Journal of Applied Mathematics and Mechanics (about journal) 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)

Russian  English English About Journal | Issues | Editorial Board | Contact Us
 


 Web hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2011-4pp.378-389

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 75, Issue 4 / 2011 | Next article >>
A.G. Kulikovskii, "Multi-parameter fronts of strong discontinuities in continuum mechanics," J. Appl. Math. Mech. 75 (4), 378-389 (2011)
Year 2011 Volume 75 Issue 4 Pages 378-389
Title Multi-parameter fronts of strong discontinuities in continuum mechanics
Author(s) A.G. Kulikovskii (Moscow, Russia, kulik@mi.ras.ru)
Abstract The strong discontinuities in solutions of hyperbolic systems of equations of continuum mechanics are considered. It is assumed that there is a flow of mass through the discontinuity front. If the number of boundary conditions that must be satisfied at a discontinuity (which follow from conservation laws or from other laws and assumptions) is less than the number of unknowns in the system of equations describing the state and motion of the medium behind the discontinuity, then as the discontinuity propagates along a specified fixed state of the medium, the set of possible states behind the discontinuity (shock adiabat) can depend on more than one parameter (multi-parameter discontinuities). The number of parameters on which a possible state behind a discontinuity depends can be reduced by introducing additional boundary conditions, which appear as conditions that ensure the existence of a solution for the discontinuity structure problem. These additional boundary conditions are specified by small-scale processes that occur within the structure, and terms corresponding to these processes must be introduced into the hyperbolic equations to describe them. Two examples of systems of equations related to the mechanics of deformable solids when multi-parameter discontinuities appear are considered, their structure is studied, and problems in which such discontinuities appear are considered. One of these examples is the description of a version of a phase transformation in the form of the formation of a non-linear elastic Kelvin-Voigt medium when a stream of non-interacting particles is compacted. In the other example the very simple case of the formation of a multi-parameter discontinuity as a consequence of the appearance of residual strains in a discontinuity is described.
Received 6 December 2010
Link to Fulltext http://www.sciencedirect.com/science/journal/00218928
<< Previous article | Volume 75, Issue 4 / 2011 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 245, 119526 Moscow, Russia (+7 495) 434-2149 pmm@ipmnet.ru pmmedit@ipmnet.ru http://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Journals on Mechanics Ltd.
© Journals on Mechanics Ltd.
Webmaster: Alexander Levitin
Rambler's Top100