Abstract:
A Couette flow of a viscoelastic medium is considered that is described by the Johnson–Segalman–Oldroyd model with two relaxation times. The development of singularities related to the appearance of internal discontinuities is studied both analytically and numerically within one-dimensional nonstationary hyperbolic models of viscoelastic Maxwell-type media. A numerical model for calculating nonstationary one-dimensional discontinuous solutions is constructed, discontinuous solutions are studied, and the hysteresis phenomenon, i.e., the dependence of the structure of a steady Couette flow on the prehistory of its formation, is analyzed.
Citation:
V. Yu. Liapidevskii, “Couette flow of a viscoelastic Maxwell-type medium with two relaxation times”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 146–157; Proc. Steklov Inst. Math., 300 (2018), 137–148
\Bibitem{Lya18}
\by V.~Yu.~Liapidevskii
\paper Couette flow of a~viscoelastic Maxwell-type medium with two relaxation times
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 146--157
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968518010119}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2018
\vol 300
\pages 137--148
\crossref{https://doi.org/10.1134/S008154381801011X}
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https://www.mathnet.ru/eng/tm3854
https://doi.org/10.1134/S0371968518010119
https://www.mathnet.ru/eng/tm/v300/p146
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