The relationship between active areas and boundaries with energy input in snapping shells

New research looks at how the geometry of shells relates to the energy input required to actuate snap-through instability.

New York | Heidelberg, 5 April 2022

In nature, diverse organisms such as the hummingbird and Venus flytrap use rapid snapping motions to capture prey, inspiring engineers to create designs that function using snap-through instability of shell structures. Snapping rapidly releases stored elastic energy and does not require a continuously applied stimulus to maintain an inverted shape in bistable structures.

A new paper published in EPJ E authored by Lucia Stein-Montalvo, Department of Civil and Environmental Engineering, Princeton University, and Douglas P. Holmes, Department of Mechanical Engineering, Boston University, along with co-authors Jeong-Ho Lee, Yi Yang, Melanie Landesberg, and Harold S. Park, examines how restricting the active area of the shell boundary allows for a large reduction in its size, and decreases the energy input required to actuate snap-through behaviour in the shell to guide the design of efficient snapping structures.

In the paper, the authors point out snap-through instability is a particularly attractive mechanism for devices like robotic actuators or mechanical muscles, optical devices, and even dynamic building façades. All of these rely on a combination of geometric bi-stability and snap-inducing stimulus to function that ranges from the mechanical, like the torque in a child’s popping jumping cap toy, or non-mechanical like temperature, voltage, a magnetic field, differential growth or swelling.

The researchers conducted two sets of experiments, one using the residual swelling of bilayer silicone elastomers – a process that mimics differential growth, the other using a magneto-elastomer to induce curvatures that cause snap-through.

This mechanics-informed approach uncovered an analogy to the bending-dominated boundary layer in inverted spherical caps. They found that just as with inverted, passive spherical caps, the size of the boundary layer is closely tied to stability. Additionally, the team discovered that the location and size of the imposed bending region determine whether it competes against or cooperates with the geometric boundary layer, where the shell “wants” to bend.

Thus, the team’s results reveal the underlying mechanics of snap-through in spherical shells, offering an intuitive route to optimal design for efficient snap-through.

References: Stein-Montalvo, L., Lee, JH., Yang, Y. et al. Efficient snap-through of spherical caps by applying a localized curvature stimulus., Eur. Phys. J. E 45, 3 (2022). https://doi.org/10.1140/epje/s10189-021-00156-0