A decagonal quasicrystal with a Griffith crack

The crack theory in conventional linear elasticity fracture mechanics is ex tended to quasicrystal linear elasticity fracture mechanics. A decagonal qu asicrystal containing a Griffith crack penetrating through the solid along the period direction is considered. By means of a general solution, the ana lytical expressions for the entire stress field are obtained. The asymptoti c behaviour of the stress around the crack tip indicates that the stress ne ar the crack tip exhibits the square root singularity. The singularity in t he phason stress field arises from that the phonon and phason fields couple with each other. The crack strain energy and energy release rate are also given.