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.
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
\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 Trudy 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{https://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}
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https://www.mathnet.ru/eng/tm3618
https://doi.org/10.1134/S0371968515020107
https://www.mathnet.ru/eng/tm/v289/p178
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