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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2017, Volume 58, Issue 5, Pages 178–189
DOI: https://doi.org/10.15372/PMTF20170518 (Mi pmtf671) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Dynamics of deformation of an elastic medium with initial stresses

E. I. Romenskiiab, E. V. Lysc, V. A. Tcheverdac, M. I. Èpovc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
c Trofimuk Institute of Oil and Gas Geology and Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Full-text PDF (246 kB) Citations (9)
DOI: https://doi.org/10.15372/PMTF20170518
Abstract: The constitutive equations of motion of an elastic medium with given initial stresses are formulated in the form of a hyperbolic system of differential equations of the first order. Equations describing the propagation of small perturbations in a prestressed isotropic medium with an arbitrary energy dependence of the elastic deformation in the strain tensor are derived, and equations for the quadratic dependence of elastic strain energy on the strain tensor are given.
Keywords: motion of an elastic medium, initial stresses, elastic waves.
Funding agency Grant number
Russian Foundation for Basic Research 15-05-01310
Russian Academy of Sciences - Federal Agency for Scientific Organizations 121
Received: 24.04.2017
English version:
Journal of Applied Mechanics and Technical Physics, 2017, Volume 58, Issue 5, Pages 914–923
DOI: https://doi.org/10.1134/S0021894417050182
Bibliographic databases:
Document Type: Article
UDC: 539.3: 517.958
Language: Russian
Citation: E. I. Romenskii, E. V. Lys, V. A. Tcheverda, M. I. Èpov, “Dynamics of deformation of an elastic medium with initial stresses”, Prikl. Mekh. Tekh. Fiz., 58:5 (2017), 178–189; J. Appl. Mech. Tech. Phys., 58:5 (2017), 914–923
Citation in format AMSBIB
\Bibitem{RomLysTch17}
\by E.~I.~Romenskii, E.~V.~Lys, V.~A.~Tcheverda, M.~I.~\`Epov
\paper Dynamics of deformation of an elastic medium with initial stresses
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2017
\vol 58
\issue 5
\pages 178--189
\mathnet{http://mi.mathnet.ru/pmtf671}
\crossref{https://doi.org/10.15372/PMTF20170518}
\elib{https://elibrary.ru/item.asp?id=30295645}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2017
\vol 58
\issue 5
\pages 914--923
\crossref{https://doi.org/10.1134/S0021894417050182}
Linking options:
  • https://www.mathnet.ru/eng/pmtf671
  • https://www.mathnet.ru/eng/pmtf/v58/i5/p178
    • This publication is cited in the following 9 articles:
    1. A. A. Markin, M. Yu. Sokolova, “Dynamic Equations for the Propagation of Acoustic Waves in Pre-Deformed Materials”, Mech. Solids, 59:2 (2024), 679  crossref
    2. A. A. Markin, M. Yu. Sokolova, “Dynamic equations of acoustic wave propagation in pre-deformed materials”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, no. 2, 166  crossref
    3. Anastasiia Yu. Kutishcheva, Mikhail I. Epov, 2024 IEEE 3rd International Conference on Problems of Informatics, Electronics and Radio Engineering (PIERE), 2024, 980  crossref
    4. Markus Hütter, Michal Pavelka, “Particle-based approach to the Eulerian distortion field and its dynamics”, Continuum Mech. Thermodyn., 35:5 (2023), 1943  crossref
    5. Vladislav Balashov, Evgeny Savenkov, “A regularized phase field model for solid–fluid dynamics description”, Continuum Mech. Thermodyn., 35:2 (2023), 625  crossref
    6. Remya Ampadi Ramachandran, Christine Lee, Lu Zhang, Supriya M. H, Divya Bijukumar, P. Srinivasa Pai, Kharma Foucher, Sheng-Wei Chi, Didem Ozevin, Mathew T. Mathew, “Total hip replacement monitoring: numerical models for the acoustic emission technique”, Med Biol Eng Comput, 60:5 (2022), 1497  crossref
    7. V. A. Balashov, E. B. Savenkov, “A regularized phase field model for «solid–fluid» system accounting for chemical reactions”, Keldysh Institute preprints, 2021, 82–20  mathnet  mathnet  crossref
    8. Vladislav Balashov, “A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations”, Russian Journal of Numerical Analysis and Mathematical Modelling, 36:4 (2021), 197  crossref
    9. Maurizio Tavelli, Michael Dumbser, Dominic Etienne Charrier, Leonhard Rannabauer, Tobias Weinzierl, Michael Bader, “A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography”, Journal of Computational Physics, 386 (2019), 158  crossref
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