Engineering inspired by origami has the potential to impact several areas in the development of morphing structures and mechanisms. Self-folding capabilities in particular are necessary in situations when it may be impractical to exert external manipulations to produce the desired folds (e.g., as in remote applications such as in space systems). In this work, origami principles are utilized to allow planar sheets to self-fold into complex structures along arbitrary folds (i.e., no hinges or pre-engineered locations of folding). The sheets considered herein are composed of shape memory alloy (SMA)-based laminated composites. SMAs are materials that can change their shape by thermal and/or mechanical stimuli. The generation of sheets that can be folded into the desired structures is done using origami design software such as Tachi's freeform origami. Also, a novel in-house fold pattern design software capable of generating straight and curved fold patterns has been developed. The in-house software generates creased and uncreased fold patterns and converts them into finite element meshes that can be analyzed in finite element analysis (FEA) software considering the thermomechanically coupled constitutive response of the SMA material. Finite element simulations are performed to determine whether by appropriately heating the planar unfolded sheet it is possible to fold it into the desired structure. The results show that a wide range of self-folding structures can be folded via thermal stimulus. This is demonstrated by analyzing the folding response of multiple designs generated from freeform origami and the newly developed in-house origami design software.

References

References
1.
Schenk
,
M.
, and
Guest
,
S. D.
,
2011
, “
Origami Folding and Foldability: A Structural Engineering Approach
,”
Fifth International Meeting of Origami Science, Mathematics, and Education
(
5OSME
), Singapore, July 13–17, pp.
291
304
.
2.
Peraza-Hernandez
,
E.
,
Hartl
,
D.
,
Malak
,
R.
, Jr.
, and
Lagoudas
,
D.
,
2014
, “
Origami-Inspired Active Structures: A Synthesis and Review
,”
Smart Mater. Struct.
,
23
(
9
), p.
094001
.
3.
Greenberg
,
H. C.
,
Gong
,
M. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2011
, “
Identifying Links Between Origami and Compliant Mechanisms
,”
Mech. Sci.
,
2
(
2
), pp.
217
225
.
4.
Dureisseix
,
D.
,
2012
, “
An Overview of Mechanisms and Patterns With Origami
,”
Int. J. Space Struct.
,
27
(
1
), pp.
1
14
.
5.
Bowen
,
L. A.
,
Grames
,
C. L.
,
Magleby
,
S. P.
,
Howell
,
L. L.
, and
Lang
,
R. J.
,
2013
, “
A Classification of Action Origami as Systems of Spherical Mechanisms
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111008
.
6.
Bowen
,
L. A.
,
Baxter
,
W. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2014
, “
A Position Analysis of Coupled Spherical Mechanisms Found in Action Origami
,”
Mech. Mach. Theory
,
77
, pp.
13
24
.
7.
Hawkes
,
E.
,
An
,
B.
,
Benbernou
,
N.
,
Tanaka
,
H.
,
Kim
,
S.
,
Demaine
,
E. D.
,
Rus
,
D.
, and
Wood
,
R. J.
,
2010
, “
Programmable Matter by Folding
,”
Proc. Natl. Acad. Sci.
,
107
(
28
), pp.
12441
12445
.
8.
Lagoudas
,
D.
,
2008
,
Shape Memory Alloys: Modeling and Engineering Applications
,
Springer
,
New York
.
9.
Peraza-Hernandez
,
E.
,
Hartl
,
D.
,
Galvan
,
E.
, and
Malak
,
R.
,
2013
, “
Design and Optimization of a Shape Memory Alloy-Based Self-Folding Sheet
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111007
.
10.
Peraza-Hernandez
,
E.
,
Hartl
,
D.
, and
Malak
,
R.
, Jr.
,
2013
, “
Design and Numerical Analysis of an SMA Mesh-Based Self-Folding Sheet
,”
Smart Mater. Struct.
,
22
(
9
), p.
094008
.
11.
Peraza Hernandez
,
E.
,
Hu
,
S.
,
Kung
,
H.
,
Hartl
,
D.
, and
Akleman
,
E.
,
2013
, “
Towards Building Smart Self-Folding Structures
,”
Comput. Graphics
,
37
(
6
), pp.
730
742
.
12.
Powledge
,
A.
,
Hartl
,
D.
, and
Malak
,
R.
