  Helical structures, almost ubiquitous in biological systems, have inspired
the design and manufacturing of helical devices with applications in
nanoelecromechanical systems (NEMS), morphing structures, optoelectronics,
micro-robotics and drug delivery devices. Meanwhile, multi-stable structures,
represented by the Venus flytrap and slap bracelet, have attracted increasing
attention due to their applications in making artificial muscles, bio-inspired
robots, deployable aerospace components and energy harvesting devices. Here we
show that the mechanical anisotropy pertinent to helical deformation, together
with geometric nonlinearity associated with multi-stability, can lead to novel
selection principle of the geometric shape and multi-stability in spontaneous
helical ribbons. Simple table-top experiments were also performed to illustrate
the working principle. Our work will promote understanding of spontaneous
curling, twisting, wrinkling of thin objects and their instabilities, and serve
as a tool in developing functional structures and devices with tunable,
morphing geometries and smart actuation mechanism that can be applied in a
spectrum of areas.
