Critical slowing down in purely elastic `snap-through' instabilities

TL;DR

This paper investigates the dynamics of elastic snap-through instabilities, revealing that even in ideal, non-dissipative systems, the transition slows down near the critical point, akin to critical phenomena.

Contribution

It demonstrates that elastic snap-through exhibits critical slowing down near the transition point, providing new insights into the dynamics of elastic bistability without dissipation.

Findings

Snap-through dynamics slow down near the transition point.

Critical slowing down occurs even without dissipation.

Provides a new perspective on tuning elastic bistable systems.

Abstract

Many elastic structures have two possible equilibrium states: from umbrellas that become inverted in a sudden gust of wind, to nano-electromechanical switches, origami patterns and the hopper popper, which jumps after being turned inside-out. These systems typically transition from one state to the other via a rapid `snap-through'. Snap-through allows plants to gradually store elastic energy, before releasing it suddenly to generate rapid motions, as in the Venus flytrap. Similarly, the beak of the hummingbird snaps through to catch insects mid-flight, while technological applications are increasingly exploiting snap-through instabilities. In all of these scenarios, it is the ability to repeatedly generate fast motions that gives snap-through its utility. However, estimates of the speed of snap-through suggest that it should occur more quickly than is usually observed. Here, we study the dynamics of snap-through in detail, showing that, even without dissipation, the dynamics slow down close to the snap-through transition. This is reminiscent of the slowing down observed in critical phenomena, and provides a handheld demonstration of such phenomena, as well as a new tool for tuning dynamic responses in applications of elastic bistability.