  We perform extensive molecular dynamics simulations of 2D frictionless
granular materials to determine whether these systems can be characterized by a
single static yield shear stress. We consider boundary-driven planar shear at
constant volume and either constant shear force or constant shear velocity.
Under steady flow conditions, these two ensembles give similar results for the
average shear stress versus shear velocity. However, near jamming it is
possible that the shear stress required to initiate shear flow can differ
substantially from the shear stress required to maintain flow. We perform
several measurements of the shear stress near the initiation and cessation of
flow. At fixed shear velocity, we measure the average shear stress
$\Sigma_{yv}$ in the limit of zero shear velocity. At fixed shear force, we
measure the minimum shear stress $\Sigma_{yf}$ required to maintain steady flow
at long times. We find that in finite-size systems $\Sigma_{yf} > \Sigma_{yv}$,
which implies that there is a jump discontinuity in the shear velocity from
zero to a finite value when these systems begin flowing at constant shear
force. However, our simulations show that the difference $\Sigma_{yf} -
\Sigma_{yv}$, and thus the discontinuity in the shear velocity, tend to zero in
the infinite system size limit. Thus, our results indicate that in the large
system limit, frictionless granular systems are characterized by a single
static yield shear stress. We also monitor the short-time response of these
systems to applied shear and show that the packing fraction of the system and
shape of the velocity profile can strongly influence whether or not the shear
stress at short times overshoots the long-time average value.
