  We investigate impact of a sphere onto a floating elastic sheet and the
resulting formation and evolution of wrinkles in the sheet. Following impact,
we observe a radially propagating wave, beyond which the sheet remains
approximately planar but is decorated by a series of radial wrinkles whose
wavelength grows in time. We develop a mathematical model to describe these
phenomena by exploiting the asymptotic limit in which the bending stiffness is
small compared to stresses in the sheet. The results of this analysis show
that, at a time $t$ after impact, the transverse wave is located at a radial
distance $r\sim t^{1/2}$ from the impactor, in contrast to the classic $r\sim
t^{2/3}$ scaling observed for capillary--inertia ripples produced by dropping a
stone into a pond. We describe the shape of this wave, starting from the
simplest case of a point impactor, but subsequently addressing a finite-radius
spherical impactor, contrasting this case with the classic Wagner theory of
impact. We show also that the coarsening of wrinkles in the flat portion of the
sheet is controlled by the inertia of the underlying liquid: short-wavelength,
small-amplitude wrinkles form at early times since they accommodate the
geometrically-imposed compression without significantly displacing the
underlying liquid. As time progresses, the liquid accelerates and the wrinkles
grow larger and coarsen. We explain this coarsening quantitatively using
numerical simulations and scaling arguments, and we compare our predictions
with experimental data.

Soft Condensed Matter;Fluid Dynamics