 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 42, Issue 5 / 2007 | Next article >> |
| E. L. Aero and A. N. Bulygin, "Strongly nonlinear theory of nanostructure formation owing to elastic and nonelastic strains in crystalline solids," Mech. Solids. 42 (5), 807-822 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
5 |
Pages |
807-822 |
| Title |
Strongly nonlinear theory of nanostructure formation owing to elastic and nonelastic strains in crystalline solids |
| Author(s) |
E. L. Aero (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr-t 61, St. Petersburg, 199178, Russia, aero@microm.ipme.ru)
A. N. Bulygin (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr-t 61, St. Petersburg, 199178, Russia) |
| Abstract |
We develop an essentially nonlinear theory of elastic and nonelastic microstrains resulting in the formation of nanostructures. Using the model of mutually penetrating lattices, we generalize the well-known theory of acoustic and optical vibrations to the case of nonlinear interaction between sublattices. This permits treating the sublattice interaction forces as periodic (for example, sinusoidal) functions of the relative displacement of the sublattices. We obtain equations for the macroscopic and microscopic displacement fields containing two characteristic scales of the nanostructure. We find a number of their solutions describing the effects of decrease in the potential interatomic barriers in the external stress field and the formation of defects and domain nanostructure as a result of bifurcation transitions. We prove their stability. |
| References |
| 1. | M. Born and Huang Kun, Dynamic Theory of Crystal Lattices
(Inostr. Lit., Moscow, 1958) [in Russian]. |
| 2. | A. M. Kosevich,
Crystal Lattice Theory
(Vishcha Shkola, Khar'kov, 1988)
[in Russian]. |
| 3. | I. A. Kunin,
Theory of Elastic Media with Microstructure
(Nauka, Moscow, 1975)
[in Russian]. |
| 4. | E. L. Aero, "Strongly Nonlinear Theory of Elastic and Nonelastic
Strains in Crystal Bodies," in Mathematical Modeling of
Systems and Processes (Izd-vo Perm Tekhn. Univ., Perm, 2006),
pp. 27-55 [in Russian]. |
| 5. | E. L. Aero,
"Micromechanics of a Double Continuum in a Model of a Medium
with Variable Periodic Structure,"
J. Eng. Math.
1, 1-15 (2005). |
| 6. | V. S. Boiko, R. I. Garber, and A. M. Kosevich,
Reversible Plasticity in Crystals
(Nauka, Moscow, 1991)
[in Russian]. |
| 7. | P. Hirth and J. Lothe,
Theory of Dislocations
(McGraw-Hill, New York, 1968; Atomizdat, Moscow, 1972). |
|
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