,
2014
, “
Experimental Analysis of Self-Folding SMA-Based Sheet Design for Simulation Validation
,”
ASME
Paper No. SMASIS2014-7546.
13.
Powledge
,
A. C.
,
2015
, “
Experimental Characterization and Validated Multi-Fidelity Analysis of Reconfigurable Curvature in Shape Memory Alloy Composite Sheets
,” Master's thesis, Texas A&M University, College Station, TX.
14.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
15.
Onal
,
C. D.
,
Wood
,
R. J.
, and
Rus
,
D.
,
2011
, “
Towards Printable Robotics: Origami-Inspired Planar Fabrication of Three-Dimensional Mechanisms
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Shanghai, May 9–13, pp.
4608
4613
.
16.
Tachi
,
T.
,
2010
, “
Freeform Variations of Origami
,”
J. Geom. Graphics
,
14
(
2
), pp.
203
215
.
17.
Tachi
,
T.
,
2010
, “
Freeform Rigid-Foldable Structure Using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh
,”
Advances in Architectural Geometry 2010
,
Springer-Verlag
,
Vienna, Austria
, pp.
87
102
.
18.
Tachi
,
T.
, “
Freeform Origami
,” http://www.tsg.ne.jp/TT/software/
19.
Huffman
,
D. A.
,
1976
, “
Curvature and Creases: A Primer on Paper
,”
IEEE Trans. Comput.
,
C-25
(
10
), pp.
1010
1019
.
20.
Demaine
,
E.
,
Demaine
,
M.
,
Koschitz
,
D.
, and
Tachi
,
T.
,
2011
, “
Curved Crease Folding: A Review on Art, Design and Mathematics
,”
IABSE-IASS Symposium: Taller, Longer, Lighter (IABSE-IASS2011)
,
London
, Sept. 20–23, pp.
20
23
.
21.
Kilian
,
M.
,
Flöry
,
S.
,
Chen
,
Z.
,
Mitra
,
N. J.
,
Sheffer
,
A.
, and
Pottmann
,
H.
,
2008
, “
Curved Folding
,”
ACM Trans. Graphics
,
27
(
3
), p.
75
.
22.
Dias
,
M. A.
,
Dudte
,
L. H.
,
Mahadevan
,
L.
, and
Santangelo
,
C. D.
,
2012
, “
Geometric Mechanics of Curved Crease Origami
,”
Phys. Rev. Lett.
,
109
(
11
), p.
114301
.
23.
Jackson
,
P.
,
2011
,
Folding Techniques for Designers: From Sheet to Form
,
Laurence King Publishing
,
London
.
24.
Akleman
,
E.
,
Chen
,
J.
, and
Meric
,
B.
,
2000
, “
Intuitive and Effective Design of Periodic Symmetric Tiles
,”
ACM Multimedia
,
21
(
4
), pp.
100
108
.
25.
Schwarzenberger
,
R.
,
1974
, “
The 17 Plane Symmetry Groups
,”
Math. Gaz.
,
58
(
404
), pp.
123
131
.
26.
Hu
,
S.
,
Xing
,
Q.
,
Akleman
,
E.
,
Chen
,
J.
, and
Gross
,
J.
,
2012
, “
Pattern Mapping With Quad-Pattern-Coverable Quad-Meshes
,”
Comput. Graphics
,
36
(
5
), pp.
455
465
.
27.
Bartels
,
R.
,
Beatty
,
J.
, and
Barsky
,
B.
,
1987
,
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling
,
Morgan Kaufmann
,
Los Altos, CA
.
28.
Gross
,
J.
, and
Tucker
,
T.
,
2001
,
Topological Graph Theory
,
Courier Dover Publications
,
New York
.
29.
Akleman
,
E.
,
Xing
,
Q.
,
Garigipati
,
P.
,
Taubin
,
G.
,
Chen
,
J.
, and
Hu
,
S.
,
2013
, “
Hamiltonian Cycle Art: Surface Covering Wire Sculptures and Duotone Surfaces
,”
Comput. Graphics
,
37
(
5
), pp.
316
332
.
30.
Akleman
,
E.
, and
Chen
,
J.
,
1999
, “
Guaranteeing the 2-Manifold Property for Meshes With Doubly Linked Face List
,”
Int. J. Shape Model.
,
5
(
2
), pp.
149
177
.
31.
Akleman
,
E.
, and
Chen
,
J.
