  We propose a unifying rheological framework for dense suspensions of
non-Brownian spheres, predicting the onsets of particle friction and particle
inertia as distinct shear thickening mechanisms, while capturing quasistatic
and soft particle rheology at high volume fractions and shear rates
respectively. Discrete element method simulations that take suitable account of
hydrodynamic and particle-contact interactions corroborate the model
predictions, demonstrating both mechanisms of shear thickening, and showing
that they can occur concurrently with carefully selected particle surface
properties under certain flow conditions. Microstructural transitions
associated with frictional shear thickening are presented. We find very
distinctive divergences of both the microstructural and dynamic variables with
respect to volume fraction in the thickened and non-thickened states.
