Elliptic hole in octagonal quasicrystals

doi:10.1088/1674-1056/22/1/016102

Abstract The stress potential function theory for plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method (Lekhnitskii method) for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.

Keywords: quasicrystals plane elasticity elliptic hole stress potential

Received: 17 March 2012
Revised: 07 June 2012
Accepted manuscript online:

PACS:	61.44.Br	(Quasicrystals)
	62.20.D-	(Elasticity)
	02.30.Em	(Potential theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11026175, 11262017, and 10761005), the Key Project of Ministry of Education of China (Grant No. 212029), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2009MS0102 and 2009BS0104), and the Natural Science Foundation of Inner Mongolia Department of Public Education, China (Grant Nos. NJzy08024 and NJ10047).

Corresponding Authors: Li Lian-He
E-mail: nmglilianhe@163.com

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Li Lian-He (李联和) Elliptic hole in octagonal quasicrystals 2013 Chin. Phys. B 22 016102

[1]	Shechtman D, Blech I, Gratias D and Cahn J W 1984 Phys. Rev. Lett. 53 1951
[2]	Bindi L, Steinhardt Paul J, Yao N and Lu Peter J 2009 Science 324 1306
[3]	Bak P 1985 Phys. Rev. B 32 5764
[4]	Hu C Z, Wang R H and Ding D H 2000 Rep. Prog. Phys. 63 1
[5]	Fan T Y, Xie L Y, Fan L and Wang Q Z 2011 Chin. Phys. B 20 076102
[6]	Hu C Z, Wang R H, Yang W G and Ding D H 1996 Acta Cryst. A 52 251
[7]	Fan T Y 2010 Mathematical Theory of Elasticity of Quasicrystals and Application (New York: Springer)
[8]	Li W 2011 Chin. Phys. B 20 116201
[9]	Wang J B, Mancini L, Wang R H and Gastaldi J 2003 J. Phys.: Condens. Matter 15 L363
[10]	Li X F and Fan T Y 2002 Chin. Phys. 11 266
[11]	Li L H 2010 Chin. Phys. B 19 046101
[12]	Gao Y, Zhao Y T and Zhao B S 2007 Physica B 394 56
[13]	Gao Y, Ricoeur A and Zhang L L 2011 Phys. Lett. A 375 2775
[14]	Zhou W M and Fan T Y 2001 Chin. Phys. 10 743
[15]	Lekhnitskii S G 1963 Theory of Elasticity of an Anisotropic Body (Moscow: MIR)

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