A wrinkled cylindrical shell as a tunable locking material

Abstract

A buckled sheet offers a reservoir of material that can be unfurled at a later time. For sufficiently thin yet stiff materials, this geometric process has a striking mechanical feature: when the slack runs out, the material locks to further extension. Here we establish a simple route to a tunable locking material - a system with an interval where it is freely deformable under a given deformation mode, and where the endpoints of this interval can be changed continuously over a wide range. We demonstrate this type of mechanical response in a thin cylindrical shell subjected to axial twist and compression, and we rationalize our results with a simple geometric model.

Figures (1)

• Figure 1: Morphology and mechanics of a twisted cylindrical shell. (a) A 6 $\mu$m thick shell of height $H=26.9$ mm and radius $R=9.5$ mm is mounted between parallel plates, compressed axially and then twisted. At a threshold twist angle, the shell transitions from a disordered buckled state to an ordered wrinkled state. Left: $\varphi=0$. Right: $\varphi=90^\circ$. (b,c) Torque and vertical force on the top plate, as this cylinder is twisted cyclically between $\pm 90^{\circ}$ at constant separation ($h=22.2$ mm). The curves are reproducible over multiple cycles. Coinciding with the transition to ordered wrinkles, the data rapidly increase in magnitude at the "locking angle" $\varphi_\ell$. Our model predicts $\varphi_\ell = 81^{\circ}$ for this shell (see Eq. \ref{['eq:phi_l']}).