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Abstract

The balance equations of mass, momentum, energy and entropy at a phase boundary imply phase boundary conditions which determine the position of the boundary as a function of temperature. This is true when either the phase boundary is sharp or when it occurs through a transition zone, albeit the latter case seems to require strongly symmetric geometry.

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References

  1. S.R. de Groot and P. Mazur, Anwendung der Thermodynamik irreversibler Prozesse. Bibliographisches Institut, Mannheim (1974).

    Google Scholar 

  2. R. Abeyaratne and J.K. Knowles, On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (1990) 345–360.

    MathSciNet  Google Scholar 

  3. E. Fried, Energy release, friction and supplemental relations at phase interphases. Continuum Mech. Thermodyn. 7 (1995) 111–121.

    MATH  MathSciNet  Google Scholar 

  4. J.D. Eshelby, The elastic energy momentum tensor. J. Elasticity 5 (1975) 321–335.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Heidug and F.K. Lehner, Thermodynamics of coherent phase transformations in non-hydrostatically stressed solids. Pure Appl. Geophys. 123 (1985) 91–98.

    Article  Google Scholar 

  6. L.M. Truskinovsky, Dynamics of non-equilibrium phase boundaries in a heat-conducting non-linearly elastic medium. J. Appl. Math. Mech. PMM USSR 51 (1987) 777–784.

    MathSciNet  Google Scholar 

  7. M.E. Gurtin, The dynamics of solid-solid phase transitions — 1. Coherent transitions. Arch. Rational Mech. Anal. 123 (1993) 305–335.

    Article  MATH  MathSciNet  Google Scholar 

  8. I-Shih Liu, On interface equilibrium and inclusion problems. Continuum Mech. Thermodyn. 4 (1992) 177–188.

    Article  MATH  Google Scholar 

  9. I. Schmidt, Gleich gewicht smorphologien elastischer Einschlüsse. Dissertation TU Darmstadt. Shaker Verlag (1997).

    Google Scholar 

  10. R. Müller, 3D-Simulation der Mikrostrukturentwicklung in Zwei-Phasen-Materialien. Dissertation TU Darmstadt (2001).

    Google Scholar 

  11. G.A. Maugin, Material forces: Concepts and applications. ASME Appl. Mech. Rev. 48 (1995) 213–245.

    MathSciNet  Google Scholar 

  12. R. Kienzler and G.A. Maugin, Configurational Mechanics of Materials. CISM Internat. Centre for Mechanical Sciences, Courses and Lectures 427 (1999).

    Google Scholar 

  13. P. Podio-Guidugli, Configurational balances via variational arguments. Interfaces Free Boundaries 3 (2001) 1–13.

    MATH  MathSciNet  Google Scholar 

  14. I. Müller, Thermodynamics. Pitman, Boston (1985).

    Google Scholar 

  15. I. Müller, Eshelby tensor and phase equilibrium. Theor. Appl. Mech. 25 (1999) 77–89.

    MATH  Google Scholar 

  16. C. Truesdell and R. Toupin, The classical field theories. In: Handbuch der Physik, Vol. III/1. Springer, Heidelberg (1960) pp. 226–793.

    Google Scholar 

  17. Y. Huo and I. Müller, Thermodynamics of pseudoelasticity — an analytical approach. Acta Mechanica 99 (1993) 1–19.

    Google Scholar 

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Dedicated to C.A. Truesdell, who taught us rational thinking

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© 2004 Kluwer Academic Publishers

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Buratti, G., Huo, Y., Müller, I. (2004). Eshelby Tensor as a Tensor of Free Enthalpy. In: Man, CS., Fosdick, R.L. (eds) The Rational Spirit in Modern Continuum Mechanics. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2308-1_9

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  • DOI: https://doi.org/10.1007/1-4020-2308-1_9

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1828-2

  • Online ISBN: 978-1-4020-2308-8

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