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 Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 178–194 (Mi tm3618)

Shock waves in elastoplastic media with the structure defined by the stress relaxation process

A. G. Kulikovskii, A. P. Chugainova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We study nonlinear waves in a Maxwell medium in which residual strains and hardening occur. The properties of the medium are defined so that for slow processes with characteristic times much greater than the stress relaxation time, the medium behaves as an elastoplastic medium. We analyze continuous travelling waves in the form of smoothed steps regarded as discontinuity structures in an elastoplastic medium and demonstrate the dependence of relations at discontinuities on the definition of the stress relaxation process in the discontinuity structure.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This work is supported by the Russian Science Foundation under grant 14-50-00005.

DOI: https://doi.org/10.1134/S0371968515020107

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 167–182

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Document Type: Article

Citation: A. G. Kulikovskii, A. P. Chugainova, “Shock waves in elastoplastic media with the structure defined by the stress relaxation process”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 178–194; Proc. Steklov Inst. Math., 289 (2015), 167–182

Citation in format AMSBIB
\Bibitem{KulChu15} \by A.~G.~Kulikovskii, A.~P.~Chugainova \paper Shock waves in elastoplastic media with the structure defined by the stress relaxation process \inbook Selected issues of mathematics and mechanics \bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov \serial Tr. Mat. Inst. Steklova \yr 2015 \vol 289 \pages 178--194 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3618} \crossref{https://doi.org/10.1134/S0371968515020107} \elib{http://elibrary.ru/item.asp?id=23738468} \transl \jour Proc. Steklov Inst. Math. \yr 2015 \vol 289 \pages 167--182 \crossref{https://doi.org/10.1134/S0081543815040100} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000358577300010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938880544} 

• http://mi.mathnet.ru/eng/tm3618
• https://doi.org/10.1134/S0371968515020107
• http://mi.mathnet.ru/eng/tm/v289/p178

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This publication is cited in the following articles:
1. A. G. Kulikovskii, A. P. Chugainova, “Study of discontinuities in solutions of the Prandtl-Reuss elastoplasticity equations”, Comput. Math. Math. Phys., 56:4 (2016), 637–649
2. A. G. Kulikovskii, A. P. Chugainova, “A self-similar wave problem in a Prandtl–Reuss elastoplastic medium”, Proc. Steklov Inst. Math., 295 (2016), 179–189
3. A. G. Kulikovskii, A. P. Chugainova, “Shock waves in anisotropic cylinders”, Proc. Steklov Inst. Math., 300 (2018), 100–113
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