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On boundary conditions for polar materials

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Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

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.

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. S. C. Cowin,The Theory of Polar Fluids, Adv. Appl. Mech.14, 279 (1974).

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  2. I. Müller,On the Entropy Inequality, Arch. Rational Mech. Anal.26, 118 (1967).

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  3. P. Brunn,The Velocity Slip of Polar Fluids, Rheol. Acta.14, 1039 (1975).

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  4. E. L. Aero, A. N. Bulygin andE. V. Kuvshinskii,Asymmetric Hydromechanics, PMM29, 297 (1965).

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  5. S. C. Cowin andC. J. Pennington,On the Steady Rotational Motion of Polar Fluids, Rheol. Acta9, 307 (1970).

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  6. H. Lamb,Hydrodynamics, 6th Ed., Cambridge University Press (1959).

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Author information

Authors and Affiliations

  1. Dept. of Applied Mathematics and Computing Science, University of Sheffield, England

    R. J. Atkin

  2. Dept. of Mechanical Engineering, Tulane University, New Orleans, Louisiana, USA

    S. C. Cowin

  3. Dept. of Applied Mathematics and Computing Science, University of Sheffield, England

    N. Fox

Authors
  1. R. J. Atkin
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  2. S. C. Cowin
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  3. N. Fox
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Atkin, R.J., Cowin, S.C. & Fox, N. On boundary conditions for polar materials. Journal of Applied Mathematics and Physics (ZAMP) 28, 1017–1026 (1977). https://doi.org/10.1007/BF01601669

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  • DOI: https://doi.org/10.1007/BF01601669

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