Crumple-Origami Transition for Twisting Cylindrical Shells

TL;DR

This paper investigates a morphological transition in twisted cylindrical shells between origami-like and crumple-like states, using experiments and simulations to develop an analytical model explaining the transition driven by geometric frustration.

Contribution

It introduces a new model that explains the crumple-origami transition in twisted shells, extending to various geometries and providing analytical descriptions.

Findings

Identified a morphological transition between origami and crumple states.

Developed an analytical model explaining the transition based on geometric frustration.

Extended the model to truncated cones and polygonal cylinders, predicting multiple transitions.

Abstract

Origami and crumpling are two extreme tools to shrink a 3-D shell. In the shrink/expand process, the former is reversible due to its topological mechanism, while the latter is irreversible because of its random-generated creases. We observe a morphological transition between origami and crumple states in a twisted cylindrical shell. By studying the regularity of crease pattern, acoustic emission and energetics from experiments and simulations, we develop a model to explain this transition from frustration of geometry that causes breaking of rotational symmetry. In contrast to solving von Karman-Donnell equations numerically, our model allows derivations of analytic formula that successfully describe the origami state. When generalized to truncated cones and polygonal cylinders, we explain why multiple and/or reversed crumple-origami transitions can occur.