  Discrete particle simulations are used to study the shear rheology of dense,
stabilized, frictional particulate suspensions in a viscous liquid, toward
development of a constitutive model for steady shear flows at arbitrary stress.
These suspensions undergo increasingly strong continuous shear thickening (CST)
as solid volume fraction $\phi$ increases above a critical volume fraction, and
discontinuous shear thickening (DST) is observed for a range of $\phi$. When
studied at controlled stress, the DST behavior is associated with non-monotonic
flow curves of the steady-state stress as a function of shear rate. Recent
studies have related shear thickening to a transition between mostly lubricated
to predominantly frictional contacts with the increase in stress. In this
study, the behavior is simulated over a wide range of the dimensionless
parameters $(\phi,\tilde{\sigma}$, and $\mu)$, with $\tilde{\sigma} =
\sigma/\sigma_0$ the dimensionless shear stress and $\mu$ the coefficient of
interparticle friction: the dimensional stress is $\sigma$, and $\sigma_0
\propto F_0/ a^2$, where $F_0$ is the magnitude of repulsive force at contact
and $a$ is the particle radius. The data have been used to populate the model
of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev.
Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity
divergences or \textquotedblleft jamming\textquotedblright\ points at volume
fraction $\phi_{\rm J}^0 = \phi_{\rm rcp}$ (random close packing) for the
low-stress lubricated state, and at $\phi_{\rm J} (\mu) < \phi_{\rm J}^0$ for
any nonzero $\mu$ in the frictional state; a generalization provides the normal
stress response as well as the shear stress. A flow state map of this material
is developed based on the simulation results.
