A twodimensional binary model quasicrystal (Roth-Mikulla tiling) was subjected to shear of constant rate (Lees-Edwards boundary conditions). Lennard-Jones forces were applied between the atoms and the evolution of the system was followed by isothermal molecular dynamics simulations. Temperature was controlled by a Nosé-Hoover thermostat. Dislocation dipoles were created followed by phason walls, which broadened with increasing shear. Widening happens by transversal shear induced diffusion. It starts with the onset of failure and is saturating after reaching two planes of high interface energy parallel to the glide plane. Thus a structurally damaged layer arises along which viscous glide is developing. The transverse diffusion constant follows an Arrhenius law at low temperature. With increasing temperature it is bending to a flatter slope similar as in the model of phason induced diffusion by Kalugin and Katz. First results of temperature-dependent crack-propagation are reported, too.