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Using Origami for
Deployable Structures and
Adaptable Metamaterials
Department of Mechanical Engineering,
École polytechnique fédérale de Lausanne
February 9, 2016
1. University of Illinois
at Urbana Champaign
3. The University
of Tokyo
2. Georgia Institute
of Technology
Evgueni T. Filipov1
Prof. Glaucio H. Paulino1,2
Prof. Tomohiro Tachi3
1
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Origami in Engineering
Structural Analysis of Origami
Coupling of Origami Tubes
Cross-Section and Other Variations
Cellular Assemblages
Future Research Plans
Presentation Outline
2
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Origami as Art Origami as Entertainment
Origami in EducationOrigami as Fashion
Origami Dresshttp://www.julewaibel.com/
Origami Braceletwww.tinederuysser.com/
Orchfini by E. Joiselwww.ericjoisel.com/gallery.html
Elk 358 by R. Langhttp://www.langorigami.com/
Origami Fortune Tellerwww.origami-instructions.com/
Paper Airplanehttp://www.foldnfly.com/
Geometry - A. Tubis 6OSME 2014
Gaussian Curvature - T. Hull 20123
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• Tunable • Multi-Functional • Adaptable
Kiefer Technic Showroom ISS – NASA 2011
Wood (2008) Kuribayashi et al.
(2006)
Marras et al.
(2015)
100nm
Felton et al. (2014)
Engineering Applications of Origami
• Compact • Deployable • Pre-Fabricated • Self-Assembly
Martinez et al. (2012)
4
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Origami
EngineeringMaterials & Fabrication
Theory and Analysis System Design
Living hingeLee et al. (2013)Black LAB Architects (2014) C. Hoberman (2012) Graphene sheet
Narain et al. (2013)
Wei et al. (2013)
Tachi (2010)
Hawkes et al.
(2010)
Chen et al. (2015)Demaine and Demaine (2012)
Belcastro and Hull (2013)
5
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Kinematic “rigid” folding
Elastic deformations
Miura-ori Tube
Miura-ori Tube Origami
6
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SPanel Shear &
Stretching B Panel Bending F Fold Bending
Model with bars elements Model with rotational hinge Model with rotational hinge
Full tube model Full tube model Full tube model
Curvature
Straight
Straight
Prescribed fold line
Elastic Modeling for Origami
7
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1. Simplicity in the design and use
2. Insight on stiffness properties
7. Elasto-plastic folds
6. Large displacements
Sch
en
k a
nd
Gue
st (2
01
0)
Fili
po
v, T
ach
i, P
au
lino
(20
16
) O
rig
am
i 6 3. Scalability
5. Material properties- Thickness t
- Poisson’s Ratio 𝜈
- Young’s modulus E
- Density ρ
4. Model isotropy
Fili
po
v, L
iu, Ta
ch
i, P
au
lino
(20
16
) In
Pre
pa
ratio
n
Nagasawa et al. (2003)
Benefits of the Bar and Hinge Model
1 2
3
4, 5
6 7
8
𝝂 = 1/3
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Bar stiffness definitions
Poisson’s ratio: 𝜈
Young’s modulus: E
Thickness: t
S Bar Model for Panel Shear & Stretching
Poisson effect
Bar areas:
Poisson’s ratio (𝜈)
0 0.1 0.2 0.3 0.4 0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Poisson Ration ()
Pro
po
rtio
n o
f to
tri
bu
tary
are
a
Edge Bars
Diagonal Bars
X & Y bars
Diagonal bars
Ba
r A
rea
s
9
𝜀𝑥 = 𝜈 ∗ 𝜀𝑦
𝝂 = 1/3𝐘
𝐗
𝐾𝑆 =𝐸𝐴𝐵𝑎𝑟𝑠
𝐿
𝐴𝑌 = 𝑡𝑊2 − ν𝐻2
2𝑊 1 − ν2
𝐴𝐷 = 𝑡𝜈 𝐻2 −𝑊2 3/2
2𝐻𝑊 1 − ν2
𝝂 = 1/2𝝂 ≈ 0
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B Bending Thin Sheet with Restricted Edges
Constant curvature bending Bending restricted at edges
Curvature
Straight
• Bending is localized in the
center of span
• Stiffness is higher than with
constant curvature bending
Lobkovsky AE (1996)10
𝐾𝐵 = 𝐶𝐵𝐸𝑡3
12(1 − ν2)
𝐿2𝑡
1/3
Sagging
Fixed
edges
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• RFP = 1/10 relates panel to fold stiffness
• Stiffness scales with LF
• RFP may depend on physical and
material properties
StraightLF
F Modeling Prescribed Fold Lines
Bending restricted at edges Bending at prescribed fold line
11
𝐾𝐹 = 𝑅𝐹𝑃𝐶𝐵𝐿𝐹2
𝐸𝑡3
12(1 − ν2)
1
𝑡
1/3
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SPanel Shear &
Stretching B Panel Bending F Fold Bending
Curvature
Straight
Prescribed fold line
• Scalability
• Material properties t, E, and 𝜈
• Model isotropy
Filipov E, Tachi T, and Paulino GH (2016) Origami 6
Straight
12
𝐊 =𝐂𝐉𝐵𝐉𝐹
𝑇 𝐊𝑆 𝟎 𝟎𝟎 𝐊𝐵 𝟎𝟎 𝟎 𝐊𝐹
𝐂𝐉𝐵𝐉𝐹
Filipov E, Liu K, Tachi T, and Paulino GH (2016) In Preparation
𝐾𝐹 = 𝑅𝐹𝑃𝐶𝐵𝐿𝐹2
𝐸𝑡3
12(1 − ν2)
1
𝑡
13
𝐾𝑆 =𝐸𝐴𝐵𝑎𝑟𝑠
𝐿𝐾𝐵 = 𝐶𝐵
𝐸𝑡3
12(1 − ν2)
𝐿2𝑡
13
FX = 0.5 FX = 0.5
Δ𝑥
𝑾 = 𝟏
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Eigenvalue Analyses
K = Stiffness matrix
M = Mass matrixEigenvalue Eigen-mode
Mode 7
Mode 8
Mode 9
Mode 7
Mode 8
Mode 9
Sheet Tube
13
𝐊𝐯𝑖 = λ𝑖𝐌𝐯𝑖 𝑖 = 1,… , 𝑁𝑑𝑜𝑓
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Tube Assemblages
Aligned coupling Internal coupling Zipper coupling
Schenk and Guest (2013)
14