,
2006
, “
Insight for Practical Subdivision Modeling With Discrete Gauss–Bonnet Theorem
,” 4th International Conference of
Geometry Modeling and Processing
(
GMP 2006
), Pittsburgh, PA, July 26–28,
Springer
,
Berlin
, pp.
287
298
.
32.
Peraza-Hernandez
,
E.
,
Hartl
,
D.
, and
Lagoudas
,
D.
,
2013
, “
Modeling of Shape Memory Alloy Wire Meshes Using Effective Lamina Properties for Improved Analysis Efficiency
,”
ASME
Paper No. SMASIS2013-3094.
33.
Peraza Hernandez
,
E. A.
,
Kiefer
,
B.
,
Hartl
,
D. J.
,
Menzel
,
A.
, and
Lagoudas
,
D. C.
,
2015
, “
Analytical Investigation of Structurally Stable Configurations in Shape Memory Alloy-Actuated Plates
,”
Int. J. Solids Struct.
,
6970
, pp.
442
458
.
34.
Lagoudas
,
D.
,
Hartl
,
D.
,
Chemisky
,
Y.
,
Machado
,
L.
, and
Popov
,
P.
,
2012
, “
Constitutive Model for the Numerical Analysis of Phase Transformation in Polycrystalline Shape Memory Alloys
,”
Int. J. Plast.
,
32
, pp.
155
183
.
35.
Boehler
,
J. P.
, ed.,
1986
,
Applications of Tensor Functions in Solid Mechanics
(CISM International Centre for Mechanical Sciences),
Springer-Verlag
,
Wien, Austria
.
36.
Peraza-Hernandez
,
E.
,
Hartl
,
D.
,
Kotz
,
A.
, and
Malak
,
R.
, Jr.
,
2014
, “
Design and Optimization of an SMA-Based Self-Folding Structural Sheet With Sparse Insulating Layers
,”
ASME
Paper No. SMASIS2014-7540.
37.
Hughes
,
T.
, and
Winget
,
J.
,
1980
, “
Finite Rotation Effects in Numerical Integration of Rate Constitutive Equations Arising in Large-Deformation Analysis
,”
Int. J. Numer. Methods Eng.
,
15
(
12
), pp.
1862
1867
.
38.
Hartl
,
D. J.
, and
Lagoudas
,
D. C.
,
2009
, “
Constitutive Modeling and Structural Analysis Considering Simultaneous Phase Transformation and Plastic Yield in Shape Memory Alloys
,”
Smart Mater. Struct.
,
18
(
10
), p.
104017
.
39.
Peraza-Hernandez
,
E. A.
,
Frei
,
K. R.
,
Hartl
,
D. J.
, and
Lagoudas
,
D. C.
,
2014
, “
Folding Patterns and Shape Optimization Using SMA-Based Self-Folding Laminates
,”
Proc. SPIE
,
9057
, p.
90571G
.
40.
DeGarmo
,
E. P.
,
Black
,
J. T.
, and
Kohser
,
R. A.
,
2003
,
Materials and Process in Manufacturing
,
Wiley
,
New York
.
41.
Demaine
,
E. D.
,
Demaine
,
M. L.
,
Hart
,
V.
,
Price
,
G. N.
, and
Tachi
,
T.
,
2011
, “
(Non)Existence of Pleated Folds: How Paper Folds Between Creases
,”
Graphs Combinatorics
,
27
(
3
), pp.
377
397
.
42.
Abel
,
J.
,
Luntz
,
J.
, and
Brei
,
D.
,
2013
, “
Hierarchical Architecture of Active Knits
,”
Smart Mater. Struct.
,
22
(
12
), p.
125001
.
43.
Abel
,
J.
,
Luntz
,
J.
, and
Brei
,
D.
,
2012
, “
A Two-Dimensional Analytical Model and Experimental Validation of Garter Stitch Knitted Shape Memory Alloy Actuator Architecture
,”
Smart Mater. Struct.
,
21
(
8
), p.
085011
.
44.
Demaine
,
E. D.
,
Demaine
,
M. L.
,
Huffman
,
D. A.
,
Koschitz
,
D.
, and
Tachi
,
T.
,
2015
, “
Characterization of Curved Creases and Rulings: Design and Analysis of Lens Tessellations
,”
Origami6: I. Mathematics
,
American Mathematical Society
,
Providence, RI
, pp.
209
230
.
You do not currently have access to this content.