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, Trudy Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 178–194; Proc. Steklov Inst. Math., 289 (2015), 167

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 289, Pages 178–194
DOI: https://doi.org/10.1134/S0371968515020107 (Mi tm3618)

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

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

Full-text PDF (1292 kB) Citations (7)

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

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.

Received: January 15, 2015

English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 289, Pages 167–182
DOI: https://doi.org/10.1134/S0081543815040100

Bibliographic databases:

Document Type: Article

Language: Russian

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, Trudy Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 178–194; Proc. Steklov Inst. Math., 289 (2015), 167–182

Citation in format AMSBIB

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\pages 178--194

\publ MAIK Nauka/Interperiodica

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Linking options:

https://www.mathnet.ru/eng/tm3618

https://doi.org/10.1134/S0371968515020107

https://www.mathnet.ru/eng/tm/v289/p178

This publication is cited in the following 7 articles:

V. M. Sadovskii, “On the Theory of Shock Waves in Isotropic Hardening Plastic Media”, Prikladnaya matematika i mekhanika, 87:2 (2023), 254
V. M. Sadovskii, “On the Theory of Shock Waves in Isotropically Hardening Plastic Media”, Mech. Solids, 58:7 (2023), 2610
Chugainova A.P. Kulikovskii A.G., “Shock Waves in An Incompressible Anisotropic Elastoplastic Medium With Hardening and Their Structures”, Appl. Math. Comput., 401 (2021), 126077
A. G. Kulikovskii, A. P. Chugainova, “Simple One-Dimensional Waves in an Incompressible Anisotropic Elastoplastic Medium with Hardening”, Proc. Steklov Inst. Math., 310 (2020), 175–184
A. G. Kulikovskii, A. P. Chugainova, “Shock waves in anisotropic cylinders”, Proc. Steklov Inst. Math., 300 (2018), 100–113
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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