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Duhamel’s Pioneering Work in Thermo-elasticity and Its Legacy

  • Gérard A. Maugin
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 214)

Abstract

This is a short introduction to the original chapter published in 1837 by the French mathematician J. M. C. Duhamel, in which the first equations of thermo-mechanical couplings or thermo-elasticity are introduced for three-dimensional elastic bodies. This contribution offers a short discussion of the basic ideas behind Duhamel’s historical chapter, the strategy applied by Duhamel for combining ideas from Navier’s elasticity and Fourier’s theory of heat propagation, the illustration by the solution of general equations in some well-chosen problems, and the heritage of Duhamel in thermo-mechanical sciences.

Keywords

Thermo-elasticity Heat conduction Thermo-mechanical couplings Duhamel-Neumann equations 

References

  1. 1.
    Abeyaratne R, Knowles JK (2001) Evolution of phase transitions. Cambridge University Press, UKGoogle Scholar
  2. 2.
    Bachelard G (1927) Etude sur l’évolution d’un problème de physique: la propagation thermique dans les solides (Complementary Thesis, Paris, 1927) (reprinted by Librairie philosophique Vrin, Paris, 1973, with a foreword by A. Lichnerowicz)Google Scholar
  3. 3.
    Boley BA, Weiner JH (1960) Theory of thermal stresses. Wiley, New YorkMATHGoogle Scholar
  4. 4.
    Brillouin L (1938) Tensors in mechanics and elasticity (original French edn in Paris, Dover reprint 1946; First English translation, Academic Press, New York, 1963)Google Scholar
  5. 5.
    Chadwick P (1960) Thermoelasticity. The dynamical theory. In: Sneddon IN, Hill R (eds) Progress in solid mechanics, vol I. North-Holland, Amsterdam, pp 263–328Google Scholar
  6. 6.
    Coleman BD, Gurtin ME, Herrera I, Truesdell CA (1965) Wave propagation in dissipative materials. Springer, New York (collection of reprints of papers)Google Scholar
  7. 7.
    Duhamel JMC (1832) Sur les équations générales de la propagation de chaleur dans les corps solides dont la conductibilité n’est pas la même dans tous les sens (On the general equations of heat propagation in solid bodies the conductibility of which differs according to the direction). J de l’Ecole Polytechnique, Tome 13, Cahier 21, pp 356–399Google Scholar
  8. 8.
    Duhamel JMC (1837) Second mémoire sur les phénomènes thermo-mécaniques (Second memoir on thermo-mechanical phenomena). J de l’Ecole Polytechnique, Tome 15, Cahier 25, pp 1–57Google Scholar
  9. 9.
    Duhem P (1906) Recherches sur l’élasticité. Gauthier-Villars, Paris (collection of four papers with a total of 218 pages)Google Scholar
  10. 10.
    Hetnarski RB (1986) Thermal stresses, vol 1. Mechanics and mathematical methods. North-Holland, AmsterdamGoogle Scholar
  11. 11.
    Hetnarski RB (2014) General editor: encyclopaedia of thermal stresses. Springer, BerlinCrossRefGoogle Scholar
  12. 12.
    Hetnarski RB, Eslami MR (2009) Thermal stresses—advanced theory and applications. Springer, DordrechtMATHGoogle Scholar
  13. 13.
    Inoue T (1997) Metallo-thermo-mechanics. Wiley, New YorkGoogle Scholar
  14. 14.
    Melan E, Parkus H (1953) Warmespannungen Infolge stationarer temperaturfelder. Springer, ViennaGoogle Scholar
  15. 15.
    Mićunović M (1974) A geometrical treatment of thermoelasticity of simple inhomogeneous bodies: I –geometric and kinematic relations. Bull Acad Pol Sci Sér Sci Techn 22:579–588; II (Constitutive equations), & III. (Approximations), 22:633–641, 23:89–97 (1975)Google Scholar
  16. 16.
    Neumann FE (1885) Vorlesung über die Theorie des Elasticität der festen Körper und des Lichtäthers. Teubner, LeipzigGoogle Scholar
  17. 17.
    Nowacki W (1986) Thermoelasticity. Pergamon Press, Oxford (2nd revised edn; translated from the Polish; original Polish edition, P.W.N., Warsaw, 1962)Google Scholar
  18. 18.
    Parkus H (1959) Instationäre wärmespannungen. Springer, WienCrossRefMATHGoogle Scholar
  19. 19.
    Parkus H (1968) Thermoelasticity. Blaisdell, WalthamGoogle Scholar
  20. 20.
    Signorini A (1943) Trasfomazioni termoelastiche finite, Memoria 1. Ann di Mat Pura ed Applicata (4) 22:33–143; Memoria 2, ibid, 30:1–72 (1949); Memoria 3, ibid, 39:147–201 (1955)Google Scholar
  21. 21.
    Timoshenko SP (1953) History of the strength of materials. McGraw Hill, New York (Dover reprint, New York, 1983)Google Scholar
  22. 22.
    Truesdell CA (1952) Mechanical foundations of elasticity and fluid mechanics. J Rat Mech Anal 1:125–300 (section 44)MATHMathSciNetGoogle Scholar
  23. 23.
    Truesdell CA (1961) General and exact theory of waves in finite elastic strain. Arch Rat Mech Anal 8:263–296CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Voigt W (1910) Lehrbuch der kristallphysik. Teubner, BerlinGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut Jean Le Rond d’AlembertUniversité Pierre et Marie CurieParis Cedex 05France

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