This article is cited in 3 scientific papers (total in 3 papers)
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,
c Institute for Problems in Mechanics of RAS, 101-1, Vernadskogo ave., 119526, Moscow, Russia
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.
micropolar thermoelasticity, type-I continuum, type-II continuum, weak discontinuity, strong discontinuity, shock wave, longitudinal wave, transverse wave, compatibility condition, jump.
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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
\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.
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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
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
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
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