Year: 2023
Type: article
Abstract: Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside out. This snap through is a general motif for the storage and rapid release of elastic energy, and it is exploited by many biological and engineered systems from the Venus flytrap to mechanical metamaterials. Shape transitions are known to be related to the type of bifurcation the system undergoes, however, to date, there is no general understanding of the mechanisms that select these bifurcations. Here we analyze numerically and analytically two systems proposed in recent literature in which an elastic strip, initially in a buckled state, is driven through shape transitions by either rotating or translating its boundaries. We show that the two systems are mathematically equivalent, and identify three cases that illustrate the entire range of transitions described by previous authors. Importantly, using reduction order methods, we establish the nature of the underlying bifurcations and explain how these bifurcations can be predicted from geometric symmetries and symmetry-breaking mechanisms, thus providing universal design rules for elastic shape transitions.
Source: Physical Review Letters
Authors: Basile Radisson, Eva Kanso
Institution: University of Southern California
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G2000486918, RAISE: Collective neuromechanical control in the locomotion of sea stars, RUI: Collaborative Research: Optimized design principles inspired by compliant natural propulsors, G6318948403, G6789696670, G688579498, G8875448644, Quantitative analysis of mucociliary clearance in airway ciliopathies
OpenAlex ID: W4379880574