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Elasticity Theory of One-Dimensional Quasicrystals and Simplification

  • Tian-You FanEmail author
Chapter
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 246)

Abstract

As mentioned in Chap.  4, there exist three one-, two- and three-dimensional quasicrystals. Each can be further divided into subclasses with respect to symmetry consideration.

Keywords

Plane Elasticity Space Elasticity Deformation Geometry Phonon Field Elastic Constant Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Wang R H,Yang W G, Hu C Z and Ding D H, 1997, Point and space groups and elastic behaviour of one-dimensional quasicrystals, J. Phys.:Condens. Matter, 9(11), 2411-2422.Google Scholar
  2. 2.
    Fan T Y, 2000, Mathematical theory of elasticity and defects of quasicrystals, Advances in Mechanics (in Chinese), 30(2),161-174.Google Scholar
  3. 3.
    Fan T Y and Mai Y W, 2004, Elasticity theory, fracture mechanics and some relevant thermal properties of quasicrystalline materials, Appl. Mech. Rev., 57(5), 325-344.Google Scholar
  4. 4.
    Liu G T, Fan T Y and Guo R P, 2004,Governing equations and general solutions of plane elasticity of one-dimensional quasicrystals, Int. J. Solid and Structures, 41(14), 3949-3959. Google Scholar
  5. 5.
    Liu G T, 2004,The complex variable function method of the elastic theory of quasicrystals and defects and auxiliary equation method for solving some nonlinear evolution equations,, Dissertation (in Chinese), Beijing Institute of Technology.Google Scholar
  6. 6.
    Peng Y Z and Fan T Y, 2000, Elastic theory of 1-D quasiperiodic stacking 2-D crystals, J. Phys.:Condens. Matter, 12(45), 9381-9387.Google Scholar
  7. 7.
    Peng Y Z, 2001, Study on elastic three-dimensional problems of cracks for quasicrystals, Dissertation (in Chinese), Beijing Institute of Technology.Google Scholar
  8. 8.
    Fan T Y, Xie L Y, Fan L and Wang Q Z, 2011, Study on interface of quasicrystal-crystal, Chin Phys B, 20(7), 076102.Google Scholar
  9. 9.
    Chen W Q, Ma Y L and Ding H J, 2004, On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies, Mech. Res. Commun., 31(5), 633-641.Google Scholar
  10. 10.
    Wang X, 2006, The general solution of one-dimensional hexagonal quasicrystal, Appl. Math. Mech., 33(4), 576-580.Google Scholar
  11. 11.
    Gao Y, Zhao Y T and Zhao B S, 2007, Boundary value problems of holomorphic vector functions in one-dimensional hexagonal quasicrystals, Physica B, Vol.394(1), 56–61.Google Scholar
  12. 12.
    Li X Y, 2013, Fundamental solutions of a penny shaped embedded crack and half-infinite plane crack in infinite space of one-dimensional hexagonal quasicrystals under thermal loading, Proc Roy Soc A, 469, 20130023.Google Scholar

Copyright information

© Science Press and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Beijing Institute of TechnologyBeijingChina

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