Wrinkle patterns in active viscoelastic thin sheets

Abstract

We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodeling, such as during fast growth, 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 remodeling are unable to relax to a configuration that minimizes the elastic energy and the sheet is inherently out of equilibrium. We argue that this nonequilibrium 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 minimize 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.