  In this work we study the rheological features of yield stress materials that
exhibit non-homogeneous steady flows and that are subjected to an additional
mechanical noise. Using a mesoscale elasto-plastic model accounting for a
viscosity bifurcation in the flow response to an external shear stress, we find
that additional sources of noise can lead to a fluidisation effect. As we
increase the noise intensity we evidence a transition from a non-monotonic to a
monotonic rheology, associated with giant fluctuations of the macroscopic shear
rate and long-time correlated dynamics. Although distinct noise models can lead
to different rheological behaviours in the low stress regime, we show that the
noise-induced transition from shear-localised to homogeneous flow at higher
stresses appears very generic. The observed features in the dynamics can be
interpreted as a result of an out-of-equilibrium phase transition, for which we
estimate the critical exponents that appear to be independent of the specific
choice of the noise implementation for the microscopic dynamics.
