 | | 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 46, Issue 1 / 2011 | Next article >> |
| R.R. Mulyukov and A.I. Pshenichnyuk, "Deformation of Nanocrystalline Materials in the Formalism of Coupled Mode Theory," Mech. Solids. 46 (1), 123-128 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
1 |
Pages |
123-128 |
| DOI |
10.3103/S0025654411010183 |
| Title |
Deformation of Nanocrystalline Materials in the Formalism of Coupled Mode Theory |
| Author(s) |
R.R. Mulyukov (Institute for Metals Superplasticity Problems, Russian Academy of Sciences, St. Khalturina 39, Ufa, 450001 Russia, radic@anrb.ru)
A.I. Pshenichnyuk (Institute for Metals Superplasticity Problems, Russian Academy of Sciences, St. Khalturina 39, Ufa, 450001 Russia, apish@anrb.ru) |
| Abstract |
In the present paper, we suggest to use the coupled mode theory (CMT) to describe the strain behavior of nanomaterials. Our approach is based on the analogy between nanocrystalline and granulated materials, on the similarity in the behavior of granulated materials, concentrated suspensions, and amorphous materials, and on the efficiency of CMT in the description of glass and suspension rheology. We use the successive approximation method for solving the nonlinear integro-differential equation of the CMT and show that already the first approximation describes the main qualitative properties of numerical solutions quite well. The Laplace transform is written out for the second approximation, which permits integrating the correlator over time and writing out the rheological relation implicitly. |
| Keywords |
nanocrystalline materials, granulated materials, suspensions, glasses, deformation mechanisms, shear bands, rheology |
| References |
| 1. | H. A. Padilla II and B. L. Boyce,
"A Review of Fatigue Behavior in Nanocrystalline Metals,"
Experim. Mech.
50 (1), 5-23 (2010). |
| 2. | A. P. Zhilyaev and A. I. Pshenichnyuk,
Superplasticity and Grain Boundaries
in Ultrafine-Grained Materials
(Fizmatlit, Moscow, 2008; Cambridge Int. Sci. Publ., Cambridge, 2010). |
| 3. | M. Yu. Gutkin, I. A. Ovid'ko, and C. S. Pande,
"Theoretical Models of Plastic Deformation Processes
in Nanocrystalline Materials,"
Rev. Adv. Mater. Sci.
2, 80-102 (2001). |
| 4. | N. I. Noskova and R. R. Mulyukov,
Submicrocrystalline and Nanocrystalline Metals and Alloys
(UrO RAN, Ekaterinburg, 2003)
[in Russian]. |
| 5. | S. E. Aleksandrov and R. V. Goldshtein,
"A Model of a Medium with Allowance for the Formation of Rigid Blocks
with Deformable Interlayers under the Action of Loading,"
Dokl. Ross. Akad. Nauk
368 (6), 768-770 (1999)
[Dokl. Phys. (Engl. Transl.)
44 (10), 712-714 (1999)]. |
| 6. | A. J. Liu and S. R. Nagel,
"Nonlinear Dynamics: Jamming is not Cool Anymore,"
Nature
396, 21-22 (1998). |
| 7. | P. Olsson and S. Teitel,
"Critical Scaling of Shear Viscosity at the Jamming Transition,"
Phys. Rev. Lett.
99, 178001 (2007). |
| 8. | M. Otsuki and H. Hayakawa,
"Universally Scaling in the Jamming Transition,"
URL: http://lanl.arxiv. org/list/cond-mat/0809.0171
(application date: 05.10.2008). |
| 9. | S. Fazekas, J. Torok, and J. Kertesz,
"Critical Packing in Granular Shear Bands,"
Phys. Rev. E
75, 011302 (2007). |
| 10. | J. Torok, T. Unger, J. Kertesz, and D. E. Wolf,
"Shear Zones in Granular Materials: Optimization in a Self-Organized Random Potential,"
Phys. Rev. E
75, 011305 (2007). |
| 11. | F. Cruz, F. Chevoir, D. Bonn, and P. Coussot,
"Viscosity Bifurcation in Granular Materials, Foams, and Emulsion,"
Phys. Rev. E
66, 051305 (2002). |
| 12. | M. van Hecke,
"Jamming of Soft Particles: Geometry, Mechanics, Scaling, and Isostaticity,"
URL: http://lanl.arxiv.org/list/cond-mat/0911.1384
(application date: 16.11.2009). |
| 13. | P. D. Olmsted,
"Perspectives on Shear Banding in Complex Fluids,"
Rheol. Acta
47 (3), 283-300 (2008). |
| 14. | G. Varlez, S. Rodts, X. Chateau, and P. Coussot,
"Phenomenology and Physical Origin of Shear Localization
and Shear Banding in Complex Fluids,"
Rheol. Acta
48 (8), 831-844 (2009). |
| 15. | M. D. Dimetriou, W. L. Johnson, and K. Samver,
"Coarse-Grained Description of Localized Inelastic Deformation in Amorphous Metals,"
Appl. Phys. Lett.
94, 1919095 (2009). |
| 16. | M. L. Falk and J. S. Langer,
"Dynamics of Viscoplastic Deformation in Amorphous Solids,"
Phys. Rev. E
57 (6), 7192-7205 (1998). |
| 17. | W. Gotze,
"Aspects of Structural Glass Transitions,"
in Liquids, Freezing, and the Glass Transition,
Ed. by J. P. Hansen et al.
(North-Holland, Amsterdam, 1989),
pp. 287-503. |
| 18. | W. Gotze,
"The Essentials for the Mode-Coupling Theory for Glassy Dynamics,"
Condens. Matter Phys.
1 (4), 873-904 (1998). |
| 19. | C. B. Holmes, M. E. Cates, M. Fuchs, and P. Sollich,
"Glass Transitions and Shear Thickening Suspension Rheology,"
URL: http://lanl.arxiv.org/list/cond-mat/0406422
(application date: 8.12.2009). |
| 20. | I. Gazuz, A. M. Puertas, Th. Voigtmann, and M. Fuchs,
"Active and Nonlinear Microrheology in Dense Colloidal Syspensions,"
Phys. Rev. Lett.
102, 248302 (2009). |
| 21. | J. Wang, H. L. Duan, Z. P. Huang, and B. L. Karihaloo,
"A Scaling Law for Properties of Nano-Structures Materials,"
Proc. Roy. Soc. London. Ser. A
462 (2069), 1355-1363 (2006). |
|
| Received |
22 January 2010 |
| Link to Fulltext |
|
| << Previous article | Volume 46, Issue 1 / 2011 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English