  The shear rheology of dense colloidal and granular suspensions is strongly
nonlinear, as these materials exhibit shear-thinning and shear-thickening,
depending on multiple physical parameters. We numerically study the rheology of
a simple model of soft repulsive particles at large densities, and show that
nonlinear flow curves reminiscent of experiments on real suspensions can be
obtained. By using dimensional analysis and basic elements of kinetic theory,
we rationalize these multiple rheological regimes and disentangle the relative
impact of thermal fluctuations, glass and jamming transitions, inertia and
particle softness on the flow curves. We characterize more specifically the
shear-thickening regime and show that both particle softness and the emergence
of a yield stress at the jamming transition compete with the inertial effects
responsible for the observed thickening behaviour. This allows us to construct
a dynamic state diagram, which can be used to analyze experiments.
