  We consider suspensions of deformable particles in a Newtonian fluid by means
of fully Eulerian numerical simulations with a one-continuum formulation. We
study the rheology of the visco-elastic suspension in plane Couette flow in the
limit of vanishing inertia and examine the dependency of the effective
viscosity $\mu$ on the solid volume-fraction $\Phi$, the capillary number
$\mbox{Ca}$, and the solid to fluid viscosity ratio $\mbox{K}$. The suspension
viscosity decreases with deformation and applied shear (shear-thinning) while
still increasing with volume fraction. We show that $\mu$ collapses to an
universal function, $\mu \left( \Phi^{\rm e} \right)$, with an effective volume
fraction $\Phi^{\rm e}$, lower than the nominal one owing to the particle
deformation. This universal function is well described by the Eilers fit, which
well approximate the rheology of suspension of rigid spheres at all $\Phi$. We
provide a closure for the effective volume fraction $\Phi^{\rm e}$ as function
of volume fraction $\Phi$ and capillary number $\mbox{Ca}$ and demonstrate it
also applies to data in literature for suspensions of capsules and red-blood
cells. In addition, we show that the normal stress differences exhibit a
non-linear behavior, with a similar trend as in polymer and filament
suspensions. The total stress budgets reveals that the particle-induced stress
contribution increases with the volume fraction $\Phi$ and decreases with
deformability.
