Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 95–108
Problem of the motion of an elastic medium formed at the solidification front
A. G. Kulikovskiia, E. I. Sveshnikovab
a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
The following self-similar problem is considered. At the initial instant of time, a phase transformation front starts moving at constant velocity from a certain plane (which will be called a wall or a piston, depending on whether it is assumed to be fixed or movable); at this front, an elastic medium is formed as a result of solidification from a medium without tangential stresses. On the wall, boundary conditions are defined for the components of velocity, stress, or strain. Behind the solidification front, plane nonlinear elastic waves can propagate in the medium formed, provided that the velocities of these waves are less than the velocity of the front. The medium formed is assumed to be incompressible, weakly nonlinear, and with low anisotropy. Under these assumptions, the solution of the self-similar problem is described qualitatively for arbitrary parameters appearing in the statement of the problem. The study is based on the authors' previous investigation of solidification fronts whose structure is described by the Kelvin–Voigt model of a viscoelastic medium.
|Russian Foundation for Basic Research
|This work was supported by the Russian Foundation for Basic Research, project nos. 17-01-00180 and 15-01-00361.
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Proceedings of the Steklov Institute of Mathematics, 2018, 300, 86–99
Received: October 16, 2017
A. G. Kulikovskii, E. I. Sveshnikova, “Problem of the motion of an elastic medium formed at the solidification front”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Tr. Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 95–108; Proc. Steklov Inst. Math., 300 (2018), 86–99
Citation in format AMSBIB
\by A.~G.~Kulikovskii, E.~I.~Sveshnikova
\paper Problem of the motion of an elastic medium formed at the solidification front
\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 Tr. Mat. Inst. Steklova
\publ MAIK Nauka/Interperiodica
\jour Proc. Steklov Inst. Math.
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