  The dynamics of a single elastoviscoplastic (EVP) drop immersed in plane
shear flow of a Newtonian fluid is studied by 3D direct numerical simulations
using a finite-difference and level-set method combined with the Saramito model
for the EVP fluid. This model gives rise to a yield stress behavior, where the
unyielded state of the material is described as a Kelvin-Voigt viscoelastic
solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an
initially solid drop of Carbopol is simulated under successively increasing
shear rates. We proceed to examine the roles of nondimensional parameters on
the yielding process; in particular, the Bingham number ($Bi$), capillary
number ($Ca$), Weissenberg number ($Wi$), and ratio of solvent and total drop
viscosity. We find that all of these parameters, and not only $Bi$, have a
significant influence on the drop dynamics. Numerical simulations predict that
the volume of the unyielded region inside the droplet increases with $Bi$ and
$Wi$, while it decreases with $Ca$ at low $Wi$ and $Bi$. A new regime map is
obtained for the prediction of the yielded, unyielded, and partly yielded modes
as a function of $Bi$ and $Wi$. The drop deformation is studied and explained
by examining the stresses in the vicinity of the drop interface. The
deformation has a complex dependence on $Bi$ and $Wi$. At low $Bi$, the droplet
deformation shows a nonmonotonic behavior with an increasing $Wi$. In contrast,
at moderate and high $Bi$, droplet deformation always increases with $Wi$.
Moreover, it is found that the deformation increases with $Ca$ and with the
solvent to total drop viscosity ratio. A simple ordinary differential equation
model is developed to explain the various behaviours observed numerically. The
presented results are in contrast with the heuristic idea that viscoelasticity
in the dispersed phase always inhibits deformation.
