  This study proposes a coherent scenario of the formation of permanent shear
bands in the flow of yield stress materials. It is a well accepted point of
view that flow in disordered media is occurring via local plastic events,
corresponding to small size rearrangements, that yield a long range stress
redistribution over the system. Within a minimalistic mesoscopic model that
incorporates these local dynamics, we study the spatial organisation of the
local plastic events. The most important parameter in this study is the typical
restructuring time needed to regain the original structure after a local
rearrangement. In agreement with a recent mean field study [Coussot \textit{et
al., Eur. Phys. J. E}, 2010, \textbf{33}, 183] we observe a spontaneous
formation of permanent shear bands, when this restructuring time is large
compared to the typical stress release time in a rearrangement. The bands
consist of a large number of plastic events within a solid region that remains
elastic. This heterogeneous flow behaviour is different in nature from the
transient dynamical heterogeneities that one observes in the small shear rate
limit in flow without shear-banding [Martens \textit{et al., Phys. Rev. Lett.},
2011, \textbf{106}, 156001]. We analyse in detail the dependence of the shear
bands on system size, shear rate and restructuring time. Further we rationalise
the scenario within a mean field version of the spatial model, that produces a
non monotonous flow curve for large restructuring times. This explains the
instability of the homogeneous flow below a critical shear rate, that
corresponds to the minimum of the curve. Our study therefore strongly supports
the idea that the characteristic time scales involved in the local dynamics are
at the physical origin of permanent shear bands.
