Advertisement

Annali di Matematica Pura ed Applicata

, Volume 108, Issue 1, pp 189–199 | Cite as

On thermodynamics and intrinsically equilibrated materials

  • Bernard D. Coleman
  • David R. Owen
Article

Summary

The existence and uniqueness of free energy functions is demonstrated for a class of materials broad enough to contain as special cases those of the theory of finite elasticity, the theory of hypo-elasticity, and the theory of internal state variables for which the path of evolution is invariant under rescalings of time.

Keywords

Energy Function Free Energy Internal State Free Energy Function Internal State Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. D. Coleman -D. R. Owen,A mathematical foundation for thermodynamics, Archive for Rational Mechanics and Analysis,54 (1974), pp. 1–104.CrossRefMathSciNetzbMATHGoogle Scholar
  2. [2]
    B. D. Coleman -D. R. Owen,On thermodynamics and elastic-plastic materials, Archive for Rational Mechanics and Analysis,59 (1975), pp. 25–51.CrossRefMathSciNetzbMATHGoogle Scholar
  3. [3]
    D. R. Owen -W. O. Williams,On the time derivatives of equilibrated response functions, Archive for Rational Mechanics and Analysis,33 (1969), pp. 288–306.MathSciNetzbMATHGoogle Scholar
  4. [4]
    W. Noll,A new mathematical theory of simple materials, Archive for Rational Mechanics and Analysis,48 (1972), pp. 1–50, particularly p. 46 (§ 20).CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    C. Truesdell,Hypo-elasticity, Journal of Rational Mechanics and Analysis,4 (1955), pp. 83–133.zbMATHMathSciNetGoogle Scholar
  6. [6]
    C. Truesdell -W. Noll,The non-linear field theories of mechanics, Handbuch der Physik, vol. III/3, ed. S. Flugge, Berlin-Heidelberg-New York: Springer-Verlag (1965), §§ 99–103 pp. 401–426.Google Scholar
  7. [7]
    B. Bernstein,Hypo-elasticity and elasticity, Archive for Rational Mechanics and Analysis,6 (1960), pp. 89–104.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    L. Caprioli,Su un criterio per l'esistenza dell'energia di deformazione, Bollettino della Unione Matematica Italiana (III),10 (1955), pp. 481–483.zbMATHMathSciNetGoogle Scholar
  9. [9]
    B. Bernstein -J. L. Ericksen,Work functions in hypo-elasticity, Archive for Rational Mechanics and Analysis,5 (1958), pp. 396–409.MathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Bernard D. Coleman
    • 1
  • David R. Owen
    • 1
  1. 1.PittsburghU.S.A.

Personalised recommendations