Reshaping of a Janus ring

TL;DR

This paper analyzes the stability and shape transformations of Janus rings with intrinsic curvature, revealing thresholds for instability and multiple stable configurations through analytical and numerical methods.

Contribution

It introduces a combined analytical and numerical approach to study the stability and shape bifurcations of Janus rings with intrinsic curvature.

Findings

Instability thresholds depend on the ratio of intrinsic curvature to original radius.

Twisted circles are proven to be absolutely unstable.

Multiple stable and metastable states with different looping numbers exist.

Abstract

We consider reshaping of closed Janus filaments acquiring intrinsic curvature upon actuation of an active component -- a nematic elastomer elongating upon phase transition. Linear stability analysis establishes instability thresholds of circles with no imposed twist, dependent on the ratio $q$ of the intrinsic curvature to the inverse radius of the original circle. Twisted circles are proven to be absolutely unstable but the linear analysis well predicts the dependence of the looping number of the emerging configurations on the imposed twist. Modeling stable configurations by relaxing numerically the overall elastic energy detects multiple stable and metastable states with different looping numbers. The bifurcation of untwisted circles turns out to be subcritical, so that nonplanar shapes with a lower energy exist at $q$ below the critical value. The looping number of stable shapes generally increases with $q$.