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Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

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Abstract

The complex variable method for the plane elasticity theory of icosahedral quasi-crystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.

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Authors and Affiliations

  1. Department of Physics, Beijing Institute of Technology, Beijing, 100081, China

    LianHe Li & TianYou Fan

  2. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, China

    LianHe Li

Authors
  1. LianHe Li
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  2. TianYou Fan
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Correspondence to LianHe Li.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10372016 and 10761005), the Natural Science Foundation of Inner Mongolia of China (Grant No. 200607010104), and the Natural Science Foundation of Inner Mongolia Normal University (Grant No. QN07034)

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Li, L., Fan, T. Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem. Sci. China Ser. G-Phys. Mech. Astron. 51, 773–780 (2008). https://doi.org/10.1007/s11433-008-0071-0

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  • DOI: https://doi.org/10.1007/s11433-008-0071-0

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