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Some theorems on generalized thermoelastic diffusion

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Abstract

The objective of the present work is to establish a convolutional type (Gurtin in Arch. Rat. Mech. Anal. 16:34–50, 1964) variational theorem and a reciprocity theorem for the linear theory of generalized thermoelastic diffusion for homogeneous and isotropic elastic solids.

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References

  1. Nowacki W.: Dynamical problems of thermoelastic diffusion in solids I. Bull. Acad. Pol. Sci. Ser. Sci. Tech. 22, 55–64 (1974)

    MathSciNet  Google Scholar 

  2. Nowacki W.: Dynamical problems of thermoelastic diffusion in solids II. Bull. Acad. Pol. Sci. Ser. Sci. Tech. 22, 129–135 (1974)

    Google Scholar 

  3. Nowacki W.: Dynamical problems of thermoelastic diffusion in solids III. Bull. Acad. Pol. Sci. Ser. Sci. Tech. 22, 257–266 (1974)

    Google Scholar 

  4. Nowacki W.: Dynamical problems of thermoelastic diffusion in elastic solids. Proc. Vib. Prob. 15, 105–128 (1974)

    MATH  MathSciNet  Google Scholar 

  5. Gawinecki J., Kacprzyk P., Bar-Yoseph P.: Initial boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermoelastic diffusion in solid body. J. Anal. Appl. 19, 121–130 (2000)

    MATH  MathSciNet  Google Scholar 

  6. Gawinecki J.A., Szymaniec A.: Global solution of the Cauchy problem in nonlinear thermoelastic diffusion in solid body. PAMM Proc. Appl. Math. Mech. 1, 446–447 (2002)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Dhaliwal R.S., Singh A.: Dynamic Coupled Thermoelasticity. Hindustan Pub. Corp., Delhi (1980)

    Google Scholar 

  9. Parkus H.: Variational Principles in Thermo- and Magneto-Elasticity. Springer-Verlag, Vienna (1972)

    MATH  Google Scholar 

  10. Nowacki W.: Dynamic Problems of Thermoelasticity. PWN-Polish Sci. Pub. Warszawa, Poland (1975)

    Google Scholar 

  11. Carlson, D.E.: Linear thermoelasticity, of Flügge’s Handbuch der Physik, vol. VI a/2 (Edited by C. Truesdell), pp. 297–345. Springer-Verlag, Berlin-Heidelberg-New York (1972)

  12. Gurtin, M.E.: The linear theory of elasticity, of Flügge’s Handbuch der Physik, vol. VI a/2 (Edited by C. Truesdell), pp. 1–295. Springer-Verlag, Berlin-Heidelberg-New York (1972)

  13. Lebon G.: Variational Principles in Thermomechanics. Springer, Wien (1980)

    Google Scholar 

  14. Ignaczak J.: A completeness problem for stress equations of motion in the linear elasticity theory. Arch. Mech. Stosow. 15, 225–235 (1963)

    MATH  MathSciNet  Google Scholar 

  15. Gurtin M.E.: Variational principles for linear elastodynamics. Arch. Rat. Mech. Anal. 16, 34–50 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  16. Gurtin M.E.: Variational principles for linear initial-value problems. Q. Appl. Math. 22, 252 (1964)

    MATH  Google Scholar 

  17. Biot M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240–253 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  18. Biot M.A.: New thermoelastical reciprocity relations with application to thermal stresses. J. Aeronaut Space Sci. 7, 26 (1959)

    Google Scholar 

  19. Hermann G.: On variational principles in thermoelasticity and heat conduction. Q. Appl. Math. 21, 151 (1963)

    Google Scholar 

  20. Ben-Amoz M.: On variational theorem in coupled thermoelasticity. J. Appl. Mech. 32, 943–945 (1965)

    Google Scholar 

  21. Iesan D.: Principes variationnels dans la theorie de la thermoelasticite couplee, Ann, Sci. Univ. “Al. I. Cuza” Iasi. Mathematica 12, 439–456 (1966)

    MATH  Google Scholar 

  22. Nickell R.E., Sackman J.L.: Variational principles for linear coupled thermoelasticity. Q. Appl. Math. 26, 11–26 (1968)

    MATH  MathSciNet  Google Scholar 

  23. Weiner J.: A uniqueness theorem for the coupled thermoelastic problem. Q. Appl. Math. 15, 102–105 (1957)

    MATH  MathSciNet  Google Scholar 

  24. Iesan D.: On thermodynamics of non-simple elastic material with two temperatures. J. Appl. Math. Phys (ZAMP) 21, 583–591 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  25. Ignaczak J.: Uniqueness in generalized thermoelasticity. J. Therm. Stress. 2, 171–179 (1979)

    Article  Google Scholar 

  26. Sherief H.H., Dhaliwal R.S.: A uniqueness theorem and variational principle for generalized thermoelasticity. J. Therm. Stress. 3, 223–230 (1980)

    Article  Google Scholar 

  27. Chandrasekharaiah D.S., Srikantaiah K.R.: Some theorem in temperature- rate-dependent theory of thermoelasticity. Proc. Indian Acad. Sci. (Math. Sci.) 92, 135–141 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  28. Wang J.R., Dhaliwal S., Majumdar S.R.: Some theorems in the generalized theory of thermoelasticity for pre-stressed bodies. Indian J. Pure Appl. Math. 28, 267–275 (1997)

    MATH  MathSciNet  Google Scholar 

  29. Chandrasekharaiah D.S.: Variational and reciprocal principles in thermoelasticity without energy dissipation. Proc. Indian Acad. Sci. (Math. Sci.) 108, 209–215 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  30. Kumar R., Prasad R., Mukhopadhyay S.: Variational and reciprocal principles in two-temperature generalized thermoelasticity. J. Therm. Stress. 33, 161–171 (2010)

    Article  Google Scholar 

  31. Aouadi M.: Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion. J. Therm. Stress. 30, 665–678 (2007)

    Article  MathSciNet  Google Scholar 

  32. Aouadi M.: Generalized theory of thermoelastic diffusion for anisotropic media. J. Therm. Stress. 31, 1–16 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, 221005, Varanasi, India

    Roushan Kumar, Shweta Kothari & Santwana Mukhopadhyay

  2. Birla Institute of Technology, Mesra, Deoghar Campus, Jasidih, 714142, India

    Roushan Kumar

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  1. Roushan Kumar
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  2. Shweta Kothari
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  3. Santwana Mukhopadhyay
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Correspondence to Santwana Mukhopadhyay.

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Kumar, R., Kothari, S. & Mukhopadhyay, S. Some theorems on generalized thermoelastic diffusion. Acta Mech 217, 287–296 (2011). https://doi.org/10.1007/s00707-010-0401-y

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  • DOI: https://doi.org/10.1007/s00707-010-0401-y

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