  We use particle simulations to map comprehensively the shear rheology of dry
and wet granular matter, in both fixed pressure and fixed volume protocols. At
fixed pressure we find non-monotonic constitutive curves that are shear
thinning, whereas at fixed volume we find non-monotonic constitutive curves
that are shear thickening. We show that the presence of one non-monotonicity
does not imply the other. Instead, there exists a signature in the volume
fraction measured under fixed pressure that, when present, ensures
non-monotonic constitutive curves at fixed volume. In the context of dry
granular flow we show that gradient and vorticity bands arise under fixed
pressure and volume respectively, as implied by the constitutive curves. For
wet systems our results are consistent with a recent experimental observation
of shear thinning at fixed pressure. We furthermore predict discontinuous shear
thickening in the absence of critical load friction.
