Adding programmable function to elastic metamaterials makes them versatile and intelligent. The objective of this study is to design and demonstrate thermomechanically tunable metamaterials with a compliant porous structure (CPS) and to analyze their thermomechanical behaviors. CPS, the unit cell of the metamaterial, is composed of rectangular holes, slits, and bimaterial hinges. By decomposing kinematic rotation of a linked arm and elastic deformation of a bimaterial hinge, a thermomechanical constitutive model of CPS is constructed, and the constitutive model is extended to a three-dimensional (3D) polyhedron structure for securing isotropic thermal properties. Temperature-dependent properties of base materials are implemented to the analytical model. The analytical model is verified with finite element (FE) based numerical simulations. A controllable range of temperature and strain is identified that is associated with a thermal deformation of the bimaterial hinge and contact on the slit surfaces of CPS. We also investigate the effect of geometry of CPS on the thermal expansion and effective stiffness of the metamaterial. The metamaterial with CPS has multiple transformation modes in response to temperature while keeping the same mechanical properties at room temperature, such as effective moduli and Poisson’s ratios. This work will pave the road toward the design of programmable metamaterials with both mechanically and thermally tunable capability, providing unique thermomechanical properties with a programmable function.

References

References
1.
Lakes
,
R.
,
1987
, “
Foam Structures With a Negative Poisson’s Ratio
,”
Science
,
235
(
4792
), pp.
1038
1040
.
2.
Evans
,
K. E.
, and
Alderson
,
A.
,
2000
, “
Auxetic Materials: Functional Materials and Structures From Lateral Thinking
,”
Adv. Mater.
,
12
(
9
), pp.
617
628
.
3.
Mitschke
,
H.
,
Schwerdteger
,
J.
,
Fabian
,
S.
,
Stingl
,
M.
,
Korner
,
C.
,
Singer
,
R. F.
,
Robins
,
V.
,
Mecke
,
K.
, and
Schroder-Turk
,
G.
,
2011
, “
Finding Auxetic Frameworks I Periodic Tessellations
,”
Adv. Mater.
,
23
(22–23), pp.
2669
2674
.
4.
Lakes
,
R.
,
1996
, “
Cellular Solid Structures With Unbounded Thermal Expansion
,”
J. Mater. Sci. Lett.
,
15
(
6
), pp.
475
477
.
5.
Sigmund
,
O.
, and
Torquato
,
S.
,
1996
, “
Composites With Extremal Thermal Expansion Coefficients
,”
Appl. Phys. Lett.
,
69
(
21
), pp.
3203
3205
.
6.
Sarilis
,
A. A.
,
Pasala
,
D. T. R.
,
Constantinou
,
M. C.
,
Reinhorn
,
A. M.
,
Nagarajaiah
,
S.
, and
Tayor
,
D. P.
,
2013
, “
Negative Stiffness Device for Seismic Protection of Structures
,”
ASCE J. Struct. Eng.
,
139
(
7
), pp.
1124
1133
.
7.
Duoss
,
E. B.
,
Weisgraber
,
T. H.
,
Zhu
,
C.
,
Small
,
I. V. W.
,
Metz
,
T. R.
,
Verice
,
J. J.
,
Barth
,
H. D.
,
Kuntz
,
J. D.
,
Maxwell
,
R. S.
,
Spadacini
,
C. M.
, and
Wilson
,
T. S.
,
2014
, “
Three-Dimensional Printing of Elastomeric, Cellular Architectures With Negative Stiffness
,”
Adv. Funct. Mater.
,
24
(
31
), pp.
4905
4913
.
8.
Shim
,
J.
,
Shan
,
S.
,
Kosmrlj
,
A.
,
Kang
,
S. H.
,
Chen
,
E. R.
,
Weaver
,
J. C.
, and
Bertoldi
,
K.
,
2013
, “
Harnessing Instabilities for Design of Soft Reconfigurable Auxetic/Chiral Materials
,”
Soft Matter
,
9
(
34
), pp.
8198
8202
.
9.
Rafsanjani
,
A.
,
Akbarzadeh
,
A.
, and
Pasini
,
D.
