 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| E.L. Aero, A.N. Bulygin, and Yu.V. Pavlov, "Nonlinear Model of Deformation of Crystalline Media Allowing for Martensitic Transformations: Plane Deformation," Mech. Solids. 54 (5), 797-806 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
5 |
Pages |
797-806 |
| DOI |
10.3103/S0025654419050029 |
| Title |
Nonlinear Model of Deformation of Crystalline Media Allowing for Martensitic Transformations: Plane Deformation |
| Author(s) |
E.L. Aero (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178 Russia)
A.N. Bulygin (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178 Russia, bulygin_an@mail.ru)
Yu.V. Pavlov (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178 Russia) |
| Abstract |
This article is devoted to development of mathematical solutions of statics equations of
plane nonlinear deformation of crystalline media with a complex lattice allowing for martensitic transformations. Statics equations comprised of a set of four coupled nonlinear equations are reduced to a
set of separate equations. The macrodisplacement vector is sought in the Papkovich–Neuber form.
The microdisplacement vector is determined by the sine–Gordon equation with a variable coefficient
(amplitude) before the sine and Poisson’s equation. For the case of constant amplitude the class of
doubly periodic solutions has been determined which are expressed via elliptical Jacobian functions.
It has been demonstrated that nonlinear theory leads to a combination of solutions describing fragmentation of the crystalline medium, occurrence of structural imperfections of various types, phase
transformations, and other peculiarities of deformation which occur under the action of intensive
loads and are not described by classical continuum mechanics. |
| Keywords |
crystalline media, the sine–Gordon equation, intensive loads |
| Received |
12 May 2017 | Revised |
13 October 2017 | Accepted |
27 December 2017 |
| Link to Fulltext |
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