Scholar
  2. [2]
    I. Müller,On the Entropy Inequality, Arch. Rational Mech. Anal.26, 118 (1967).Google Scholar
  3. [3]
    P. Brunn,The Velocity Slip of Polar Fluids, Rheol. Acta.14, 1039 (1975).Google Scholar
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    E. L. Aero, A. N. Bulygin andE. V. Kuvshinskii,Asymmetric Hydromechanics, PMM29, 297 (1965).Google Scholar
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    S. C. Cowin andC. J. Pennington,On the Steady Rotational Motion of Polar Fluids, Rheol. Acta9, 307 (1970).Google Scholar
  6. [6]
    H. Lamb,Hydrodynamics, 6th Ed., Cambridge University Press (1959).Google Scholar

Copyright information

© Birkhäuser Verlag 1977

Authors and Affiliations

  • R. J. Atkin
    • 1
  • S. C. Cowin
    • 2
  • N. Fox
    • 3
  1. 1.Dept. of Applied Mathematics and Computing ScienceUniversity of SheffieldEngland
  2. 2.Dept. of Mechanical EngineeringTulane UniversityNew OrleansUSA
  3. 3.Dept. of Applied Mathematics and Computing ScienceUniversity of SheffieldEngland

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