Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Kovalev V. A., Murashkin E. V., Radayev Y. N. ON WEAK DISCONTINUITIES AND JUMP EQUATIONS ON WAVE SURFACES IN MICROPOLAR THERMOELASTIC CONTINUA. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 1, pp. 79-89. DOI: 10.18500/1816-9791-2015-15-1-79-89, EDN: TMMCMH

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.03.2015
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Russian
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UDC: 
539.3
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TMMCMH

ON WEAK DISCONTINUITIES AND JUMP EQUATIONS ON WAVE SURFACES IN MICROPOLAR THERMOELASTIC CONTINUA

Autors: 
Kovalev Vladimir Aleksandrovich, Moscow City Government University of Management Moscow, Russia
Murashkin Evgenii Valeryevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Radayev Yuri Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
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.

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Received: 
29.10.2014
Accepted: 
24.02.2015
Published: 
31.03.2015