Snapping of Bistable, Prestressed Cylindrical Shells

TL;DR

This paper investigates how residual prestress influences the shape, stability, and snap-through behavior of bistable cylindrical shells using non-Euclidean shell theory and simulations.

Contribution

It introduces a theoretical framework to predict mean curvature and snap-through stimuli in prestressed shells, highlighting the role of residual stress and boundary Gaussian curvature.

Findings

Residual prestress affects shell shape and snap thresholds.

Gaussian curvature in the boundary layer influences stability.

Theoretical predictions align with numerical simulations.

Abstract

Bistable shells can reversibly change between two stable configurations with very little energetic input. Understanding what governs the shape and snap-through criteria of these structures is crucial for designing devices that utilize instability for functionality. Bistable cylindrical shells fabricated by stretching and bonding multiple layers of elastic plates will contain residual stress that will impact the shell's shape and the magnitude of stimulus necessary to induce snapping. Using the framework of non-Euclidean shell theory, we first predict the mean curvature of a nearly cylindrical shell formed by arbitrarily prestretching one layer of a bilayer plate with respect to another. Then, beginning with a residually stressed cylinder, we determine the amount of the stimuli needed to trigger the snapping between two configurations through a combination of numerical simulations and theory. We demonstrate the role of prestress on the snap-through criteria, and highlight the important role that the Gaussian curvature in the boundary layer of the shell plays in dictating shell stability.