  We study the rheological properties of colloidal microphases in two
dimensions simulating a model of colloidal particles with competing
interactions. Due to the competition between short-range attraction and
long-range repulsion, as a function of the density the model exhibits a variety
of microphases such as clusters, stripes or crystals with bubbles. We prepare
the system in a confined microphase employing Monte-Carlo simulations and then
quench the system at T=0. The resulting configurations are then sheared by
applying a drag force profile. We integrate numerically the equation of motion
for the particles and analyze the dynamics as a function of the density and the
applied strain rate. We measure the stress-strain curves and characterize the
yielding of the colloidal microphases. The results depend on the type of
microphase: (i) clusters are easily sheared along layers and the relative
motion is assisted by rotations. (ii) Stripes shear easily when they are
parallel to the flow and tend to jam when are perpendicular to it. Under a
sufficiently strong shear rate perpendicular stripes orient in the flow
direction. (iii) Crystals with bubbles yield by fracturing along the bubbles
and eventually forming stripes. We discuss the role of dislocations, emitted by
the bubbles, in the yielding process.
