Abstract:
We consider a self-similar piston problem in which stresses on the boundary of a half-space are changed instantaneously. The half-space is filled with a Prandtl–Reuss medium in a uniform stressed state. It is assumed that the formation of shock waves is possible in the medium. We prove the existence of a solution to the problem in the cases when two or all three stress components are changed at the initial moment.
Citation:
A. G. Kulikovskii, A. P. Chugainova, “A self-similar wave problem in a Prandtl–Reuss elastoplastic medium”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 195–205; Proc. Steklov Inst. Math., 295 (2016), 179–189
\Bibitem{KulChu16}
\by A.~G.~Kulikovskii, A.~P.~Chugainova
\paper A self-similar wave problem in a~Prandtl--Reuss elastoplastic medium
\inbook Modern problems of mechanics
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 295
\pages 195--205
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3758}
\crossref{https://doi.org/10.1134/S0371968516040117}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 295
\pages 179--189
\crossref{https://doi.org/10.1134/S0081543816080113}
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Linking options:
https://www.mathnet.ru/eng/tm3758
https://doi.org/10.1134/S0371968516040117
https://www.mathnet.ru/eng/tm/v295/p195
This publication is cited in the following 5 articles:
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, E. I. Sveshnikova, “Problem of the motion of an elastic medium formed at the solidification front”, Proc. Steklov Inst. Math., 300 (2018), 86–99
V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736
A. G. Kulikovskii, E. I. Sveshnikova, “Formation fronts of a nonlinear elastic medium from a medium without shear stresses”, Moscow University Mechanics Bulletin, 72:3 (2017), 59–65
Citation in format AMSBIB
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