Skip to main content
SpringerLink
Log in

Material symmetry and constitutive equations

  • Published:
Ingenieur-Archiv Aims and scope Submit manuscript

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.

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Voigt, W.: Lehrbuch der Kristallphysik. Leipzig 1910

  2. Lokhin, V. V., Sedov, L. I.: Prikl. Mat. Mech. 27 (1963) 393–417

    MathSciNet  Google Scholar 

  3. Smith, G. F.: Ann. N.Y. Acad. Sci. 172 (1970) 57–105

    Google Scholar 

  4. Spencer, A. J. M.: Theory of Invariants. In: Eringen, A. C. (ed.): Continuum Mechanics, Vol. 1. New York 1971, pp. 239–253

  5. Rivlin, R. S.: Notes on the Theory of Constitutive Equations. In: Graffi D. (ed.): Materials with Memory, Naples 1979, 185–294

  6. Weyl, H.: The Classical Groups. Princeton 1946.

  7. Pipkin, A. C.; Wineman, A. S.: Arch. Rational Mech. Anal 12 (1963) 420–426

    Article  MathSciNet  MATH  Google Scholar 

  8. Wineman, A. S.; Pipkin, A. C.: Arch. Rational Mech. Anal 17 (1964) 184–214

    Article  MathSciNet  MATH  Google Scholar 

  9. Green, A. E.; Rivlin, R. S.: Arch. Rational Mech. Anal. 1 (1957) 1–21

    Article  MathSciNet  MATH  Google Scholar 

  10. Murnaghan, F. D.: The Theory of Group Representations. Baltimore 1938

  11. Smith, G. F.; Rivlin, R. S.: Trans. Amer. Math. Soc. 88 (1958) 175–193

    Article  MathSciNet  MATH  Google Scholar 

  12. Smith, G. F.; Smith, M. M.; Rivlin, R. S.: Arch. Rational Mech. Anal 12 (1963) 93–133

    Article  MathSciNet  MATH  Google Scholar 

  13. Smith, G. F.; Rivlin, R. S.: Arch. Rational Mech. Anal 15 (1964) 169–221

    Article  MathSciNet  Google Scholar 

  14. Smith, G. F.: Q. Appl. Math. 25 (1967) 218–221

    MATH  Google Scholar 

  15. Smith, G. F.; Kiral, E.; Rend. Circolo Matematico Palermo 18 (1969) 5–22

    MathSciNet  MATH  Google Scholar 

  16. Kiral, E.; Smith, G. F.: Int. J. Eng. Sci. 12 (1974) 471–490

    Article  MathSciNet  MATH  Google Scholar 

  17. Rivlin, R. S.: J. Rational Mech. Anal 4 (1955) 681–702

    MATH  MathSciNet  Google Scholar 

  18. Spencer, A. J. M.; Rivlin, R. S.: Arch. Rational Mech. Anal. 2 (1959) 309–336

    Article  MathSciNet  MATH  Google Scholar 

  19. Spencer, A. J. M.; Rivlin, R. S.: Arch. Rational Mech. Anal. 2 (1959) 435–446

    Article  MathSciNet  MATH  Google Scholar 

  20. Spencer, A. J. M.; Rivlin, R. S.: Arch. Rational Mech. Anal 4 (1960) 214–230

    Article  MathSciNet  MATH  Google Scholar 

  21. Spencer, A. J. M.; Arch. Rational Mech. Anal. 7 (1961) 64–77

    Article  MATH  MathSciNet  Google Scholar 

  22. Smith, G. F.: Arch. Rational Mech. Anal. 5 (1960) 382–389

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for the Application of Mathematics, Lehigh University, Pa. 18015, Bethlehem, USA

    R. S. Rivlin

Authors
  1. R. S. Rivlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor Hans Ziegler on the occasion of his 70th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rivlin, R.S. Material symmetry and constitutive equations. Ing. arch 49, 325–336 (1980). https://doi.org/10.1007/BF02426911

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02426911

Keywords

Search

Navigation