Cutting holes in bistable folds

TL;DR

This paper investigates how cutting holes in bistable folded disks affects their stability, revealing anisotropic critical dimensions and re-entrant behavior, with a developable strip model explaining experimental and simulation results.

Contribution

It introduces a model of a developable strip to explain how hole size and shape influence bistability in folded disks, highlighting anisotropic and re-entrant effects.

Findings

Critical hole dimensions are anisotropic and depend on shape.

Removing material can re-stabilize the inverted state.

A developable strip model captures experimental observations.

Abstract

A folded disk is bistable, as it can be popped through to an inverted state with elastic energy localized in a small, highly-deformed region on the fold. Cutting out this singularity relaxes the surrounding material and leads to a loss of bistability when the hole dimensions reach a critical size. These dimensions are strongly anisotropic and feature a surprising re-entrant behavior, such that removal of additional material can re-stabilize the inverted state. A model of the surface as a wide annular developable strip is found to capture the qualitative observations in experiments and simulations. These phenomena are consequential to the mechanics and design of crumpled elastic sheets, developable surfaces, origami and kirigami, and other deployable and compliant structures.