中文摘要：

以准晶线性弹性理论为基础,将准晶近似看做线性弹性体,在小变形情形下,采用有限差分法求解十次对称准晶中的动力学裂纹扩展问题的数值解,其中重点考虑了中心裂纹Griffith矩形试样,并与单边裂纹Griffith矩形试样作了对比.在裂纹扩展问题上,从裂纹的动态初始和裂纹的快速扩展两个方面,考查了裂纹尖端处的位移、应力、应变场变量随时间的变化规律,揭示了准晶裂纹扩展的动力学物理特性,进一步验证了声子场的波动行为和相位子场的扩散行为,以及声子场-相位子场的耦合效应.

英文摘要：

Based on the theory of linear elastic quasicrystals,the quasicrystals are often seen as linear elastic body.In the state of small deformation,applying for the method of finite difference,the elasto-dynamical problem in quasicrystals with point group 10 mm is studied to find the numerical solution of the dynamic crack propagation.We laid on thinking over the rectangular sample with a Griffith crack in the center,contrasted with a Griffith crack unilateral,with the problem of crack propagation,we mainly discuss two phases：the dynamic initiation of crack growth and the fast crack propagation.We focus on investigating the variation about displacement,stress,the variables of stress field around the crack tip,which revealing the dynamic physical characteristics of crack propagation of quasicrystals,further checking the wave behaviour of phonon,and spread behaviour of phason,as well as the phonon-phason coupling effect.