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.
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)).
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
\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 9 articles:
E. V. Murashkin, Yu. N. Radaev, “Volnovye chisla garmonicheskikh ploskikh voln translyatsionnykh i spinornykh peremeschenii v poluizotropnoi termouprugoi srede”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 28:3 (2024), 445–461
E. V. Murashkin, Yu. N. Radayev, “Coupled Harmonic Plane Waves in a Semi-Isotropic Thermoelastic Medium”, Mech. Solids, 59:4 (2024), 2387
E. V. Murashkin, Yu. N. Radayev, “Plane Thermoelastic Waves in Ultrahemitropic Micropolar Solid”, Mech. Solids, 59:5 (2024), 3212
E. V. Murashkin, Yu. N. Radayev, “Wavenumbers of Doublet and Triplet Plane Thermoelastic Wave in Ultraisotropic Micropolar Medium”, Mech. Solids, 59:6 (2024), 3681
E. V. Murashkin, Y. N. Radayev, “Polarization Vectors of Plane Waves in Semi-Isotropic Thermoelastic Micropolar Solids”, Mech. Solids, 59:7 (2024), 3880
E. V. Murashkin, Y. N. Radayev, “Full thermomechanical coupling in modelling of micropolar thermoelasticity”, Journal of Physics: Conference Series, 991 (2018), 012061
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
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
E. V. Murashkin, Y. N. Radayev, “Divergent conservation laws in hyperbolic thermoelasticity”, AIP Conference Proceedings, 1959 (2018), 070025
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