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Aligned Internal ZipperSingle tube
15
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Commentary by:
Reis PM, López Jiménez F,
and Marthelot J
Filipov EF, Tachi T, and Paulino GH (2015) PNAS Vol. 112, No. 40 16
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Sheet
Zipper
Tube
Energy Distribution
17
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Stiffness in Y-Z Plane
Load applied
perpendicular
to X axis
At 70% extensionAt 40% extension At 95% extension
18
Zipper Aligned Internal
Zipper
Aligned
Internal
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Cellular Assemblages as Metamaterials
Aizenberg et al. (2005) Heimbs (2013)Meza et al. (2014)Ashby et al. (1985)
Nature Engineering
• High stiffness to weight ratios
• Hierarchical properties (e.g. lattice systems)
• Novel properties (auxetics or asymmetry)
• Deployable
• Self-assembly
• Tunable characteristics
With origami:
19
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Cartesian compression tests
3D Printed Metamaterials
Zipper + Aligned AssemblageA
lig
ned
20
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Self-Interlocking Structure
Bridge Structure
21
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• Geometric variations
• Thickness
• Material
• Fabrication
• ….
• Tailored applications
at different scales
• Localized adaptations
Extensions and Future of Zipper Tubes
22
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Filipov, Tachi, and Paulino (2016) Proceeding of the Royal Society – A, Vol. 472, No. 2185
Tachi and Miura (2009)
Foldable Polygonal Tubes
23
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Any Section w/ Translational Symmetry
24Filipov et al. (2016) PRSA
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Projection Definitions
25Filipov et al. (2016) PRSA
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No
n-s
ym
me
tric
X-Y
Sym
me
tric
X-Y
-Z
26Filipov et al. (2016) PRSA
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Reconfiguration
27Filipov et al. (2016) PRSA
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𝒏 = 2switches
Reconfiguration with 𝒏 = 2 Switches
28Filipov et al. (2016) PRSA
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Switches # Configurations
𝑛 = 0 1
𝑛 = 1 2
𝑛 = 2 6
𝑛 = 3 20
𝑛 = 4 70
𝑛 = 5 252
Central Binomial Coefficient𝒏 = 4
65 more!!
Physical model, 𝒏 = 4 switches
I II
Reconfiguration with More Switches
29Filipov et al. (2016) PRSA
# Configurations =2𝑛 !
(𝑛!)2
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Filipov et al. (2016) PRSA
Analy
tical
ϕ = 85˚
ϕ = 65˚
Out-of-Plane Compression of a Pipe
ϕ=
65°
ϕ=
85°
30
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• Improved structural analysis
for origami
• A variety of cellular systems
• Zipper-coupled systems
engage thin sheet in
shear/stretching
• Polygonal cross-sections
and curved profiles
• Structural tuning through
reconfiguration
Summary of E. Filipov Ph.D. Research
31
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2 Cellular Assemblages
1 Analytical Methods for Folding Structures
3 Hinged Structures
Nonlinearity Multi-Physical
Thickness
Multi-FunctionalDesign and Manufacturing
Ma and You (2014)
Hobermban (1990)
Bianchi et al. (2015)
Future Research Directions
32
Actuation & Assembly
Hawkes et al. (2010)
Mechanical Function Tunable Systems
Hinges
Paik et al. (2011)
Silverberg
et al. (2015)
Deployment
Zirbel et al. (2013)
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33Bianchi et al. (2015)
Heat Transfer / Heat Effects
Gattas & You (2015)
Cellular Reconfiguration
1 Analytical Methods for Folding Structures
Electromagnetics
Thermo-Mechanical Thermodynamics Fluid-Structure
Acoustics
Large Displacements Instabilities Hinge Eccentricity
Energy Dissipation Stress Concentrations Nonlinearities
Parametric Unit-Cell Analyses
Cheung et al. (2014)
Multi-Physical Models
Bistable Square-Twist
Silverberg et al. (2015) Nature Mat.
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34
2 Metamaterials from Cellular Assemblages
Thermal BridgingHigh Insulation
Variable Thermal Conductivity
Cho and Gracias
(2009)
In S
pace
On
Eart
h
Thermal Bridging High Insulation
Schenk et al. (2014)
Mechanical Metamaterials
Alderson (1999)
HyRel 3D Printers (2016)
Blast Resistance Auxetic
Non-auxetic
Ad
dit
ive
Ma
nu
fac
turi
ng
Se
lf-A
ss
em
bly
of
Pe
rfo
rate
d S
he
ets
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35
3 Hinged Systems with Thickness
Tachi (2010)
• Added function with hinges
Chen et al. (2015) Science
Hobermban (1990)
• Optimal packing and panels
with varying thickness
• Hinge packing
System Design for:
• Efficient and safe deployment/motion
• Multi-functional reconfiguration
• Pre-fabrication and modular systemsHawkes et al.
(2010)
• Hinge design
Roche, Mattoni & Weinand (2015)