  Mode coupling theory (MCT) has had notable successes in addressing the
rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such
as star-polymers. Here, we explore the properties of a recently developed
MCT-based schematic constitutive equation under idealized experimental
protocols involving single and then double step strains. We find strong
deviations from expectations based on factorable, BKZ-type constitutive models.
Specifically, a nonvanishing stress remains long after the application of two
equal and opposite step strains; this residual stress is a signature of plastic
deformation. We also discuss the distinction between hypothetically
instantaneous step strains and fast ramps. These are not generally equivalent
in our MCT approach, with the latter more likely to capture the physics of
experimental `step' strains. The distinction points to the different role
played by reversible anelastic, and irreversible plastic rearrangements.
