Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack

This present work is concerned with planar cracks embedded in an infinite space of one-dimensional hexagonal quasicrystals. The potential theory method together with the general solutions is used to develop the framework of solving the crack problems in question. The mode I problems of three common planar cracks (a penny-shaped crack, an external circular crack and a half-infinite crack) are solved in a systematic manner. The phonon and phason elastic fundamental fields along with some important parameters in crack analysis are explicitly presented in terms of elementary functions. Several examples are given to show the applications of the present fundamental solutions. The validity of the present solutions is discussed both analytically and numerically. The derived analytical solutions of crack will not only play an important role in understanding the phonon–phason coupling behavior in quasicrystals, but also serve as benchmarks for future numerical studies and simplified analyses.