 | | 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 |
|
| << Previous article | Volume 47, Issue 5 / 2012 | Next article >> |
| P.E. Tovstik and T.P. Tovstik, "Static and Dynamic Analysis of Two-Dimensional Graphite Lattices," Mech. Solids. 47 (5), 517-524 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
5 |
Pages |
517-524 |
| DOI |
10.3103/S0025654412050044 |
| Title |
Static and Dynamic Analysis of Two-Dimensional Graphite Lattices |
| Author(s) |
P.E. Tovstik (St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, peter.tovstik@mail.ru)
T.P. Tovstik (St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia) |
| Abstract |
Plane problems of statics and dynamics of graphite lattice are considered in the linear approximation. Comparative analysis of two models of interatomic interaction is carried out. One of these models is based on pairwise moment interaction, and the other is the Brenner model where the variation in the angles between the segments connecting the atom under study with three nearest neighbors is additionally taken into account. The lattice tensile and shear rigidity in two directions is studied by straightforward calculations. The propagation of harmonic tensile and shear waves it two directions is considered. In problems of both statics and wave propagation, the results are compared with similar results for the equivalent continuum. It turned out that in the problems of statics, the Brenner model (after averaging) leads to an isotropic momentless continuum, while the model with pair interaction lead to the moment Cosserat continuum. In problems of wave propagation, both of these models give the same qualitative results. The velocities of acoustic parallel extension-compression wave propagation in a lattice are close to the wave velocity in the continuum but do not coincide with it. The difference increases with decreasing wave length and depends on the wave propagation direction. In the case of shear wave propagation in a lattice, the velocity of acoustic shear wave propagation in the pair moment potential model significantly (in the leading terms) depends on the direction of its propagation. The optical short waves are discovered and some of their properties are described. |
| Keywords |
graphite lattice, pair interaction, Brenner model, constitutive relations, longitudinal and shear waves, acoustic and optical modes |
| References |
| 1. | M. Born and H. Kun,
Dynamical Theory of Crystal Lattices
(Claderon Press, Oxford, 1954; Izd-vo Inostr. Liter., Moscow, 1958). |
| 2. | A. M. Kosevich,
Foundations of Mechanics of Crystal Lattice
(Nauka, Moscow, 1972)
[in Russian]. |
| 3. | N. F. Morozov and M. V. Paukshto,
Discrete and Hybrid Models of Fracture Mechanics
(Izd-vo SPbGU, St. Petersburg, 1995)
[in Russian]. |
| 4. | A. M. Krivtsov,
Deformation and Failure of Solids with Microstructure
(Fizmatlit, Moscow, 2007)
[in Russian]. |
| 5. | A. P. Byzov and E. A. Ivanova,
"Mathematical Simulation of Moment Interactions of Particles with Rotational
Degrees of Freedom,"
Nauchno-Tekhn. Vedomosti SPbGPU,
No. 2, 260-278 (2007). |
| 6. | I. E. Berinskii, E. A. Ivanova, A. M. Krivtsov, and N. F. Morozov,
"Application of Moment Interaction to the
Construction of a Stable Model of Graphite Crystal Lattice,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 6-16 (2007)
[Mech. Solids (Engl. Transl.)
42 (5), 663-671 (2007)]. |
| 7. | D. W. Brenner,
"Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of
Diamond Films,"
Phys. Rev. B
42 (15), 9458-9471 (1990). |
| 8. | E. A. Ivanova, A. M. Krivtsov, N. F. Morozov, and A. D. Firsova,
"Inclusion of the Moment Interaction in the Calculation of the Flexural Rigidity of Nanostructures,"
Dokl. Ross. Akad. Nauk
391 (6), 764-768 (2003)
[okl. Phys. (Engl. Transl.)
48 (8), 455-458 (2003)]. |
| 9. | E. A. Ivanova, A. M. Krivtsov, and N. F. Morozov,
"Derivation of Macroscopic Relations of the Elasticity of Complex Crystal
Lattices Taking into Account the Moment Interactions at the Microlevel,"
Prikl. Mat. Mekh.
71 (4), 595-615 (2007)
[J. Appl. Math. Mech. (Engl. Transl.)
71 (4), 543-561 (2007)]. |
| 10. | P. E. Tovstik and T. P. Tovstik,
"A Model of Two-Dimensional Graphite Layer,"
Vestnik S.-Peterburg. Univ.
Ser. I, No. 3, 134-142 (2009). |
| 11. | V. A. Kuz'kin and A. M. Krivtsov,
"Description for Mechanical Properties of Graphene Using Particles with
Rotational Degrees of Freedom,"
Dokl. Ross. Akad. Nauk
440 (4), 476-479 (2011)
[Dokl. Phys. (Engl. Transl.)
56 (10), 527-530 (2011)]. |
| 12. | D. W. Brenner, O. A. Shenderova, J. A. Harrison, et al.,
"A Second-Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression
for Hydrocarbons,"
J. Phys. Condens. Matter.
14 (4), 783-802 (2002). |
| 13. | B. D. Annin, S. N. Korobeinikov, and A. V. Babichev,
"Computer Simulation of a Twisted Nanotube Buckling,"
Sib. Zh. Industr. Mat.
11 (1), 3-22 (2008)
[J. Appl. Industr. Math. (Engl. Transl.)
3 (3), 318-333 (2009)]. |
| 14. | N. F. Morozov,
Mathematical Problems of Crack Theory
(Nauka, Moscow, 1984)
[in Russian]. |
| 15. | N. F. Morozov,
Lectures in Selected Problems of Continuum Mechanics
(Izd-vo LGU, Leningrad, 1975)
[in Russian]. |
| 16. | I. E. Berinskii, N. G. Dvas, A. M. Krivtsov, et al.
Theoretical Mechanics. Elastic Properties of One-Atomic and Two-Atomic Crystals,
Ed. by A. M. Krivtsov
(Izd-vo Politekh. Univ., St. Petersburg, 2009)
[in Russian]. |
|
| Received |
21 June 2012 |
| Link to Fulltext |
|
| << Previous article | Volume 47, Issue 5 / 2012 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English