Abstract

Foldable structures have been of great interest due to their ability to reduce in size from deployed to folded state, enabling easier storage in scenarios with space constraints such as aerospace and medical applications. Hexagonal structural components have been of interest, due to their ability to tessellate, or cover without gap, 2D and 3D surfaces. However, the study on effective folding strategies for hexagon-based structures and the hexagon geometry itself is limited. Here, we report a strategy of snap-folding hexagonal rings, to result in folded states with only 10.6% the initial area of a single ring. Motivated by this significant packing, we utilize a combination of experiments and finite element analysis to study effective folding strategies and packing abilities of various 2D and 3D hexagonal ring assemblies, with structures that can be folded to 1.5% and 0.4% of their initial area and volume, respectively. The effect of geometric parameters of hexagonal rings on the mechanical stability of their assemblies is investigated. Additionally, the instabilities of rings can be utilized to facilitate the automatic deployment of folded ring assemblies under small perturbations. Furthermore, an assembly with rigid functional panels is explored to demonstrate the functionality and design space for hexagonal ring assemblies. With such significant demonstrated area and volume changes upon snap-folding, it is anticipated that hexagonal ring assemblies could inspire future aerospace or biomedical designs, where reconfiguration and large packing are required.

References

1.
Zirbel
,
S. A.
,
Lang
,
R. J.
,
Thomson
,
M. W.
,
Sigel
,
D. A.
,
Walkemeyer
,
P. E.
,
Trease
,
B. P.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2013
, “
Accommodating Thickness in Origami-Based Deployable Arrays
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111005
.
2.
Chen
,
T.
,
Bilal
,
O. R.
,
Lang
,
R.
,
Daraio
,
C.
, and
Shea
,
K.
,
2019
, “
Autonomous Deployment of a Solar Panel Using Elastic Origami and Distributed Shape-Memory-Polymer Actuators
,”
Phys. Rev. Appl.
,
11
(
6
), p.
064069
.
3.
Kuribayashi
,
K.
,
Tsuchiya
,
K.
,
You
,
Z.
,
Tomus
,
D.
,
Umemoto
,
M.
,
Ito
,
T.
, and
Sasaki
,
M.
,
2006
, “
Self-Deployable Origami Stent Grafts as a Biomedical Application of Ni-Rich TiNi Shape Memory Alloy Foil
,”
Mater. Sci. Eng. A
,
419
(
1
), pp.
131
137
.
4.
Wu
,
S.
,
Ze
,
Q.
,
Dai
,
J.
,
Udipi
,
N.
,
Paulino
,
G. H.
, and
Zhao
,
R.
,
2021
, “
Stretchable Origami Robotic Arm With Omnidirectional Bending and Twisting
,”
Proc. Natl. Acad. Sci.
,
118
(
36
), p.
e2110023118
.
5.
Lahikainen
,
M.
,
Zeng
,
H.
, and
Priimagi
,
A.
,
2018
, “
Reconfigurable Photoactuator Through Synergistic Use of Photochemical and Photothermal Effects
,”
Nat. Commun.
,
9
(
1
), p.
4148
.
6.
Wu
,
S.
,
Ze
,
Q.
,
Zhang
,
R.
,
Hu
,
N.
,
Cheng
,
Y.
,
Yang
,
F.
, and
Zhao
,
R.
,
2019
, “
Symmetry-Breaking Actuation Mechanism for Soft Robotics and Active Metamaterials
,”
ACS Appl. Mater. Interfaces
,
11
(
44
), pp.
41649
41658
.
7.
Kamrava
,
S.
,
Mousanezhad
,
D.
,
Ebrahimi
,
H.
,
Ghosh
,
R.
, and
Vaziri
,
A.
,
2017
, “
Origami-Based Cellular Metamaterial With Auxetic, Bistable, and Self-Locking Properties
,”
Sci. Rep.
,
7
(
1
), p.
46046
.
8.
Iniguez-Rabago
,
A.
,
Li
,
Y.
, and
Overvelde
,
J. T. B.
,
2019
, “
Exploring Multi-Stability in Prismatic Metamaterials Through Local Actuation
,”
Nat. Commun.
,
10
(
1
), p.
5577
.
9.
Jenett
,
B.
,
Cameron
,
C.
,
Tourlomousis
,
F.
,
Rubio
,
A. P.
,
Ochalek
,
M.
, and
Gershenfeld
,
N.
,
2020
, “
Discretely Assembled Mechanical Metamaterials
,”
Sci. Adv.
,
6
(
47
), p.
eabc9943
.
