Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Editorial staff
Guidelines for authors
License agreement
Editorial policy

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2014, Issue 1(34), Pages 66–85
DOI: https://doi.org/10.14498/vsgtu1310
(Mi vsgtu1310)
 

This article is cited in 7 scientific papers (total in 8 papers)

Mechanics of Solids

On Nonlinear Strain Vectors and Tensors in Continuum Theories of Mechanics

V. A. Kovaleva, Yu. N. Radayevb

a Moscow City Government University of Management Moscow, Moscow, 107045, Russian Federation
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russian Federation
Full-text PDF (683 kB) Citations (8)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of $4$-covariant field theoretical formalism. Fine microstructure is represented by $d$-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. $4$-covariant field equations of hyperbolic thermoelasticity are obtained. Constitutive equations of microstructural hyperbolic thermoelasticity are discussed. Virtual microstructural inertia is added to the considered action density. It is also concerned to the thermal inertia. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws in a plane space–time. For micropolar type-II thermoelastic Lagrangians following the usual procedure independent rotationally invariant functional arguments are obtained. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extra strain vectors and tensors.
Keywords: thermoelasticity, microstructure, field, extra field, action, covariance, conservation law, $d$-tensor, $4$-current, energy–momentum tensor, kinematic constraint, Lagrange multiplier, rotation, frame indifference principle, extrastrain tensor.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00139
This work is partially supported by RFBR, project no. 13–01–00139 “Hyperbolic Thermal Waves in Solid Bodies with Microstructure”.
Original article submitted 19/I/2014
revision submitted – 21/II/2014
Bibliographic databases:
Document Type: Article
UDC: 539.3
MSC: 74A60, 74F05
Language: Russian
Citation: V. A. Kovalev, Yu. N. Radayev, “On Nonlinear Strain Vectors and Tensors in Continuum Theories of Mechanics”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 66–85
Citation in format AMSBIB
\Bibitem{KovRad14}
\by V.~A.~Kovalev, Yu.~N.~Radayev
\paper On Nonlinear Strain Vectors and Tensors in Continuum Theories of Mechanics
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 1(34)
\pages 66--85
\mathnet{http://mi.mathnet.ru/vsgtu1310}
\crossref{https://doi.org/10.14498/vsgtu1310}
\zmath{https://zbmath.org/?q=an:06968826}
\elib{https://elibrary.ru/item.asp?id=22813961}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu1310
  • https://www.mathnet.ru/eng/vsgtu/v134/p66
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
    Statistics & downloads:
    Abstract page:732
    Full-text PDF :245
    References:94
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024