Anomalous dynamics of snap-through instabilities

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• Michael Gomez (University of Cambridge)
• Thursday 17 January 2019, 13:00-14:00
• MR11, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Anne Herrmann.

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 artificial heart valves. In biology, snap-through has long been exploited to convert energy stored slowly into explosive movements: both the leaf of the Venus flytrap and the beak of the hummingbird snap-through to catch prey unawares. 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) must be causing the system to lose energy and slow down.

In this talk we first demonstrate that anomalously slow dynamics are, in fact, possible in elastic systems with little or no 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.

This talk is part of the DAMTP BioLunch series.

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