  Motivated by recent experimental studies of rheological hysteresis in soft
glassy materials, we study numerically strain rate sweeps in simple yield
stress fluids and viscosity bifurcating yield stress fluids. Our simulations of
downward followed by upward strain rate sweeps, performed within fluidity
models and the soft glassy rheology model, successfully capture the
experimentally observed monotonic decrease of the area of the rheological
hysteresis loop with sweep time in simple yield stress fluids, and the bell
shaped dependence of hysteresis loop area on sweep time in viscosity
bifurcating fluids. We provide arguments explaining these two different
functional forms in terms of differing tendencies of simple and viscosity
bifurcating fluids to form shear bands during the sweeps, and show that the
banding behaviour captured by our simulations indeed agrees with that reported
experimentally. We also discuss the difference in hysteresis behaviour between
inelastic and viscoelastic fluids. Our simulations qualitatively agree with the
experimental data discussed here for four different soft glassy materials.
