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Izv. Saratov Univ. Math. Mech. Inform., 2015, Volume 15, Issue 1, Pages 79–89 (Mi isu568)  

This article is cited in 3 scientific papers (total in 3 papers)

Mechanics

On weak discontinuities and jump equations on wave surfaces in micropolar thermoelastic continua

V. A. Kovaleva, E. V. Murashkinb, Yu. N. Radayevc

a Moscow City Government University of Management Moscow, 28, Sretenka str., 107045, Moscow, Russia
b National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 31, Kashirskoe shosse, 115409, Moscow, Russia
c Institute for Problems in Mechanics of RAS, 101-1, Vernadskogo ave., 119526, Moscow, Russia

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) continua. Problems of propagation of weak discontinuities in type-I MPTE continua are discussed. Geometrical and kinematical compatibility conditions due to Hadamard and Thomas are used to study possible wave surfaces of weak discontinuities. Weak discontinuities are discriminated according to spatial orientations of the discontinuities polarization vectors (DPVs). It is shown that the surfaces of weak discontinuities can propagate exist without weak discontinuities of the temperature field. Second part of the paper is concerned the 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 obtained $4$-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.

Key words: micropolar thermoelasticity, type-I continuum, type-II continuum, weak discontinuity, strong discontinuity, shock wave, longitudinal wave, transverse wave, compatibility condition, jump.

DOI: https://doi.org/10.18500/1816-9791-2015-15-1-79-89

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UDC: 539.3
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Citation: V. A. Kovalev, E. V. Murashkin, Yu. N. Radayev, “On weak discontinuities and jump equations on wave surfaces in micropolar thermoelastic continua”, Izv. Saratov Univ. Math. Mech. Inform., 15:1 (2015), 79–89

Citation in format AMSBIB
\Bibitem{KovMurRad15}
\by V.~A.~Kovalev, E.~V.~Murashkin, Yu.~N.~Radayev
\paper On weak discontinuities and jump equations on wave surfaces in micropolar thermoelastic continua
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 1
\pages 79--89
\mathnet{http://mi.mathnet.ru/isu568}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-1-79-89}
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\elib{https://elibrary.ru/item.asp?id=23144244}


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    Citing articles on Google Scholar: Russian citations, English citations
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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”, 5Th International Conference on Topical Problems of Continuum Mechanics With a Special Session in Honor of Alexander Manzhirov's 60th Birthday, Journal of Physics Conference Series, 991, IOP Publishing Ltd, 2018, 012061  crossref  isi  scopus
    2. V. A. Kovalev, E. V. Murashkin, Y. N. Radayev, “On deformation of complex continuum immersed in a plane space”, Eighth Polyakhov's Reading, AIP Conf. Proc., 1959, eds. E. Kustova, G. Leonov, N. Morosov, M. Yushkov, M. Mekhonoshina, Amer. Inst. Phys., 2018, 070018  crossref  isi  scopus
    3. E. V. Murashkin, Y. N. Radayev, “Divergent conservation laws in hyperbolic thermoelasticity”, Eighth Polyakhov's Reading, AIP Conf. Proc., 1959, eds. E. Kustova, G. Leonov, N. Morosov, M. Yushkov, M. Mekhonoshina, Amer. Inst. Phys., 2018, 070025  crossref  isi  scopus
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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