Delayed bifurcation in elastic snap-through

Snap-through buckling is a striking instability in which an elastic object rapidly jumps from one state to another. Despite the ubiquity of snap-through in nature and engineering, its dynamics is not well understood. To explore the dynamic feature of elastic snap-through, here we study a model system: an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. By combining numerical simulation and asymptotic analysis, we investigate when and how the arch transitions between two stable states and show that the end-shortening at which the fast ‘snap’ happens depends on the rate at which the end-shortening is reduced. The results obtained here may have important consequences for understanding complex instabilities in both biological and engineering settings. They may also lead to new routes of controlling snap-through in applications.