Skip to main content
SpringerLink
Log in

Eshelby Tensor as a Tensor of Free Enthalpy

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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.

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    MATH  MathSciNet  ADS  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 nonhydrostatically stressed solids. Pure Appl. Geophys. 123 (1985) 91–98.

    Article  ADS  Google Scholar 

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

    Article  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  ADS  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

  9. I. Schmidt, Gleichgewichtsmorphologien elastischer Einschlüsse. Dissertation TU Darmstadt. Shaker Verlag (1997).

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

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

    Article  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).

  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).

    MATH  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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale, Università di Pisa, Pisa, Italy

    Giovanni Buratti

  2. Department of Mechanics, Fudan University, Shanghai, PR, China

    Yongzhong Huo

  3. Thermodynamik, Technische Universität Berlin, 10623, Berlin, Germany

    Ingo Müller

Authors
  1. Giovanni Buratti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongzhong Huo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ingo Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buratti, G., Huo, Y. & Müller, I. Eshelby Tensor as a Tensor of Free Enthalpy. Journal of Elasticity 72, 31–42 (2003). https://doi.org/10.1023/B:ELAS.0000018777.15755.6d

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:ELAS.0000018777.15755.6d

Search

Navigation