Material Symmetry and Constitutive Equations

  • R. S. Rivlin

Summary

Constitutive equations which are relations between tensors are considered. It is shown how the restrictions which are imposed on the form of such relations by symmetry of the material can be obtained in canonical form.

Keywords

Hexagonal Proper Ortho 

Übersicht

Stoffgleichungen werden als Tensorbeziehungen betrachtet. Es wird gezeigt, wie die aus der Forderung nach Symmetrie des Materials folgenden Einschränkungen in kanonischer Form erhalten werden können.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Voigt, W.: Lehrbuch der Kristallphysik. Leipzig 1910Google Scholar
  2. 2.
    Lokhin, V. V., Sedov, L. I.: Prikl. Mat. Mech. 27 (1963) 393–417Google Scholar
  3. 3.
    Smith, G. F.: Ann. N.Y. Acad. Sci. 172 (1970) 57–105 *Google Scholar
  4. 4.
    Spencer, A. J. M.: Theory of Invariants. In: Eringen, A. C. (ed.): Continuum Mechanics, Vol. 1. New York 1971, pp. 239–253Google Scholar
  5. 5.
    Rivlin, R. S.: Notes on the Theory of Constitutive Equations. In: Graffi D. (ed.): Materials with Memory, Naples 1979, 185–294Google Scholar
  6. 6.
    Weyl, H.: The Classical Groups. Princeton 1946.Google Scholar
  7. 7.
    Pipkin, A. C.; Wineman, A. S.: Arch. Rational Mech. Anal 12 (1963) 420—426Google Scholar
  8. 8.
    Wineman, A. S.; Pipkin, A. C.: Arch. Rational Mech. Anal 17 (1964) 184—214Google Scholar
  9. 9.
    Green, A. E.; Rivlin, R. S.: Arch. Rational Mech. Anal. 1 (1957) 1—21Google Scholar
  10. 10.
    Murnaghan, F. D.: The Theory of Group Representations. Baltimore 1938Google Scholar
  11. 11.
    Smith, G. F.; Rivlin, R. S.: Trans. Amer. Math. Soc. 88 (1958) 175–193CrossRefGoogle Scholar
  12. 12.
    Smith, G. F.; Smith, M. M.; Rivlin, R. S.: Arch. Rational Mech. Anal 12 (1963) 93–133CrossRefGoogle Scholar
  13. 13.
    Smith, G. F.; Rivlin, R. S.: Arch. Rational Mech. Anal 15 (1964) 169–221Google Scholar
  14. 14.
    Smith, G. F.: Q. Appl. Math. 25 (1967) 218–221Google Scholar
  15. 15.
    Smith, G. F.; Kiral, E.; Rend. Circolo Matematico Palermo 18 (1969) 5–22CrossRefGoogle Scholar
  16. 16.
    Kiral, E.; Smith, G. F.: Int. J. Eng. Sci. 12 (1974) 471–490CrossRefGoogle Scholar
  17. 17.
    Rivlin, R. S.: J. Rational Mech. Anal 4 (1955) 681–702Google Scholar
  18. 18.
    Spencer, A. J. M.; Rivlin, R. S.: Arch. Rational Mech. Anal. 2 (1959) 309—336Google Scholar
  19. 19.
    Spencer, A. J. M.; Rivlin, R. S.: Arch. Rational Mech. Anal. 2 (1959) 435–446CrossRefGoogle Scholar
  20. 20.
    Spencer, A. J. M.; Rivlin, R. S.: Arch. Rational Mech. Anal 4 (1960) 214–230CrossRefGoogle Scholar
  21. 21.
    Spencer, A. J. M.: Arch. Rational Mech. Anal. 7 (1961) 64—77Google Scholar
  22. 22.
    Smith, G. F.: Arch. Rational Mech. Anal. 5 (1960) 382—389Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • R. S. Rivlin
    • 1
  1. 1.Center for the Application of MathematicsLehigh UniversityBethlehemUSA

Personalised recommendations