Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2010-4pp.529-545

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 >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100