On the Application of the Principles of Thermodynamics to Strained Solid Materials

  • J. Kestin
Part of the IUTAM Symposia book series (IUTAM)


It is shown that a meaningful analysis of strained solid materials must begin with the identification of the independent thermodynamic parameters which determine their state. For example, in plasticity it is necessary to split the total strain into a part which is and a part which is not a parameter of state. In viscoelasticity, a similar splitting affects the stress, and in creep and relaxation it is necessary to introduce one or more additional variables of state. The importance of these observations lies in the fact that thermodynamic potentials can be functions of the parameters of state only.

An outline is given of a general method which allows us to extend our knowledge of uniform systems to include continuous systems. This method is based on the acceptance of the principle of local state which has been used successfully in the theories of elasticity and fluid mechanics or heat transfer and which forms the basis of the summary treatment due to de Groot and Mazur [4].

Particular attention is paid to plastic deformation and to strain hardening. First it is pointed out that the relation between the stress and the plastic strain rate does not seem to come within the scope of Onsager’s relations whose validity is restricted to small departures from equilibrium. Secondly, a fully three-dimensional theory of elastic-plastic domains is proposed. Quoting some results obtained by J. R. Rice, it is made plausible that such a theory is likely to lead to a physically realistic description of the Bauschinger effect and of the variations in the yield surface under repeated loading cycles.


Internal Energy Yield Surface Generalize Force Slip Surface Irreversible Process 


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  1. [1]
    Bridgman, P. W.: Rev. Mod. Phys. 22, 56 (1950).ADSCrossRefGoogle Scholar
  2. [2]
    Meixner, J.: Natuurk. 26, 259 (1960). See also article by Meixner, J., and Reik, H. G., in: “Encyclopedia of Physics”, Vol. III/12, p. 413. Berlin—Göttingen—Heidelberg: Springer 1965.Google Scholar
  3. [3]
    Meixner, J.: Consequences of an Inequality in Nonequilibrium Thermodynamics. Trans. Asme (Ser. E. J. Appl. Mech.) 88, 481 (1966).CrossRefGoogle Scholar
  4. [4]
    De Groot, S. R., and P. Mazur* Non-Equilibrium Thermodynamics Amsterdam: North-Holland Publ. Co. 1962.Google Scholar
  5. [5]
    Kestin, J.: A Course in Thermodynamics. Blaisdell 1966.Google Scholar
  6. [6]
    Huber, M. T.: Czasopismo techniczne. Lwow: 1904.Google Scholar
  7. [7]
    Mises, R. Vox: Gött. Nachr. (Math. phys. Kl. ) 1913, 582.Google Scholar
  8. [8]
    Haigh, B. P.: Rep. Brit. Association 1919, 486.Google Scholar
  9. [9]
    Kluitenberg, G. A.: Physica 28, 217 (1962).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1968

Authors and Affiliations

  • J. Kestin
    • 1
  1. 1.ProvidenceUSA

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