  We show that a viscoelastic thin sheet driven out of equilibrium by active
structural remodelling develops a rich variety of shapes as a result of a
competition between viscous relaxation and activity. In the regime where active
processes are faster than viscoelastic relaxation, wrinkles that are formed due
to remodelling are unable to relax to a configuration that minimises the
elastic energy and the sheet is inherently out of equilibrium. We argue that
this non-equilibrium regime is of particular interest in biology as it allows
the system to access morphologies that are unavailable if restricted to the
adiabatic evolution between configurations that minimise the elastic energy
alone. Here, we introduce activity using the formalism of evolving target
metric and showcase the diversity of wrinkling morphologies arising from out of
equilibrium dynamics.
