 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 79, Issue 6 / 2015 | Next article >> |
| A.G. Kulikovskii and E.I. Sveshinkova, "The formation of an anisotropic elastic medium on the compaction front of a stream of particles," J. Appl. Math. Mech. 79 (6), 521-530 (2015) |
| Year |
2015 |
Volume |
79 |
Issue |
6 |
Pages |
521-530 |
| DOI |
10.1016/j.jappmathmech.2016.04.009 |
| Title |
The formation of an anisotropic elastic medium on the compaction front of a stream of particles |
| Author(s) |
A.G. Kulikovskii (Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia, kulik@mi.ras.ru)
E.I. Sveshinkova (Lomonosov Moscow State University, Moscow, Russia, sveshn@mech.math.msu.ru) |
| Abstract |
A plane transformation front of a stream of non-interacting particles into a continuous medium, which is assumed to be incompressible, elastic, anisotropic and non-linear, is considered. The structure of the compaction front is investigated using the Kelvin-Voigt model of a viscoelastic medium. It is shown that additional boundary conditions, which follow from the requirement for the existence of a discontinuity structure, must be formulated on the compaction front in certain cases along with the boundary conditions which follow from the conservation laws. These additional conditions depend on the equations that are adopted to describe the structure, and their number depends on the relations between the velocity of the front and the velocities of the small perturbations behind the front. It is shown that in the phase space of the shear strains and normal velocity of the front, the set of states behind all the possible compaction fronts (an analogue of the shock adiabat) can consist of manifolds of various dimensions (from one to three). The piston problem, which, as is shown, has a unique solution in the entire permissible region of values of shear and normal stresses assigned on the piston, is investigated. |
| Received |
09 April 2015 |
| Link to Fulltext |
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