Constitutive Equations Involving Functional Dependence of One Vector on Another

  • Ronald S. Rivlin

Abstract

There are many physical situations for which the applicable constitutive equation involves the relation between the value of one vector at the instant of measurement and the values of another vector at times up to and including the instant of measurement. Examples of such situations are the relation between the magnetic intensity and magnetic induction fields in a hysteretic magnetic material and the relation between the electric displacement and electric fields in a ‘lossy’ dielectric. In this paper we discuss how restrictions may be placed on the form of such constitutive equations as a result of the material symmetry.

Keywords

Dinate 

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References

  1. [1]
    Green, A. E., and Rivlin, R. S., Arch. Rat’l. Mech. and Anal. 1, 1 (1957).CrossRefGoogle Scholar
  2. [2]
    Green, A. E., Rivlin, R. S., and Spencer, A. J. M., Arch. Rat’l. Mech. And Anal. 3, 82 (1959).CrossRefGoogle Scholar
  3. [3]
    Rivlin, R. S., Arch. Rat’l. Mech. and Anal. 4, 262 (1960).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ronald S. Rivlin
    • 1
  1. 1.Brown UniversityProvidenceUSA

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