Steady-state propagation of dislocations in quasi-crystals

We analyze the steady propagation at constant speed, lower than the shear wave-speed, of a straight dislocation in an unbounded elastic quasicrystal with fivefold symmetry. We discuss only the ideal elastic behavior, neglecting the dissipation associated with the atomic rearrangements. Under these conditions, we provide the expressions of standard and microscopic (phason) fields in closed form. Both standard and phason stresses appear to be singular near to the dislocation core. We also find the explicit expression of the energy per unit length around a moving dislocation.