,
2015
, “
Snapping Mechanical Metamaterials Under Tension
,”
Adv. Mater.
,
27
(
39
), pp.
5931
5935
.
10.
Lakes
,
R.
, and
Wojciechowski
,
K. W.
,
2008
, “
Negative Compressibility, Negative Poisson’s Ratio, and Stability
,”
Phys. Status Solidi B
,
245
(
3
), pp.
545
551
.
11.
Huang
,
C. W.
,
Ren
,
W.
,
Nguyen
,
V. C.
,
Chen
,
Z.
,
Wang
,
J.
,
Sritharan
,
T.
, and
Chen
,
L.
,
2012
, “
Abnormal Poisson’s Ratio and Linear Compressibility in Perovskite Materials
,”
Adv. Mater.
,
24
(
30
), pp.
4170
4174
.
12.
Ortiz
,
A. U.
,
Boutin
,
A.
,
Fuchs
,
A. H.
, and
Coudert
,
F. X.
,
2012
, “
Anisotropic Elastic Properties of Flexible Metal-Organic Frameworks: How Soft Are Soft Porous Crystals?
,”
Phys. Rev. Lett.
,
109
(
19
), p.
195502
.
13.
Daraio
,
C.
,
Ngo
,
D.
,
Nesterenko
,
V. F.
, and
Fraternali
,
F.
, “
Highly Nonlinear Pulse Splitting and Recombination in a Two-Dimensional Granular Network
,”
Phys. Rev. E
,
82
(
3
), p.
036603
.
14.
Pasternak
,
E.
, and
Dyskin
,
A. V.
,
2012
, “
Materials and Structures With Macroscopic Negative Poisson’s Ratio
,”
Int. J. Eng. Sci.
,
52
, pp.
103
114
.
15.
Fraternali
,
F.
,
Senatore
,
L.
, and
Daraio
,
C.
,
2012
, “
Solitary Waves on Tensegrity Lattices
,”
J. Mech. Phys. Solids
,
60
(
6
), pp.
1137
1144
.
16.
Amendola
,
A.
,
Carpentieri
,
G.
,
De Oliveira
,
M.
,
Skelton
,
R. E.
, and
Fraternali
,
F.
,
2014
, “
Experimental Investigation of the Softening-Stiffening Response of Tensegrity Prisms under Compressive Loading
,”
Compos. Struct.
,
117
, pp.
234
243
.
17.
Zhang
,
L.-Y.
,
Li
,
Y.
,
Cao
,
Y.-P.
, and
Feng
,
X.-Q.
,
2014
, “
Stiffness Matrix Based Form-Finding Method of Tensegrity Structures
,”
Eng. Struct.
,
58
, pp.
36
48
.
18.
Schenk
,
M.
, and
Guest
,
S. D.
,
2013
, “
Geometry of Miura-Folded Metamaterials
,”
Proc. Natl. Acad. Sci. U. S. A.
,
110
(
9
), pp.
3276
3281
.
19.
Wei
,
Z. Y.
,
Guo
,
Z. V.
,
Dudte
,
L.
,
Kiang
,
H. Y.
, and
Mahadevan
,
L.
,
2013
, “
Geometric Mechanics of Periodic Pleated Origami
,”
Phys. Rev. Lett.
,
110
(
21
), p.
215501
.
20.
Shan
,
S.
,
Kang
,
S. H.
,
Wang
,
P.
,
Qu
,
C.
,
Shian
,
S.
,
Chen
,
E. R.
, and
Bertoldi
,
K.
,
2014
, “
Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves
,”
Adv. Funct. Mater.
,
24
(
31
), pp.
4935
4942
.
21.
Mun
,
J.
,
Ju
,
J.
, and
Thurman
,
J.
,
2016
, “
Indirect Fabrication of Lattice Metals With Thin Sections Using Centrifugal Casting
,”
JoVE
,
111
, p.
e53605
.https://www.jove.com/video/53605/indirect-fabrication-lattice-metals-with-thin-sections-using
22.
Mun
,
J.
,
Ju
,
J.
,
Yun
,
B.-G.
, and
Chang
,
B.-M.
