 | | 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 |
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| 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 |
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|
| Received |
21 June 2012 |
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