A decagonal quasicrystal with an arc-shaped crack

A decagonal quasicrystal, which is weakened by an arc-shaped crack penetrating through the solid in the period direction, and which is subjected to remote uniform phonon stresses, is investigated by applying the complex variable method which is just developed by the authors. It is found that the phonon and phason stresses near the crack tips exhibit inverse square root singularities. The four complex stress functions characterizing the phonon and phason fields are derived. Explicit expressions for the phonon and phason stress intensity factors, crack opening displacements and energy release rate are also presented.