10.
Melancon
,
D.
,
Gorissen
,
B.
,
García-Mora
,
C. J.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2021
, “
Multi-Stable Inflatable Origami Structures at the Metre Scale
,”
Nature
,
592
(
7855
), pp.
545
550
.
11.
Alegria Mira
,
L.
,
Thrall
,
A. P.
, and
De Temmerman
,
N.
,
2014
, “
Deployable Scissor Arch for Transitional Shelters
,”
Autom. Constr.
,
43
, pp.
123
131
.
12.
Choi
,
G. P. T.
,
Dudte
,
L. H.
, and
Mahadevan
,
L.
,
2019
, “
Programming Shape Using Kirigami Tessellations
,”
Nat. Mater.
,
18
(
9
), pp.
999
1004
.
13.
Filipov
,
E. T.
,
Tachi
,
T.
, and
Paulino
,
G. H.
,
2015
, “
Origami Tubes Assembled Into Stiff, Yet Reconfigurable Structures and Metamaterials
,”
Proc. Natl. Acad. Sci.
,
112
(
40
), pp.
12321
12326
.
14.
Mao
,
Y.
,
Yu
,
K.
,
Isakov
,
M. S.
,
Wu
,
J.
,
Dunn
,
M. L.
, and
Jerry Qi
,
H.
,
2015
, “
Sequential Self-Folding Structures by 3D Printed Digital Shape Memory Polymers
,”
Sci. Rep.
,
5
(
1
), p.
13616
.
15.
Kuang
,
X.
,
Wu
,
S.
,
Ze
,
Q.
,
Yue
,
L.
,
Jin
,
Y.
,
Montgomery
,
S. M.
,
Yang
,
F.
,
Qi
,
H. J.
, and
Zhao
,
R.
,
2021
, “
Magnetic Dynamic Polymers for Modular Assembling and Reconfigurable Morphing Architectures
,”
Adv. Mater.
,
33
(
30
), p.
2102113
.
16.
Wang
,
W.
,
Kim
,
N.-G.
,
Rodrigue
,
H.
, and
Ahn
,
S.-H.
,
2017
, “
Modular Assembly of Soft Deployable Structures and Robots
,”
Mater. Horiz.
,
4
(
3
), pp.
367
376
.
17.
Liu
,
F.
,
Jiang
,
X.
,
Wang
,
X.
, and
Wang
,
L.
,
2020
, “
Machine Learning-Based Design and Optimization of Curved Beams for Multi-Stable Structures and Metamaterials
,”
Extreme Mech. Lett.
,
41
, p.
101002
.
18.
Mhatre
,
S.
,
Boatti
,
E.
,
Melancon
,
D.
,
Zareei
,
A.
,
Dupont
,
M.
,
Bechthold
,
M.
, and
Bertoldi
,
K.
,
2021
, “
Deployable Structures Based on Buckling of Curved Beams Upon a Rotational Input
,”
Adv. Funct. Mater.
,
31
(
35
), p.
2101144
.
19.
Dudte
,
L. H.
,
Vouga
,
E.
,
Tachi
,
T.
, and
Mahadevan
,
L.
,
2016
, “
Programming Curvature Using Origami Tessellations
,”
Nat. Mater.
,
15
(
5
), pp.
583
588
.
20.
Liu
,
K.
,
Han
,
L.
,
Hu
,
W.
,
Ji
,
L.
,
Zhu
,
S.
,
Wan
,
Z.
,
Yang
,
X.
, et al
,
2020
, “
4D Printed Zero Poisson's Ratio Metamaterial With Switching Function of Mechanical and Vibration Isolation Performance
,”
Mater. Des.
,
196
, p.
109153
.
21.
Tao
,
R.
,
Xi
,
L.
,
Wu
,
W.
,
Li
,
Y.
,
Liao
,
B.
,
Liu
,
L.
,
Leng
,
J.
, and
Fang
,
D.
,
2020
, “
4D Printed Multi-Stable Metamaterials With Mechanically Tunable Performance
,”
Compos. Struct.
,
252
, p.
112663
.
22.
Rafsanjani
,
A.
,
Akbarzadeh
,
A.
, and
Pasini
,
D.
,
2015
, “
Snapping Mechanical Metamaterials Under Tension
,”
Adv. Mater.
,
27
(
39
), pp.
5931
5935
.
23.
Tian
,
D.
,
Guo
,
Z.
,
Jin
,
L.
,
Zhang
,
K.
,
Gao
,
H.
,
Fan
,
X.
