CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES |
Prev
Next
|
|
|
A model of crack based on dislocations in smectic A liquid crystals |
Fan Tian-You (范天佑), Tang Zhi-Yi (唐志毅) |
School of Physics, Beijing Institute of Technology, Beijing 100081, China |
|
|
Abstract A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to construct the solution of the crack in the phase. From the solution, we can determine the size of the plastic zone at the crack tip and the crack tip opening (tearing) displacement, which are the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics.
|
Received: 05 March 2014
Revised: 17 April 2014
Accepted manuscript online:
|
PACS:
|
61.30.-v
|
(Liquid crystals)
|
|
61.30.Dk
|
(Continuum models and theories of liquid crystal structure)
|
|
61.30.Jf
|
(Defects in liquid crystals)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11272055). |
Corresponding Authors:
Tang Zhi-Yi
E-mail: 7491903@qq.com
|
About author: 61.30.-v; 61.30.Dk; 61.30.Jf |
Cite this article:
Fan Tian-You (范天佑), Tang Zhi-Yi (唐志毅) A model of crack based on dislocations in smectic A liquid crystals 2014 Chin. Phys. B 23 106103
|
|
| [12] | Li S D, Liu M, Lou J, Xing X, Su Z J, Zhou Z Y, X F, Duh J G and Sun N X 2011 IEEE Trans. Magn. 47 10
|
|
| [1] | de Gennes P G and Prost J 1993 The Physics of Liquid Crystals (London: Clarendon) pp. 490, 493, 499
|
|
| [13] | Li S D, Wang L L, Xu J, Wang Z, Liu M, Lou J, Beguhn S, Nan T X, Xu F, Sun N X and Duh J G 2012 IEEE Trans. Magn. 48 4313
|
|
| [2] | Kleman M and Oswald P 1982 J. Physique 43 655
|
|
| [3] | Oswald P and Pieranski P 2006 Smectic and Columnar Liquid Crystals (London: Taylor & Francis) p. 123
|
|
| [4] | Landau L D and Lifshitz E M 1986 Theory of Elasticity, 3rd edn. (Oxford: Pergamon) pp. 177, 181
|
|
| [5] | Fujii S, Komura S, Ishii Y and Lu C Y D 2011 J. Phys.: Condens Matter 23 235105
|
|
| [6] | Brostow W, Cunha A M, Quintanila J and Simoes R 2002 Macromol. Theory Simul. 11 308
|
|
| [7] | Samulski E T 1985 Faraday Discuss. Chem. Soc. 79 7
|
|
| [8] | Brostow W 1990 Polymer 31 979
|
|
| [9] | Hess M 2000 High Performance Polymers in Performance of Plastics (Munich-Cincinnati: Hanser), ed. Brostow W, Chap. 21, p. 519
|
|
| [10] | Fan T Y 2012 Phil. Mag. Lett. 92 153
|
|
| [14] | Iljinas A, Dudonis J, Bručas R and Meškauskas A 2005 Nonlinear Anal. Model. Control 10 57
|
|
| [15] | Klemmer T J, Ellis K A, Chen L H, van Dover B and Jin S 2000 J. Appl, Phys. 87 830
|
|
| [11] | de Gennes P G and Kleman M 1974 Liquid Crystals and Plastic Crystals 1 92
|
|
| [12] | Fan T Y 2014 "Displacement Potentials and Elliptic Disk-shaped Crack in Three-dimensional Smectic B Liquid Crystals", submitted
|
|
| [16] | Alben R, Becker J J and Chi M C 1978 J. Appl. Phys. 49 1653
|
|
| [13] | Bilby B A, Cottrell A H and Swinden K H 1963 Proc. R. Soc. A 272 304
|
|
| [17] | Herzer G 1989 IEEE. Trans. Magn. 25 3327
|
|
| [14] | Bilby B A, Cottrell A H, Smith E and Swinden K H 1964 Proc. R. Soc. A 279 1
|
|
| [18] | Senda M, Ishii O and Koshimoto Y 1994 IEEE. Trans. Magn. 30 4611
|
|
| [19] | Zhong W D 1992 Ferromagnetics (Part Ⅱ) (Beijing: Science Press) p. 43
|
|
| [15] | Fan T Y, Trebin H R, Messerschmidt U and Mai Y W 2004 J. Phys.: Condens. Matter 16 5229
|
|
| [16] | Fan T Y 2010 Mathematical Theory of Elasticity of Quasicrystals and Its Applications (Heidelberg: Springer-Verlag) p. 307
|
|
| [17] | Kleman M 1974 J. Physique 35 595
|
|
| [18] | Pershan P S 1974 J. Appl. Phys 45 1590
|
|
| [19] | Fan T Y and Li X F 2014 Chin. Phys. B 23 046102
|
|
| [20] | Muskhelishvili N I 1956 Singular Integral Equations (Gnoningen: Noordhoff) p. 251
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|