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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2015, Volume 19, Number 1, Pages 186–202
DOI: https://doi.org/10.14498/vsgtu1412
(Mi vsgtu1412)
 

This article is cited in 1 scientific paper (total in 2 paper)

Mechanics of Solids

Hyperbolic theories and problems of continuum mechanics

Yu. N. Radaeva, V. A. Kovalevb

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526, Russian Federation
b Moscow City Government University of Management Moscow, Moscow, 107045, Russian Federation
Full-text PDF (810 kB) Citations (2)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: Theories and problems of that part of continuum thermomechanics which can not be properly formulated without partial differential equations of hyperbolic analytical type are considered. Special attention is paid to comparatively new hyperbolic continuum theories: the theory of three-dimensional perfect plasticity and the theory of micropolar thermoelasticity. The latter is accepted as type-II thermoelasticity. Three-dimensional statical and kinematical equations of the perfect plasticity theory by Ishlinskii and Ivlev are studied in order to elucidate their analytical type and opportunity to obtain integrable equations along some special lines. A new approach to hyperbolic formulations of thermoelasticity presumes consideration of referential gradients of thermodynamic state variables and extra field variables (rapid variables) as independent functional arguments in the action density. New hyperbolic thermomechanics of micropolar thermoelastic media is developed within the framework of classical field theory by the variational action integral and the least action principle.
Keywords: continuum, hyperbolicity, perfect plasticity, thermoelasticity, action, least action principle.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00139-а
Ministry of Education and Science of the Russian Federation 16.2518.2014/(K)
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 15/I/2015
revision submitted – 25/II/2015
Bibliographic databases:
Document Type: Article
UDC: 539.3
MSC: 74A60, 74F05
Language: Russian
Citation: Yu. N. Radaev, V. A. Kovalev, “Hyperbolic theories and problems of continuum mechanics”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:1 (2015), 186–202
Citation in format AMSBIB
\Bibitem{RadKov15}
\by Yu.~N.~Radaev, V.~A.~Kovalev
\paper Hyperbolic theories and problems of continuum mechanics
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 1
\pages 186--202
\mathnet{http://mi.mathnet.ru/vsgtu1412}
\crossref{https://doi.org/10.14498/vsgtu1412}
\zmath{https://zbmath.org/?q=an:06968955}
\elib{https://elibrary.ru/item.asp?id=23681749}
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  • https://www.mathnet.ru/eng/vsgtu/v219/i1/p186
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    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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