Skip to main content
SpringerLink
Log in

Dynamical theoretical model and variational principles for coupled temperature–diffusion–mechanics

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this paper, firstly, the acceleration of the temperature and concentration are assumed to need the extra increment of the heat and energy. The inertial entropy and the inertial chemical potential were proposed by Kuang (Acta Mech 203:1–11, 2009, Acta Mech 214:275–289, 2010). Secondly, the expressions of dissipative energy produced by the variation of the temperature and concentration are derived by using the second law of thermodynamics. Finally, several variational principles for coupled temperature–diffusion–mechanics are established, and their corresponding governing equations and boundary conditions are naturally presented. Meanwhile, some numerical simulations are carried out to describe the coupled reciprocity, which shows concentration diffusion with a finite velocity.

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. Favergeon J., Montesin T., Bertrand G.: Mechano-chemical aspects of hight temperature oxidation: a mesoscopic model applied to zirconium alloys. Oxid. Met. 64, 253–279 (2005)

    Article  Google Scholar 

  2. Zhou H.G., Qu J., Cherkaoui M.: Stress-oxidation interaction in selective oxidation of Cr-Fe alloys. Mech. Mater. 42, 63–71 (2010)

    Article  Google Scholar 

  3. Bennett I.J., Sloof W.G.: Modelling the influence of reactive element on the work of adhesion between a thermally grown oxide and a bond coat alloy. Mater. Corrosion-Werkstoffe und Korrosion 57, 223–229 (2006)

    Article  Google Scholar 

  4. Lin L., Yang Q.S.: Coupled chemical-mechanics theory and numerical method. Chin. J. Solid Mech. 29, 7–12 (2008) (in Chinese)

    Google Scholar 

  5. Yang Q.S., Liu B.S.: Constitutive relation and finite element equation for coupled chemo-mechanics. J. Beijing University Technol. 34, 120–125 (2008) (in Chinese)

    Google Scholar 

  6. Kuang Z.B.: Some variational principles in elastic dielectric and elastic magnetic material. Eur. J. Mech. A/Solids 27, 504–514 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kuang Z.B.: Variational principles for generalized dynamical theory of thermopiezoelectricity. Acta Mech. 203, 1–11 (2009)

    Article  MATH  Google Scholar 

  8. Yang Q.S., Qin Q.H., Ma L.H., Cui C.Q.: A theoretical model and finite element formulation for coupled thermo-electro-mechanical media. Mech. Mater. 42, 148–156 (2010)

    Article  Google Scholar 

  9. Kuang Z.B.: Internal energy variational principle and governing equations in electroelastic analysis. Int. J. Solids Struct. 46, 902–911 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lord H.W., Shulman Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)

    Article  MATH  Google Scholar 

  11. Chandrasekharaiah D.C.: A temperature-rate dependent theory of thermopiezo-elasticity. J. Therm. Stress 7, 293–306 (1984)

    Article  MathSciNet  Google Scholar 

  12. Green A.E., Naghdi P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kuang Z.B.: Variational principles for generalized thermodiffusion theory in pyroelectricity. Acta Mech. 214, 275–289 (2010)

    Article  MATH  Google Scholar 

  14. De Groot S.R.: Thermodynamics of Irreversible Processes. North-Holland, Amsterdam (1963)

    Google Scholar 

  15. Gyarmati I.: Non-equilibrium thermodynamics, Field theory and variational principles. Springer, Berlin, Heidelberg, New York (1970)

    Google Scholar 

  16. Sherief H.H, Hamza F.A., Saleh H.A.: The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci. 42, 591–608 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Lab for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Yaohong Suo & Shengping Shen

  2. School of Science, Xi’an university of Science and Technology, Xi’an, 710054, China

    Yaohong Suo

Authors
  1. Yaohong Suo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengping Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengping Shen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Suo, Y., Shen, S. Dynamical theoretical model and variational principles for coupled temperature–diffusion–mechanics. Acta Mech 223, 29–41 (2012). https://doi.org/10.1007/s00707-011-0545-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-011-0545-4

Keywords

Search

Navigation