Abstract Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors (SIFs) for mode III problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.
Received: 26 November 2007
Revised: 09 January 2008
Accepted manuscript online:
Fund: Project
supported by the National Natural Science Foundation of China (Grant
No 10761005) and the Inner Mongolia Natural Science Foundation of
China (Grant No 200607010104).
Cite this article:
Guo Jun-Hong(郭俊宏) and Liu Guan-Ting(刘官厅) Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal 2008 Chin. Phys. B 17 2610
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