Reshaping of a Janus ring

We consider the reshaping of closed Janus filaments acquiring intrinsic curvature upon actuation of a driven 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 $q$.

Figure 1

A segment of Janus filament showing the Frenet frame and a cross-section geometry with a mismatched orientation of the Frenet normal vector n and the internal normal.

Figure 2

The dependence of quantitative characteristics of nonplanar configurations with different looping numbers $n$ on the parameter $q$. (a) The energy change relative to the planar loop. (b) The mean square deviation from the original plane.

Figure 3

Configurations with the looping numbers $n=2$ at $q=9$ (left), $n=3$ at $q=16$ (middle), and $n=4$ at $q=27$ (right). The filament radius and length are the same in all cases. The driven and passive components are colored in red (dark) and yellow (light), respectively.

Figure 4

Dependences of the energy change relative to the initial state (a) and the mean square deviation from the original plane (b) on the parameter $q$ for different twist numbers $m$.

Figure 5

Reshaping twisted ring filaments leading to equilibrium planar solutions at (a) $m=1, q=5$ and (b) $m=4, q=12$, and to nonplanar conformations with (c) single ($m=3, q=5$) and (d) multiple ($m=3, q=20$) self-contacts.