 This paper presents a new approach for studying the crack propagation behavior of quasicrystal materials. The authors introduce a phase field variable to describe the damage of quasicrystals near the crack, which allows them to avoid tracking the crack tip and thus eliminates the need for remeshing. They then use this variable to simulate the crack propagation path of 2D quasicrystals and analyze how the phase and field affects their crack growth behavior. Finally, they discuss the interaction between multiple cracks and quasicrystals. This article was authored by Tonli, Jintinyang, Chinghui Su, and others.