,
2015
, “
Indirect Additive Manufacturing Based Casting of a Periodic 3D Cellular Metal—Flow Simulation of Molten Aluminum Alloy
,”
J. Manuf. Process
,
17
, pp.
28
40
.
23.
Hawkes
,
E.
,
An
,
B.
,
Benbernou
,
N. M.
,
Tanaka
,
H.
,
Kim
,
S.
,
Demaine
,
E. D.
,
Rus
,
D.
, and
Wood
,
R. J.
,
2010
, “
Programmable Matter by Folding
,”
Proc. Natl. Acad. Sci. U. S. A.
,
107
(
28
), pp.
12441
12445
.
24.
Liu
,
Y.
,
Boyles
,
J. K.
,
Genzer
,
J.
, and
Dickey
,
M.
,
2012
, “
Self-Folding of Polymer Sheets Using Local Light Absorption
,”
Soft Matter
,
8
(
6
), pp.
1764
1769
.
25.
Tibbits
,
S.
,
2014
, “
4D Printing: Multi-Material Shape Change
,”
Archit. Des.
,
84
(
1
), pp.
116
121
.
26.
Ge
,
Q.
,
Dunn
,
C. K.
,
Qi
,
H. J.
, and
Dunn
,
M. L.
,
2014
, “
Active Origami by 4D Printing
,”
Smart Mater. Struct.
,
23
(
9
), p.
09407
.
27.
Overvelde
,
J. T. B.
,
de Jong
,
T. A.
,
Shevchenko
,
Y.
,
Becerra
,
B. A.
,
Whitesides
,
G. M.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2016
, “
A Three-Dimensional Actuated Origami-Inspired Transformable Metamaterial With Multiple Degrees of Freedom
,”
Nat. Commun.
,
7
, p.
10929
.
28.
Tolley
,
M. T.
,
Kalontarov
,
M.
,
Neubert
,
J.
,
Erickson
,
D.
, and
Lipson
,
H.
,
2010
, “
Stochastic Modular Robotic Systems: A Study of Fluidic Assembly Strategies
,”
IEEE Trans. Rob.
,
26
(
3
), pp.
518
530
.
29.
Gilpin
,
K.
,
Knaian
,
A.
, and
Rus
,
D.
,
2010
, “
Robot Pebbles: One Centimeter Modules for Programmable Matter Through Self-Disassembly
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Anchorage, AK, May 3–7, pp.
2485
2492
.
30.
Davey
,
J.
,
Kwok
,
N.
, and
Yim
,
M.
,
2012
, “
Emulating Self-Reconfigurable Robots—Design of the SMORES System
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Vilamoura, Portugal, Oct. 7–12, pp. 4464–4469.
31.
Yim
,
S.
, and
Sitti
,
M.
,
2014
, “
SoftCubes: Stretchable and Self-Assembling Three-Dimensional Soft Modular Matter
,”
Int. J. Rob. Res.
,
33
(
8
), pp.
1083
1097
.
32.
Overvelde
,
J. T. B.
,
Shan
,
S.
, and
Bertoldi
,
K.
,
2012
, “
Compaction Through Buckling in 2D Periodic. Soft, and Porous Structures: Effect of Pore Shape
,”
Adv. Mater.
,
24
(
17
), pp.
2337
2342
.
33.
Florigin
,
B.
,
Coulais
,
C.
, and
van Hecke
,
M.
,
2014
, “
Programmable Mechanical Metamaterials
,”
Phys. Rev. Lett.
,
113
(
17
), p.
175503
.
34.
Sigmund
,
O.
, and
Torquato
,
S.
,
1997
, “
Design of Materials With Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method
,”
J. Mech. Phys. Solids
,
45
(
6
), pp.
1037
1067
.
35.
Steeves
,
C. A.
,
Lucato
,
S.
,
He
,
M.
,
Antinucci
,
E.
,
Hutchinson
,
J. W.
, and
Evans
,
A. G.
,
2007
, “
Concepts for Structurally Robust Materials That Combine Low Thermal Expansion With High Stiffness
,”
J. Mech. Phys. Solids
,
55
(
9
), pp.
1803
1822
.
36.
Jefferson
,
G.
