  The combined effect of fluid elasticity and yield-stress on the flow past a
circular cylinder is studied by two-dimensional direct numerical simulation. We
analyze the effects of yield-stress, elasticity, shear-thinning, and
shear-thickening on the wake characteristics using the Saramito constitutive
model. The elastoviscoplastic (EVP) wake flow is studied at a moderate Reynolds
number (Re = 100) where two-dimensional vortex shedding occurs in the Newtonian
case. We find that in the shear-thinning elastoviscoplastic flow, when yield
stress increases, the drag coefficient and root mean square of the lift
coefficient both decrease, while the length of the recirculation bubble
$L_{RB}$ increases. These changes indicate that the wake oscillation amplitude
decreases with an increasing yield stress. For shear-thickening however, the
drag coefficient $C_D$ increases at a large Bingham number, and the wake
becomes chaotic. The comparison of viscoelastic fluid and EVP fluid reveals
that the polymer stresses, tr($\tau^p$), decay considerably less downstream of
the cylinder in the EVP case, indicating that significant stresses persist at
large distances. We observe that shear-thinning competes with elastic and yield
stresses and counteracts their effect, while shear-thickening enhances elastic
and yield stress effects, so that the flow pattern can change from periodic to
a chaotic flow.
