  The capillary traction of a liquid contact line causes highly localized
deformations in soft solids, tremendously slowing down wetting and dewetting
dynamics by viscoelastic braking. Enforcing nonetheless large velocities leads
to the so-called stick-slip instability, during which the contact line
periodically depins from its own wetting ridge. The mechanism of this periodic
motion and, especially, the role of the dynamics in the fluid have remained
elusive, partly because a theoretical description of the unsteady soft wetting
problem is not available so far. Here we present the first numerical
simulations of the full unsteady soft wetting problem, with a full coupling
between the liquid and the solid dynamics. We observe three regimes of soft
wetting dynamics: steady viscoelastic braking at slow speeds, stick-slip motion
at intermediate speeds, followed by a region of viscoelastic braking where
stick-slip is suppressed by liquid damping, which ultimately gives way to
classical wetting dynamics, dominated by liquid dissipation.
