Crumpling-origami transition for twisting cylindrical shells

LM Wang and ST Tsai and CY Lee and PY Hsiao and JW Deng and HCF Chiang and YC Fei and TM Hong, PHYSICAL REVIEW E, 101, 053001 (2020).

DOI: 10.1103/PhysRevE.101.053001

Origami and crumpling are two processes to reduce the size of a membrane. In the shrink-expand process, the crease pattern of the former is ordered and protected by its topological mechanism, while that of the latter is disordered and generated randomly. We observe a morphological transition between origami and crumpling states in a twisted cylindrical shell. By studying the regularity of the 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 formulas that successfully describe the origami state. When generalized to truncated cones and polygonal cylinders, we explain why multiple and/or reversed crumpling-origami transitions can occur.

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