On the Stability of Thermoelastic Materials


A notion of material stability is introduced and discussed in the setting of nonlinear thermoelasticity. Necessary and sufficient conditions are established for the stability of a general thermoelastic material. The adiabatic theory and the theory that accounts for heat conduction are considered separately.

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  1. 1.

    J. Hadamard, Leçons sur la Propagation des Ondes et les Équations de l'Hydrodynamique, Hermann, Paris (1903).

    MATH  Google Scholar 

  2. 2.

    C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, vol. III/3, Springer-Verlag, Berlin (1965).

    Google Scholar 

  3. 3.

    M.E. Gurtin, The linear theory of elasticity, Handbuch der Physik, vol. VIa/2, Springer-Verlag, Berlin (1972).

    Google Scholar 

  4. 4.

    R.D. James, Finite deformation by mechanical twinning, Archive for Rational Mechanics and Analysis 77(1981) 143-176.

    MathSciNet  Article  ADS  MATH  Google Scholar 

  5. 5.

    R.D. James, Phase transformations and non-elliptic free energy functions. In: J. Serrin (ed.), New Perspectives in Thermodynamics. Springer-Verlag, Berlin (1986) pp. 223-239.

    Google Scholar 

  6. 6.

    J.K. Knowles and E. Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics, Journal of Elasticity 8(1978) 329-379.

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    B. Coleman and W. Noll, On the thermostatics of continuous media, Archive for Rational Mechanics and Analysis 4(1959) 97-128.

    MathSciNet  MATH  Article  ADS  Google Scholar 

  8. 8.

    J.L. Ericksen, A thermo-kinetic view of elastic stability theory, International Journal of Solids and Structures 2(1966) 573-580.

    Article  Google Scholar 

  9. 9.

    J.L. Ericksen, Thermoelastic stability, Proceedings of the Fifth U.S. National Congress of Applied Mechanics. (1966) pp. 187-193.

  10. 10.

    C. Dafermos, On the existence and asymptotic stability of solutions of the equations of linear thermoelasticity, Archive for Rational Mechanics and Analysis 29(1968) 241-271.

    MathSciNet  ADS  MATH  Article  Google Scholar 

  11. 11.

    J.E. Dunn and R.L. Fosdick, The morphology and stability of material phases, Archive for Rational Mechanics and Analysis 74(1980) 1-99.

    MathSciNet  Article  ADS  Google Scholar 

  12. 12.

    A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edition, Cambridge (1927).

  13. 13.

    D.E. Carlson, Linear Thermoelasticity, Handbuch der Physik, vol. VIa/2, Springer-Verlag, Berlin (1972).

    Google Scholar 

  14. 14.

    P. Duhem, Sur la propagation des ondes dans un milieu parfaitement élastique affecté par las déformations finies, Comptes Rendus de l'Académie des Sciences, Paris 136(1903) 1379- 1381.

    MATH  Google Scholar 

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Abeyaratne, R., Knowles, J.K. On the Stability of Thermoelastic Materials. Journal of Elasticity 53, 199–213 (1998). https://doi.org/10.1023/A:1007513631783

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  • thermoelasticity
  • stability
  • strong ellipticity.