| | 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: | | 12854 |
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
In English (Mech. Solids): | | 4810 |
|
<< Previous article | Volume 45, Issue 4 / 2010 | Next article >> |
R.V. Goldstein, V.A. Gorodtsov, and D.S. Lisovenko, "Auxetic Mechanics of Crystalline Materials," Mech. Solids. 45 (4), 529-545 (2010) |
Year |
2010 |
Volume |
45 |
Number |
4 |
Pages |
529-545 |
DOI |
10.3103/S0025654410040047 |
Title |
Auxetic Mechanics of Crystalline Materials |
Author(s) |
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru)
V.A. Gorodtsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, gorod@ipmnet.ru)
D.S. Lisovenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, lisovenk@ipmnet.ru) |
Abstract |
In the present paper, we analyze uniaxial deformation of crystals of different systems with negative Poisson's ratios, known as auxetics. The behavior of auxetic crystals is studied on the basis of extensive knowledge on the experimental values of elastic constants of different crystals, gathered in the well-known Landolt-Börnstein tables. The competition between the anisotropy of crystal structures and the orientation of deformable samples results in the dependence of the elastic characteristics of deformation, such as Young's modulus and Poisson's ratio, on the orientation angles. In the special case of a single angle, a large number of auxetics were found among crystals of cubic, hexagonal, rhombohedral, tetragonal, and orthorhombic systems and the character of variations in their response due to changes in orientation was determined. |
References |
1. | L. D. Landau and E. M. Lifshitz,
Course of Theoretical Physics, Vol. 7, Theory of Elasticity
(Nauka, Moscow, 1967, 1987; Pergamon Press, Oxford, 1970). |
2. | A. E. H. Love,
A Treatise on the Mathematical Theory of Elasticity, 4th ed.
(Cambridge Univ. Press, Cambridge, 1927; ONTI, Moscow, 1935). |
3. | M. Ya. Popereka and V. G. Balagurov,
"Ferromagnetic Films Having a Negative Poisson's Ratio,"
Fiz. Tverd. Tela
11 (12), 3507-3513 (1969)
[Sov. Phys. Solid State (Engl. Transl.)
11 (12), 2938-2943 (1970)]. |
4. | T. Akasaka,
Elastic Composites. Textile Structural Composites
(Elsevier, Amsterdam, Oxford, New York, Tokyo, 1989; Mir, Moscow, 1991). |
5. | R. S. Lakes,
"Foam Structures with a Negative Poisson's Ratio,"
Science
235 (4792), 1038-1040 (1987). |
6. | K. E. Evans, M. A. Nkansah, I. J. Hutchinson, and S. C. Rogers,
"Molecular Network Design,"
Nature
353 (6340), 124-125 (1991). |
7. | K. E. Evans,
"Auxetic Polymers: A new Range of Materials,"
Endeavour. New Series
15 (4), 170-174 (1991). |
8. | "Workshop on Auxetics and Related Systems. Bedlewo (Poland), 2004,"
Phys. Stat. Sol (b)
242 (3), 487-763 (2005). |
9. | "2nd Workshop on Auxetics and Related Systems. Bedlewo (Poland), 2005,"
Phys. Stat. Sol (b)
244 (3), 807-1124 (2007). |
10. | "First Intern. Conference on Auxetics and Anomalous Systems. Exeter (UK), 2006,"
Phys. Stat. Sol (b)
245 (3), 486-613 (2008). |
11. | "4th Intern. Workshop on Auxetics and Related Systems. Malta, September 24-26, 2007,"
Phys. Stat. Sol (b)
245 (11), 2369-2532 (2008). |
12. | "2nd Intern. Conference and 5th Intern. Workshop on Auxetics and Related Systems.
Bristol (UK), September 14-17, 2008,"
Phys. Stat. Sol (b)
246 (9), 2007-2130 (2009). |
13. | T. C. T. Ting and T. Chen,
"Poisson's Ratio for Anisotropic Elastic Materilas Can Have no Bounds,"
Quart. J. Mech. Appl. Math.
58 (1), 73-82 (2005). |
14. | Yu. I. Sirotin and M. P. Shaskol'skaya,
Foundations of Crystal Physics
(Nauka, Moscow, 1975)
[in Russian]. |
15. | J. F. Nye,
Physical Properties of Crystals: Their Representation by Tensor and Matrices
(Oxford Univ. Press, Oxford, 1957; Mir, Moscow, 1967). |
16. | Landolt-Börnstein - Group III: Crystal and Solid State Physics, Vol. 29a:
Second and Higher Order Constants
(Springer, Berlin, 1992). |
17. | U. Buchenau, M. Heiroth, H. R. Schober, et al.,
"Lattice Dynamics of Strontium and Barium,"
Phys. Rev. B
30 (6), 3502-3505 (1984). |
18. | J. Mizuki, Y. Chen, K.-M. Ho, and C. Stassis,
"Phonon Dispersion Curves of bcc Ba,"
Phys. Rev. B
32 (2), 666-670 (1985). |
19. | V. A. Gorodtsov and D. S. Lisovenko,
"To Mechanics of Carbon and Other Layered Nanowhiskers,"
Inzh. Fiz.,
No. 4, 36-38 (2009). |
20. | R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko,
"About Negativity of the Poisson's Ratio for Anisotropic Materials,"
Dokl. Ross. Akad. Nauk
429 (5), 614-616 (2009)
[Dokl. Phys. (Engl. Transl.)
54 (12), 546-548 (2009)]. |
|
Received |
17 March 2010 |
Link to Fulltext |
|
<< Previous article | Volume 45, Issue 4 / 2010 | Next article >> |
|
If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|