,
Parthasarathy
,
T. A.
, and
Kerans
,
R. J.
,
2009
, “
Tailorable Thermal Expansion Hybrid Structures
,”
Int. J. Solids Struct.
,
46
(
11
), pp.
2372
2387
.
37.
Kim
,
K.
,
Ju
,
J.
, and
Kim
,
D.-M.
,
2013
, “
Porous Materials With High Negative Poisson’s Ratios—A Mechanism Based Material Design
,”
Smart Mater. Struct.
,
22
(
8
), p.
084007
.
38.
Kim
,
K.
,
Lee
,
J.
,
Ju
,
J.
, and
Kim
,
D.-M.
,
2014
, “
Compliant Cellular Materials With Compliant Porous Structures: A Mechanism-Based Materials Design
,”
Int. J. Solids Struct.
,
51
(
23
), pp.
3889
3903
.
39.
Lee
,
J.
,
Kim
,
K.
,
Ju
,
J.
, and
Kim
,
D.-M.
,
2015
, “
Compliant Cellular Materials With Elliptical Holes for Extremely High Positive and Negative Poisson’s Ratios
,”
ASME J. Eng. Mater. Technol.
,
137
(
1
), p.
011001
.
40.
Kim
,
K.
, and
Ju
,
J.
,
2015
, “
Mechanical Metamaterials With 3D Compliant Porous Structures
,”
Composite Struct.
,
132
, pp.
874
884
.
41.
Timoshenko
,
S.
,
1925
, “
Analysis of Bi-Metal Thermostats
,”
J. Opt. Soc. Am. Rev. Sci. Instrum.
,
11
(
3
), pp.
233
255
.
42.
Heo
,
H.
,
Tessema
,
A.
,
Iqbal
,
S.
,
Ju
,
J.
, and
Kidane
,
A.
,
2015
, “Thermal Stress Analysis of Gypsum Shell Cracking in Polyjet Based Rapid Casting of Cellular Metals,”
ASME
Paper No. IMECE2015-52417.
43.
Evans
,
K. E.
, and
Caddock
,
B. D.
,
1999
, “
Micropurous Materials With Negative Poisson’s Ratios II: Mechanisms and Interpretation
,”
J. Phys. D: Appl. Phys.
,
22
(
12
), p.
1883
.
44.
Ting
,
T. C.
, and
Chen
,
T.
,
2005
, “
Poisson’s Ratio for Anisotropic Elastic Materials Can Have Not Bounds
,”
Q. J. Mech. Appl. Math.
,
58
(
1
), pp.
73
82
.
45.
Ashby
,
M.
, and
Johnson
,
K.
,
2014
,
Materials and Design
,
3rd ed., Butterworth-Heinemann, New York.
46.
Incropera Frank
,
P.
,
DeWitt
,
D. P.
,
Bergman
,
T. L.
, and
Lavine
,
A. S.
,
2013
,
Principles of Heat and Mass Transfer
,
7th ed.
,
Wiley
,
Hoboken, NJ
.
47.
Ha
,
C. S.
,
Hestekin
,
E.
,
Li
,
J.
,
Plesh
,
M. E.
, and
Lakes
,
R. S.
,
2015
, “
Controllable Thermal Expansion of Large Magnitude in Chiral Negative Poisson’s Ratio Lattices
,”
Phys. Status Solidi B
,
252
(
7
), pp.
1431
1434
.
48.
Wu
,
L.
,
Li
,
B.
, and
Zho
,
J.
,
2016
, “
Isotropic Negative Thermal Expansion Metamaterials
,”
ACS Appl. Mater. Interfaces
,
8
(
27
), pp.
17721
17727
.
49.
Lakes
,
R.
,
2007
, “
Cellular Solids With Tunable Positive or Negative Thermal Expansion of Unbounded Magnitude
,”
Appl. Phys. Lett.
,
90
(
22
), p.
221905
.
50.
Xu
,
H.
, and
Pasini
,
D.
,
2016
, “
Structurally Efficient Three-Dimensional Metamaterials With Controllable Thermal Expansion
,”
Sci. Rep.
,
6
, p.
34924
.
You do not currently have access to this content.