Bending and wrinkling as competing relaxation pathways for strained free-hanging films

TL;DR

This paper develops an equilibrium phase diagram for strained free-hanging films, revealing a transition from wrinkling to bending as strain gradients increase, and estimates the maximum number of tube rotations achievable.

Contribution

It introduces a phase diagram that predicts shape transitions in strained films and analyzes the limits of tube formation, advancing understanding of relaxation mechanisms.

Findings

Wrinkling occurs at small strain gradients.

Bending dominates at large strain gradients.

Maximum tube rotations are quantitatively estimated.

Abstract

An equilibrium phase diagram for the shape of compressively strained free-hanging films is developed by total strain energy minimization. For small strain gradients {\Delta}{\epsilon}, the film wrinkles, while for sufficiently large {\Delta}{\epsilon}, a phase transition from wrinkling to bending occurs. We consider competing relaxation mechanisms for free-hanging films, which have rolled up into tube structures, and we provide an upper limit for the maximum achievable number of tube rotations.