, and
Liu
,
Z.
, “
Design and Deployment Experiment Research on Support Mechanism for Hexagonal Prism Modular Deployable Antenna
,”
2021 IEEE 4th International Conference on Electronics Technology (ICET)
,
Chengdu, China
,
May 7–10
,pp. 627–631.
24.
Gardner
,
J. P.
,
Mather
,
J. C.
,
Clampin
,
M.
,
Doyon
,
R.
,
Greenhouse
,
M. A.
,
Hammel
,
H. B.
,
Hutchings
,
J. B.
, et al
,
2006
, “
The James Webb Space Telescope
,”
Space Sci. Rev.
,
123
(
4
), pp.
485
606
.
25.
Grumman
,
N.
, and
Gunn
,
C.
,
2020
, “
Successful Mirror Deployment Test
,” Photograph, https://www.flickr.com/photos/nasawebbtelescope/49754454197/in/album-72157691368095482/
26.
Gunn
,
C.
,
2019
, “
NASA’s James Webb Space Telescope Has Been Assembled for the First Time
,” Photograph, https://www.flickr.com/photos/nasawebbtelescope/48636487363/in/album-72157691368095482/
27.
Sahr
,
K.
,
White
,
D.
, and
Kimerling
,
A. J.
,
2003
, “
Geodesic Discrete Global Grid Systems
,”
Cartogr. Geogr. Inf. Sci.
,
30
(
2
), pp.
121
134
.
28.
Zhao
,
Z.
,
Wang
,
K.
,
Zhang
,
L.
,
Wang
,
L.-C.
,
Song
,
W.-L.
, and
Fang
,
D.
,
2019
, “
Stiff Reconfigurable Polygons for Smart Connecters and Deployable Structures
,”
Int. J. Mech. Sci.
,
161–162
, p.
105052
.
29.
Zhang
,
Y.-J.
,
Wang
,
L.-C.
,
Song
,
W.-L.
,
Chen
,
M.
, and
Fang
,
D.
,
2020
, “
Hexagon-Twist Frequency Reconfigurable Antennas Via Multi-Material Printed Thermo-Responsive Origami Structures
,”
Front. Mater.
,
7
, pp.
1
11
.
30.
Yan
,
Z.
,
Zhang
,
F.
,
Wang
,
J.
,
Liu
,
F.
,
Guo
,
X.
,
Nan
,
K.
,
Lin
,
Q.
, et al
,
2016
, “
Controlled Mechanical Buckling for Origami-Inspired Construction of 3D Microstructures in Advanced Materials
,”
Adv. Funct. Mater.
,
26
(
16
), pp.
2629
2639
.
31.
Li
,
S.
,
Deng
,
B.
,
Grinthal
,
A.
,
Schneider-Yamamura
,
A.
,
Kang
,
J.
,
Martens
,
R. S.
,
Zhang
,
C. T.
, et al
,
2021
, “
Liquid-Induced Topological Transformations of Cellular Microstructures
,”
Nature
,
592
(
7854
), pp.
386
391
.
32.
Overvelde
,
J. T. B.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2017
, “
Rational Design of Reconfigurable Prismatic Architected Materials
,”
Nature
,
541
(
7637
), pp.
347
352
.
33.
Chen
,
Y.
,
You
,
Z.
, and
Tarnai
,
T.
,
2005
, “
Threefold-Symmetric Bricard Linkages for Deployable Structures
,”
Int. J. Solids Struct.
,
42
(
8
), pp.
2287
2301
.
34.
Gao
,
W.
,
Huo
,
K.
,
Seehra
,
J. S.
,
Ramani
,
K.
, and
Cipra
,
R. J.
, “
HexaMorph: A Reconfigurable and Foldable Hexapod Robot Inspired By Origami
,”
2014 IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Chicago, IL
,
Sept. 14–18
, pp.
4598
4604
.
35.
Wu
,
S.
,
Yue
,
L.
,
Jin
,
Y.
,
Sun
,
X.
,
Zemelka
,
C.
,
Qi
,
H. J.
, and
Zhao
,
R.
,
2021
, “
Ring Origami: Snap-Folding of Rings With Different Geometries
,”
Adv. Intell. Syst.
,
3
(
9
), p.
2100107
.
36.
Wu
,
S.
,
Dai
,
J.
,
Leanza
,
S.
, and
Zhao
,
R. R.
,
2022
, “
Hexagonal Ring Origami—Snap-Folding With Large Packing Ratio
,”
Extreme Mech. Lett.
,
53
, p.
101713
.
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