A steadily propagating crack in planar quasicristals with fivefold symmetry

A closed-form solution is provided for the stress, strain and velocity fields due to a planar crack steadily propagating in an elastic quasicrystal with fivefold symmetry at speed lower than the bulk wave-speeds. The case of a semi-infinite rectilinear crack loaded on its surfaces is considered. The dynamic theory of quasicrystal with inertia forces, but neglecting dissipative phonon activity, is assumed to govern the motion of the medium. Both phonon and phason stress fields display square-root singular at crack tip. The energy release rate is positive for subsonic and subRayleigh crack propagation. The limit case of a stationary crack is then recovered as the crack tip speed becomes vanishing small.