# Wrinkle patterns in active viscoelastic thin sheets

## TL;DR

This paper investigates how active viscoelastic thin sheets develop diverse wrinkle patterns due to the interplay of viscous relaxation and active remodeling, especially when activity outpaces relaxation, leading to non-equilibrium morphologies relevant in biological systems.

## Contribution

It introduces a formalism of evolving target metric to model active remodeling in viscoelastic sheets, revealing new out-of-equilibrium wrinkle morphologies.

## Key findings

- Diverse wrinkle patterns emerge from active viscoelastic sheets.
- Out-of-equilibrium dynamics enable access to unique morphologies.
- Active processes dominate relaxation, preventing energy-minimizing configurations.

## Abstract

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.