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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 4(37), Pages 85–97 (Mi vsgtu1331)  

This article is cited in 4 scientific papers (total in 4 papers)

Mechanics of Solids

On Strong and Weak Discontinuities of the Coupled Thermomechanical Field in Micropolar Thermoelastic Type-II Continua

E. V. Murashkin, Yu. N. Radayev*

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526, Russian Federation

Abstract: The present study is devoted to problem of propagating surfaces of weak and strong discontinuities of translational displacements, microrotations and temperature in micropolar (MP) thermoelastic (TE) type-II continua. First part of the paper is concerned to discussions of the propagating surfaces of strong discontinuities of field variables in type-II MPTE continua. Constitutive relations for hyperbolic thermoelastic type-II micropolar continuum is derived by the field theory. The special form of the first variation of the action integral is used in order to obtain $4$-covariant jump conditions on wave surfaces. Three-dimensional form of the jump conditions on the surface of a strong discontinuity of thermoelastic field are derived from $4$-covariant form. Problems of propagation of weak discontinuities in type-II MPTE continua are discussed too. Geometrical and kinematical compatibility conditions due to Hadamard and Thomas are used to study possible wave surfaces of weak discontinuities. It is shown that the surfaces of weak discontinuities can propagate exist without weak discontinuities of the temperature field.

Keywords: micropolar thermoelasticity, type-II continuum, weak discontinuity, strong discontinuity, shock wave, longitudinal wave, transverse wave, compatibility condition, jump

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00139
Ministry of Education and Science of the Russian Federation 16.2518.2014
This work has been partially supported by the Russian Foundation for Basic Research (project no. 13–01–00139-a "Hyperbolic Thermal Waves in Solid Bodies with Microstructure") and by the Russian Ministry of Education and Science within the design basis portion of the state task to Samara State Technical University (project no. 16.2518.2014/(K)).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1331

Full text: PDF file (733 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 536.2:539.3
MSC: 74A15, 74F05, 74B99, 80A20
Original article submitted 03/X/2014
revision submitted – 10/XI/2014

Citation: E. V. Murashkin, Yu. N. Radayev, “On Strong and Weak Discontinuities of the Coupled Thermomechanical Field in Micropolar Thermoelastic Type-II Continua”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(37) (2014), 85–97

Citation in format AMSBIB
\Bibitem{MurRad14}
\by E.~V.~Murashkin, Yu.~N.~Radayev
\paper On Strong and Weak Discontinuities of the Coupled Thermomechanical Field in Micropolar Thermoelastic Type-II Continua
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 4(37)
\pages 85--97
\mathnet{http://mi.mathnet.ru/vsgtu1331}
\crossref{https://doi.org/10.14498/vsgtu1331}
\zmath{https://zbmath.org/?q=an:06968935}
\elib{https://elibrary.ru/item.asp?id=23464554}


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    This publication is cited in the following articles:
    1. E. V. Murashkin, Y. N. Radayev, “Full thermomechanical coupling in modelling of micropolar thermoelasticity”, Journal of Physics: Conference Series, 991 (2018), 012061  crossref  isi  scopus
    2. V. A. Kovalev, E. V. Murashkin, Y. N. Radayev, “Wave propagation problem for a micropolar elastic waveguide”, Journal of Physics: Conference Series, 991 (2018), 012047  crossref  isi  scopus
    3. V. A. Kovalev, E. V. Murashkin, Y. N. Radayev, “On deformation of complex continuum immersed in a plane space”, AIP Conference Proceedings, 1959 (2018), 070018  crossref  isi  scopus
    4. E. V. Murashkin, Y. N. Radayev, “Divergent conservation laws in hyperbolic thermoelasticity”, AIP Conference Proceedings, 1959 (2018), 070025  crossref  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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