Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(11): 116101    DOI: 10.1088/1674-1056/22/11/116101
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole

Li Lian-He (李联和)
College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China; Key Laboratory of Nanomagnetic and Functional Material, College of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China
Abstract  The generalized 2D problem of icosahedral quasicrystals containing an elliptic hole is considered by using the extended Stroh formalism. The closed-form solutions for the displacements and stresses are obtained under general loading conditions. The solution of the Griffith crack problem as a special case of the results is also observed. The stress intensity factor and strain energy release rate are given. The effect of the phonon–phason coupling elastic constant on the mechanical behavior is also discussed.
Keywords:  icosahedral quasicrystal      plane elasticity      Stroh formulism      elliptic hole  
Received:  15 November 2012      Revised:  17 April 2013      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. 11072104, 1272053, and 11262017), the Key Project of Chinese Ministry of Education (Grant No. 212029), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2013MS0114), the Natural Science Foundation of Inner Mongolia Department of Public Education, China (Grant No. NJZZ13037), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region, China (Grant No. NJYT-13-B07), and the Program of Higher-level Talents of Inner Mongolia University, China (Grant No. 125125).
Corresponding Authors:  Li Lian-He     E-mail:  nmglilianhe@163.com

Cite this article: 

Li Lian-He (李联和) Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole 2013 Chin. Phys. B 22 116101

[1] Shechtman D, Blech I, Gratias D and Cahn J W 1984 Phys. Rev. Lett. 53 1951
[2] Bak P 1985 Phys. Rev. Lett. 54 1517
[3] Hu C Z, Wang R H and Ding D H 2000 Rep. Prog. Phys. 63 1
[4] Fu H, Liao L G and Fu X J 2009 Chin. Phys. Lett. 26 056103
[5] Wen Z B, Hou Z L and Fu X J 2011 Chin. Phys. Lett. 28 046102
[6] Li L H and Fan T Y 2006 J. Phys.: Condens. Matter 18 10631
[7] Radi E and Mariano P M 2010 Int. J. Fract. 166 105
[8] Liu G T, He Q L and Guo R P 2009 Acta Phys. Sin. 58 118 (in Chinese)
[9] Li X F and Fan T Y 1998 Chin. Phys. Lett. 15 278
[10] Fan T Y and Mai Y W 2004 Appl. Mech. Rev. 57 325
[11] Wang J B, Mancini L, Wang R H and Gastaldi J 2003 J. Phys.: Condens. Matter 15 L363
[12] Fan T Y 2011 Mathematical Theory of Elasticity of Quasicrystals and Its Applications (Berlin: Springer) pp. 120–128
[13] Gao Y 2012 Pramana-J. Phys. 79 311
[14] Gao Y, Ricoeur A and Zhang L 2011 Phys. Lett. A 375 2775
[15] Li L H and Liu G T 2012 Phys. Lett. A 3769 987
[16] Wang X and Schiavone P 2013 Math. Mech. Complex Syst. 1 1
[17] Levine D, Lubensky T C, Ostlund S, Ramaswamy S, Steinhardt P J and Toner J 1985 Phys. Rev. Lett. 54 1520
[18] Gao Y, Zhao B S and Xu S P 2008 J. Elast. 93 263
[19] Ting T C T 1996 Anisotropic Elasticity: Theory and Applications (New York: Oxford Science Publications)
[20] Muskhelishvili N I 1963 Some Basic Problems of the Mathematical Theory of Elasticity (Noordhoff: Groningen)
[21] Edagawa K and Takeuchi S 2007 Dislocation in Solids 13 365
[22] Mikulla R, Gumbsch P and Trebin H R 1998 Phil. Mag. Lett. 78 369
[1] Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow
Li Lian-He (李联和), Liu Guan-Ting (刘官厅). Chin. Phys. B, 2014, 23(5): 056101.
[2] Finite size specimens with cracks of icosahedral Al–Pd–Mn quasicrystals
Yang Lian-Zhi (杨连枝), Ricoeur Andreas, He Fan-Min (何蕃民), Gao Yang (高阳). Chin. Phys. B, 2014, 23(5): 056102.
[3] Elastic fields around a nanosized elliptichole in decagonal quasicrystals
Li Lian-He (李联和), Yun Guo-Hong (云国宏). Chin. Phys. B, 2014, 23(10): 106104.
[4] Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole
Zeng Xin (曾鑫), Fang Qi-Hong (方棋洪), Liu You-Wen (刘又文), P. H. Wen. Chin. Phys. B, 2013, 22(1): 014601.
[5] Elliptic hole in octagonal quasicrystals
Li Lian-He (李联和). Chin. Phys. B, 2013, 22(1): 016102.
[6] Interface of quasicrystal and crystal
Fan Tian-You(范天佑), Xie Ling-Yun(解凌云), Fan Lei(范蕾), and Wang Qing-Zhao(王清昭). Chin. Phys. B, 2011, 20(7): 076102.
[7] Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading
Li Lian-He(李联和). Chin. Phys. B, 2010, 19(4): 046101.
[8] Dynamic behaviour of the icosahedral Al--Pd--Mn quasicrystal with a Griffith crack
Wang Xiao-Fang(王晓芳), Fan Tian-You(范天佑), and Zhu Ai-Yu(祝爱玉). Chin. Phys. B, 2009, 18(2): 709-714.
[9] Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal
Guo Jun-Hong(郭俊宏) and Liu Guan-Ting(刘官厅). Chin. Phys. B, 2008, 17(7): 2610-2620.
[10] Elastic analysis of a mode II crack in an icosahedral quasicrystal
Zhu Ai-Yu(祝爱玉) and Fan Tian-You(范天佑). Chin. Phys. B, 2007, 16(4): 1111-1118.
[11] PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM
Zhou Wang-min (周旺民), Fan Tian-you (范天佑). Chin. Phys. B, 2001, 10(8): 743-747.
[12] PERTURBATION METHOD SOLVING ELASTIC PROBLEMS OF ICOSAHEDRAL QUASICRYSTALS CONTAINING A CIRCULAR CRACK
Peng Yan-ze (彭彦泽), Fan Tian-you (范天佑). Chin. Phys. B, 2000, 9(10): 764-766.
No Suggested Reading articles found!