Skip to main content
SpringerLink
Log in

Reciprocal and variational principles in micropolar thermoelasticity of type II

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In the present paper, in the context of thermoelasticity of type II (or thermoelasticity without energy dissipation), we establish reciprocal and variational principles of convolutional type for inhomogeneous and anisotropic micropolar thermoelastic materials with a center of symmetry. The results obtained in this work tend to generalize other variational principles (previously proved by the authors) not completely characterizing the initial-boundary value problem in concern.

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. Eringen A.: Linear theory of micropolar elasticity. J. Math. Mech. 15, 909–923 (1966)

    MATH  MathSciNet  Google Scholar 

  2. Eringen A.: Theory of micropolar elasticity in fracture, vol. 2. Academic Press, New York (1968)

    Google Scholar 

  3. Eringen A.: Foundation of Micropolar Thermoelasticity, Courses and Lectures No 23. CISM, Udine, Springer, Vienna and New York (1970)

    Google Scholar 

  4. Eringen A., Kafadar C.: Polar field theories. In: Eringen, A.C. (eds) Continuum Physics IV, Academic Press, New York (1976)

    Google Scholar 

  5. Chandrasekharaiah D.: Heat-flux dependent micropolar thermoelasticity. Int. J. Eng. Sci. 24, 1389–1395 (1986)

    Article  MATH  Google Scholar 

  6. Ciarletta M.: Sui processi termoelastici per continui micropolari. Atti Sem. Mat. Fis. Univ. Modena 39, 103 (1991)

    MATH  MathSciNet  Google Scholar 

  7. Ciarletta, M., Ieşan, D.: Nonclassical elastic solids, vol. 293 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow (1993)

  8. Passarella F.: Some results in micropolar thermoelasticity. Mech. Res. Commun. 23, 349–357 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Caviglia G., Morro A., Straughan B.: Thermoelasticity at cryogenic temperatures. Int. J. Non-Linear Mech. 27, 251–263 (1992)

    Article  MathSciNet  Google Scholar 

  10. Quintanilla R., Racke R.: A note on stability in dual-phase-lag heat conduction. Int. J. Heat Mass Transf. 49, 1209–1213 (2006)

    Article  MATH  Google Scholar 

  11. Vadasz P.: Lack of oscillations in dual-phase-lagging heat conduction for a porous slab subject to imposed heat flux and temperature. Int. J. Heat Mass Transf. 48, 2822–2828 (2005)

    Article  MATH  Google Scholar 

  12. Vadasz J.J., Govender S., Vadasz P.: Heat transfer enhancement in nano-fluids suspensions: Possible mechanisms and explanations. Int. J. Heat Mass Transfer 48, 2673–2683 (2005)

    Article  Google Scholar 

  13. Green A.E., Naghdi P.M.: A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. London A 432, 171–194 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Green A.E., Naghdi P.M.: On thermodynamics and the nature of the second law. Proc. R. Soc. London A 357, 253–270 (1977)

    Article  MathSciNet  Google Scholar 

  15. Green, A.E., Naghdi, P.M.: On undamped heat waves in an elastic solid. J. Thermal Stresses 15, pp. 253–264, Sixty-fifth birthday of Bruno A. Boley Symposium, Part 2 (Atlanta, GA) (1992)

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Green A.E., Naghdi P.M.: A unified procedure for construction of theories of deformable media. i. classical continuum physics. Proc. R. Soc. London A 448, 335–356 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. Green A.E., Naghdi P.M.: A unified procedure for construction of theories of deformable media. ii. generalized continua. Proc. R. Soc. London A 448, 357–377 (1995)

    Article  MathSciNet  Google Scholar 

  19. Green A.E., Naghdi P.M.: A unified procedure for construction of theories of deformable media. iii. mixtures of interacting continua. Proc. R. Soc. London A 448, 379–388 (1995)

    Article  MathSciNet  Google Scholar 

  20. Green A.E., Naghdi P.M.: A new thermoviscous theory for fluids. J. Non-Newton. Fluid Mech. 56, 289–306 (1995)

    Article  Google Scholar 

  21. Green A.E., Naghdi P.M.: An extended theory for incompressible viscous fluid flow. J. Non-Newton. Fluid 66, 233–255 (1996)

    Article  Google Scholar 

  22. Ciarletta M.: A theory of micropolar thermoelasticity without energy dissipation. J. Thermal Stresses 22, 581–594 (1999)

    Article  MathSciNet  Google Scholar 

  23. Passarella F., Zampoli V.: On the theory of micropolar thermoelasticity without energy dissipation. J. Thermal Stresses 33, 305–317 (2010). doi:10.1080/01495731003656907

    Article  Google Scholar 

  24. Carlson D.E.: Linear thermoelasticity, S. In: Flügge, S. (eds) Encyclopedia of Physics VIa/2, Mechanics of Solids II, pp. 297–436. Springer, Berlin (1972)

    Google Scholar 

  25. Chirita S., Ciarletta M.: Reciprocal and variational principles in linear thermoelasticity without energy dissipation. Mech. Res. Commun. 37, 271–275 (2010). doi:10.1016/j.mechrescom.2010.03.001

    Article  Google Scholar 

  26. Gurtin M.E.: Linear theory of elasticity. In: Flügge, S. (eds) Encyclopedia of Physics VIa/2, Mechanics of Solids II, pp. 1–295. Springer, Berlin (1972)

    Google Scholar 

  27. Lebon G.: Variational principles in thermomechanics. In: Lebon, G., Perzyna, P. (eds) Recent developments in thermo-mechanics of solids, Springer, Wien-NewYork (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione e Matematica Applicata, Università di Salerno, 84084, Fisciano, SA, Italy

    Francesca Passarella & Vittorio Zampoli

Authors
  1. Francesca Passarella
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vittorio Zampoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vittorio Zampoli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Passarella, F., Zampoli, V. Reciprocal and variational principles in micropolar thermoelasticity of type II. Acta Mech 216, 29–36 (2011). https://doi.org/10.1007/s00707-010-0351-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-010-0351-4

Keywords

Search

Navigation