Abstract

Snap-through buckling is a type of instability in which an elastic object rapidly jumps from one state to another. Such instabilities are familiar from everyday life: children’s popper toys rapidly ‘pop’ and jump after being turned inside-out, while snap-through is harnessed to generate fast motions in applications ranging from soft robotics to switches in micro-scale electronics and artificial heart valves. Despite the ubiquity of snap-through in nature and engineering, its dynamics is usually only understood qualitatively, with many examples reported of delay phenomena in which snap-through occurs much more slowly than would be expected for an elastic instability. To explain this discrepancy, it is commonly assumed that some dissipation mechanism, such as viscoelasticity in the object, must be causing the system to lose energy and slow down.

We first demonstrate that anomalously slow dynamics are, in fact, possible in elastic systems with negligible dissipation. This time delay arises from the remnant or ‘ghost’ of the snap-through bifurcation, and is reminiscent of the ‘critical slowing down’ observed in other areas of physics such as phase transitions. However, in many real systems (including the popper toy), viscoelastic effects are present to some degree. To gain insight into the influence of viscoelasticity we then study a Mises truss as a simple model system that exhibits bistability and snap-through. Using a combination of asymptotic analysis and direct numerical solutions, we elucidate the role that viscoelastic effects play in obtaining anomalously slow snap-through dynamics, as opposed to the purely elastic slowing down. Finally, we show that our conclusions also extend to more complex viscoelastic structures used in morphing devices.