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Objectivity of the Constitutive Equation for a Material with Memory

  • R. S. Rivlin

Abstract

The restriction imposed by objectivity on the constitutive functional for a material with memory is well-known. However, the derivation usually given is open to certain objections. A more satisfactory proof is given in this note.

Keywords

Constitutive Equation Cauchy Stress Orthogonal Matrix Stress Matrix Material Frame 
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References

  1. Green, A. E. and Rivlin, R. S. (1957). The mechanics of non-linear materials with memory: Part I. Archs Ration. Mech. Analysis 1, 1–21.CrossRefGoogle Scholar
  2. Green, G. (1938). On the laws of reflexion and refraction of light at the common surface of two non-crystallized media. Trans. Camb. Phil. Soc. 7, 1–24.Google Scholar
  3. Noll, W. (1958). A mathematical theory of the mechanical behavior of continuous media. Archs. Ration. Mech. Analysis 2, 197–226.CrossRefGoogle Scholar
  4. Rivlin, R. S. (1970). An introduction to non-linear continuum mechanics. In Son-Linear Continuum Theories in Mechanics and Physics and Their Applications (Edited by R. S. Rivlin), pp. 151–309. Edizioni Cremonese, Rome.Google Scholar
  5. Rivlin, R. S. and Smith, G. F. (1987). A note on material frame indifference. Int. J. Solids Structures 23, 1639–1643.CrossRefGoogle Scholar
  6. Truesdell, C. (1960). Principles of continuum mechanics. Socony Mobil Lectures in Pure and Applied Science, No. 5.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • R. S. Rivlin
    • 1
  1. 1.Department of Mechanical EngineeringLehigh UniversityBethlehemUSA

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