Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 567489, 18 pages
Research Article

Dynamic Analysis of Cracked Octagonal Quasicrystals

1Institute of Applied Mathematics, Xuchang University, Xuchang 461000, China
2Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China

Received 29 March 2011; Accepted 5 July 2011

Academic Editor: Mehrdad Massoudi

Copyright © 2011 Wu Li and Tian You Fan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We focus on the dynamic fracture problem of octagonal quasicrystals by applying a rectangular sample with a Griffith crack which is often used in classical elastic media based on the method of finite difference. This paper mainly is to investigate the variation of phonon, phason fields, and stress singularity around the crack tip including the stress intensity factor. In addition, the moving boundary due to the crack propagation has also been treated by introducing an additional condition for determining solution. The influence of wave propagation and diffusion in the dynamic process is also discussed in detail. Through comparing the results of octagonal quasicrystals with the results of crystal, this paper proclaims the influence of phonon-phason coupling in dynamic fracture problem of octagonal quasicrystals which should not be neglected.