Materials Science

, Volume 43, Issue 3, pp 331–342 | Cite as

Thermoviscoelastic model of a layer between two bodies and conditions of their conjugation

  • I. S. Skorodyns’kyi


On the basis of the Kelvin-Voigt-type thermomechanical theory of viscoelasticity, by the method of averaging over the thickness, we develop a thermoviscoelastic model of thin intermediate layer and establish generalized Winkler-type thermomechanical conjugation conditions for solid bodies in the dynamical mode for the case of imperfect thermal contact. It is shown that these conditions can be regarded as a generalization of the classical model. Relations convenient for practical applications are deduced. Various classical conditions of thermomechanical contact and their generalizations are obtained as a result of the limiting transition performed under additional assumptions concerning the moduli of elasticity of the intermediate layer.


Intermediate Layer Conjugation Condition Contact Thermal Conductivity Glue Joint Initial Temperature Condition 
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  1. 1.
    V. M. Aleksandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers [in Russian], Nauka, Moscow (1983).Google Scholar
  2. 2.
    R. M. Martynyak and R. M. Shvets’, “Conditions of thermal contact of the bodies through thin interlayers inhomogeneous across the thickness,” Dop. Nats. Akad. Nauk Ukr., No. 9, 74–76 (1996).Google Scholar
  3. 3.
    R. M. Martynyak and R. M. Shvets’, “Mathematical model of the mechanical contact of bodies through a thin inhomogeneous interlayer,” Mat. Met. Fiz.-Mekh. Polya, 40, No. 2, 107–109 (1997).Google Scholar
  4. 4.
    B. L. Pelekh, A. V. Maksimuk, and I. M. Korovaichuk, Contact Problems for Layered Structural Elements and Bodies with Coatings [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  5. 5.
    Ya. S. Pidstryhach, “Conditions of jumps of stresses and displacements on a thin-walled elastic inclusion in the continuous medium,” Dop. Akad. Nauk Ukr. RSR. Ser. A, No. 12, 29–31 (1982).Google Scholar
  6. 6.
    Ya. S. Pidstryhach, “Temperature field in a system of solid bodies conjugated through a thin intermediate layer,” Inzh.-Fiz. Zh., 6, No. 10, 129–136 (1963).Google Scholar
  7. 7.
    Ya. S. Pidstryhach and Yu. M. Kolyano, Generalized Thermomechanics [in Russian], Naukova Dumka, Kiev (1976).Google Scholar
  8. 8.
    Ya. S. Pidstryhach, Yu. M. Kolyano, and M. M. Semerak, Temperature Fields and Stresses in Elements of Electrovacuum Devices [in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  9. 9.
    V. S. Sarkisyan and A. V. Keropyan, “On the solution of two contact problems for elastic bodies with two finite stringers of different types,” Mat. Met. Fiz.-Mekh. Polya, 46, No. 2, 114–121 (2003).Google Scholar
  10. 10.
    G. T. Sulim and I. Z. Piskozub, “Conditions of contact interaction of the bodies (a survey),” Mat. Met. Fiz.-Mekh. Polya, 47, No. 3, 110–125 (2004).Google Scholar
  11. 11.
    A. S. Freidin and R. A. Turusov, Properties and Numerical Analysis of Adhesive Joints [in Russian], Khimiya, Moscow (1990).Google Scholar
  12. 12.
    R. M. Shvets’ and R. M. Martynyak, “Integral equations of the contact problem of thermoelasticity for rough bodies,” Dop. Akad. Nauk Ukr. RSR. Ser. A, No. 11, 37–40 (1985).Google Scholar
  13. 13.
    I. G. Goryacheva, A. P. Goryachev, and F. Sadegi, “Contact of elastic bodies with thin viscoelastic coatings under the conditions of rolling or sliding friction,” Prikl. Mat. Mekh., 59, No. 4, 634–641 (1995).Google Scholar
  14. 14.
    I. G. Goryacheva, “Investigations of A. Yu. Ishlinskii in the field of rolling friction and their development,” Prikl. Mat. Mekh., 67, No. 4, 646–662 (2003).Google Scholar
  15. 15.
    I. N. Vekua, Some General Methods for the Construction of Various Versions of the Theory of Shells [in Russian], Nauka, Moscow (1982).Google Scholar
  16. 16.
    N. Petrov and G. Brankov, Contemporary Problems of Thermodynamics [in Bulgarian], Bulgarian Acad. Sci., Sofia (1982).Google Scholar
  17. 17.
    A. M. Freudental and H. Geiringer, The Mathematical Theories of Inelastic Continuum, Springer, Berlin (1958).Google Scholar
  18. 18.
    V. G. Karnaukhov and B. P. Gumenyuk, Thermomechanics of Prestrained Viscoelastic Bodies [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
  19. 19.
    Ya. S. Pidstryhach and Yu. Z. Povstenko, Introduction to the Mechanics of Surface Phenomena in Deformed Solids [in Russian], Naukova Dumka, Kiev (1985).Google Scholar

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© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • I. S. Skorodyns’kyi
    • 1
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian Academy of SciencesLviv

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