Acta Mechanica

, Volume 229, Issue 10, pp 4267–4277 | Cite as

On stability in the thermoelastostatics of dipolar bodies

  • Marin Marin
  • Andreas ÖchsnerEmail author
  • Dumitru Baleanu
Original Paper


Our study is concerned with the initial boundary value problem in the context of the thermoelastostatics of dipolar bodies. We will derive a result which describes the exponential spatial decay of solutions of this problem. We will also find a superior limit for the amplitude, which is dependent on the initial and boundary conditions.


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  1. 1.
    Choudhuri, S.K.R.: On a thermoelastic three-phase-lag model. J. Thermal Stresses 30(3), 231–238 (2007)CrossRefGoogle Scholar
  2. 2.
    Eringen, A.C.: Theory of thermo-microstretch elastic solids. Int. J. Eng. Sci. 28, 1291–1301 (1990)CrossRefGoogle Scholar
  3. 3.
    Eringen, A.C.: Microcontinuum Field Theories. Springer, New York (1999)CrossRefGoogle Scholar
  4. 4.
    Iesan, D., Ciarletta, M.: Non-Classical Elastic Solids, Longman Scientific and Technical, Harlow, Essex. Wiley, New York (1993)Google Scholar
  5. 5.
    Marin, M., Agarwal, R.P., Mahmoud, S.R.: Modeling a microstretch thermo-elastic body with two temperatures. Abstr. Appl. Anal. 2013, 1–7 (2013). Art. ID 583464CrossRefGoogle Scholar
  6. 6.
    Marin, M.: Weak solutions in elasticity of dipolar porous materials. Math. Probl. Eng. 2008, 1–8 (2008). Art. No. 158908MathSciNetCrossRefGoogle Scholar
  7. 7.
    Marin, M., Baleanu, D.: On vibrations in thermoelasticity without energy dissipation for micropolar bodies. Bound. Value Probl. 111, 1–19 (2016)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Marin, M.: An approach of a heat-flux dependent theory for micropolar porous media. Meccanica 51(5), 1127–1133 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Straughan, B.: Heat waves. In: Straughan, B. (ed.) Applied Mathematical Sciences, vol. 177, Springer, New York (2011)Google Scholar
  10. 10.
    Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Green, A.E., Rivlin, R.S.: Multipolar continuum mechanics. Arch. Ration. Mech. Anal. 17, 113–147 (1964)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Fried, E., Gurtin, M.E.: Thermomechanics of the interface between a body and its environment. Contin. Mech. Thermodyn. 19(5), 253–271 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Altenbach, H.: Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen Gleichungen. Springer, Berlin (2018)CrossRefGoogle Scholar
  14. 14.
    Horgan, C.O.: Recent developments concerning Saint–Venants principle: an update. Appl. Mech. Rev. 42, 295–303 (1989)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Horgan, C.O.: Recent developments concerning Saint–Venants principle: a second update. Appl. Mech. Rev. 49, 101–111 (1996)CrossRefGoogle Scholar
  16. 16.
    Bofill, F., Quintanilla, R.: Thermal influence on the decay of end effects in linear elasticity. Supplemento di Rendiconti del Circolo Matematico di Palermo 57, 57–62 (1998)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Quintanilla, R.: End effects in thermoelasticity. Math. Methods Appl. Sci. 24, 93–102 (2001)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Quintanilla, R., Straughan, B.: Growth and uniqueness in thermoelasticity. Proc. R. Soc. Lond. A 456, 1419–1429 (2000)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Ames, K.A., Payne, L.E.: Continuous dependence on initial-time geometry for a thermoelastic system with sign-indefinite elasticities. J. Math. Anal. Appl. 189, 693–714 (1995)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Ames, K.A., Straughan, B.: Continuous dependence results for initially prestressed thermoelastic bodies. Int. J. Eng. Sci. 30, 7–13 (1992)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Ames, K.A., Straughan, B.: Non-Standard and Improperly Posed Problems. Academic Press, San Diego (1997)Google Scholar
  22. 22.
    Wilkes, N.S.: Continuous dependence and instability in linear thermoelasticity. SIAM J. Math. Anal. 11, 292–299 (1980)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Fichera, G.: Linear Elliptic Differential System and Eigenvalue Problems, Lectures Notes in Mathematics. Springer (1965)Google Scholar
  24. 24.
    Marin, M., Öchsner, A.: Essentials of Partial Differential Equations. Springer, Cham (2018)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany
  3. 3.Department of MathematicsCankaya UniversityAnkaraTurkey
  4. 4.Institute of Space SciencesMagurele, BucharestRomania

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