The Collective Snapping of a Pair of Bumping Buckled Beams

TL;DR

This paper investigates the elastic instability in pairs of buckling beams, revealing how their interaction leads to collective snapping behavior governed by a bifurcation, with implications for metamaterials design.

Contribution

It introduces a combined experimental, simulation, and theoretical analysis of the snapping instability in parallel buckled beams, highlighting the role of beam spacing and width scaling.

Findings

The critical distance D* scales linearly with the combined beam width.

A pitchfork bifurcation governs the transition to collective snapping.

The model captures the linear scaling and predicts the bifurcation point.

Abstract

When a pair of parallel buckling beams of unequal width make lateral contact under increasing compression, eventually either the thin or the thick beam will snap, leading to collective motion of the beam pair. Using experiments and FEM simulations, we find that the distance $D$ between the beams selects which beam snaps first, and that the critical distance $D^*$ scales linear with the combined width of the two beams. To understand this behavior, we show that the collective motion of the beams is governed by a pitchfork bifurcation that occurs at strains just below snapping. Specifically, we use a model of two coupled Bellini trusses to find a closed form expression for the location of this pitchfork bifurcation that captures the linear scaling of $D^*$ with beam width. Our work uncovers a novel elastic instability that combines buckling, snapping and contact nonlinearities. This instability underlies the packing of parallel confined beams, and can be leveraged in advanced metamaterials.