Abstract

Multistable metastructure can be used as a reusable energy-absorbing structure which is usually accompanied by relatively low energy absorption capacity. In this work, a novel structure with variable cross-sectional width was designed to improve the energy dissipation efficiency of multistable structures. To this end, we theoretically obtained the specific optimization configuration of the bistable unit cell structure. Compared to the traditional bistable unit cell structure with uniform curved beam, the as-obtained optimized structure showed improved mechanical properties, while maximum strain remained relatively reduced during deformation. Systematic parameter analyses were carried out through theoretical analysis, finite element simulation, and experimental verification to determine the optimized range of the unit cell structure. Compared to the traditional structure with the same maximum strain during deformation, the mechanical properties like the maximum peak force, minimum negative force, and energy absorption efficiency of the optimized structure increased by at least 155%, 91%, and 136%, respectively.

References

1.
Schaedler
,
T. A.
, and
Carter
,
W. B.
,
2016
, “
Architected Cellular Materials
,”
Annu. Rev. Mater. Res.
,
46
(
1
), pp.
187
210
.
2.
Bertoldi
,
K.
,
Vitelli
,
V.
,
Christensen
,
J.
, and
van Hecke
,
M.
,
2017
, “
Flexible Mechanical Metamaterials
,”
Nat. Rev. Mater.
,
2
(
11
), p.
17066
.
3.
Fu
,
H.
,
Nan
,
K.
,
Bai
,
W.
,
Huang
,
W.
,
Bai
,
K.
,
Lu
,
L.
,
Zhou
,
C.
, et al
,
2018
, “
Morphable 3D Mesostructures and Microelectronic Devices by Multistable Buckling Mechanics
,”
Nat. Mater.
,
17
(
3
), pp.
268
276
.
4.
Khajehtourian
,
R.
, and
Kochmann
,
D. M.
,
2021
, “
A Continuum Description of Substrate-Free Dissipative Reconfigurable Metamaterials
,”
J. Mech. Phys. Solids
,
147
, p.
104217
.
5.
Lakes
,
R.
,
1987
, “
Foam Structures With a Negative Poisson's Ratio
,”
Science
,
235
(
4792
), pp.
1038
1040
.
6.
Bertoldi
,
K.
,
Reis
,
P. M.
,
Willshaw
,
S.
, and
Mullin
,
T.
,
2010
, “
Negative Poisson’s Ratio Behavior Induced by an Elastic Instability
,”
Adv. Mater.
,
22
(
3
), pp.
361
366
.
7.
Haghpanah
,
B.
,
Salari-Sharif
,
L.
,
Pourrajab
,
P.
,
Hopkins
,
J.
, and
Valdevit
,
L.
,
2016
, “
Multistable Shape-Reconfigurable Architected Materials
,”
Adv. Mater.
,
28
(
36
), pp.
7915
7920
.
8.
Shi
,
J.
,
Mofatteh
,
H.
,
Mirabolghasemi
,
A.
,
Desharnais
,
G.
, and
Akbarzadeh
,
A.
,
2021
, “
Programmable Multistable Perforated Shellular
,”
Adv. Mater.
,
33
(
42
), p.
e2102423
.
9.
Lin
,
X.
,
Pan
,
F.
,
Yang
,
K.
,
Guan
,
J.
,
Ding
,
B.
,
Liu
,
Y.
,
Yang
,
K.
,
Liu
,
B.
, and
Chen
,
Y.
,
2021
, “
A Stair-Building Strategy for Tailoring Mechanical Behavior of Re-customizable Metamaterials
,”
Adv. Funct. Mater.
,
31
(
37
), p.
2101808
.
10.
Liu
,
J.
,
Qin
,
H.
, and
Liu
,
Y.
,
2018
, “
Dynamic Behaviors of Phase Transforming Cellular Structures
,”
Compos. Struct.
,
184
, pp.
536
544
.
11.
Cui
,
S.
, and
Harne
,
R. L.
,
2018
, “
Characterizing the Nonlinear Response of Elastomeric Material Systems Under Critical Point Constraints
,”
Int. J. Solids Struct.
,
135
, pp.
197
207
.
12.
Meaud
,
J.
, and
Che
,
K.
,
2017
, “
Tuning Elastic Wave Propagation in Multistable Architected Materials
,”
Int. J. Solids Struct.
,
122–123
, pp.
69
80
.
13.
Goldsberry
,
B. M.
, and
Haberman
,
M. R.
,
2018
, “
Negative Stiffness Honeycombs As Tunable Elastic Metamaterials
,”
J. Appl. Phys.
,
123
(
9
), p.
091711
.
14.
Li
,
C.
,
Luo
,
H.
, and
Song
,
J.
,
2021
, “
Magnetically Driven Non-contact Transfer Printing Based on a Bi-stable Elastomeric Stamp
,”
Adv. Mater. Technol.
,
6
(
11
), p.
2100335
.
15.
Tan
,
X.
,
Chen
,
S.
,
Wang
,
B.
,
Zhu
,
S.
,
Wu
,
L.
, and
Sun
,
Y.
,
2019
, “
Design, Fabrication, and Characterization of Multistable Mechanical Metamaterials for Trapping Energy
,”
Extreme Mech. Lett.
,
28
, pp.
8
21
.
16.
Yang
,
H.
, and
Ma
,
L.
,
2020
, “
1D to 3D Multi-stable Architected Materials With Zero Poisson’s Ratio and Controllable Thermal Expansion
,”
Mater. Des.
,
188
, p.
108430
.
17.
Yu
,
H.
,
Liang
,
B.
,
Zhao
,
Z.
,
Liu
,
P.
,
Lei
,
H.
,
Song
,
W.
,
Chen
,
M.
, and
Guo
,
X.
,
2021
, “
Metamaterials With a Controllable Thermal-Mechanical Stability: Mechanical Designs, Theoretical Predictions and Experimental Demonstrations
,”
Compos. Sci. Technol.
,
207
, p.
108694
.
18.
Qiu
,
J.
,
Lang
,
J. H.
, and
Slocum
,
A. H.
,
2004
, “
A Curved-Beam Bistable Mechanism
,”
J. Microelectromech. Syst.
,
13
(
2
), pp.
137
146
.
19.
Restrepo
,
D.
,
Mankame
,
N. D.
, and
Zavattieri
,
P. D.
,
2015
, “
Phase Transforming Cellular Materials
,”
Extreme Mech. Lett.
,
4
, pp.
52
60
.
20.
Kidambi
,
N.
,
Harne
,
R. L.
, and
Wang
,
K. W.
,
2017
, “
Energy Capture and Storage in Asymmetrically Multistable Modular Structures Inspired by Skeletal Muscle
,”
Smart Mater. Struct.
,
26
(
8
), p.
085011
.
21.
Yang
,
H.
, and
Ma
,
L.
,
2018
, “
Multi-stable Mechanical Metamaterials With Shape-Reconfiguration and Zero Poisson’s Ratio
,”
Mater. Des.
,
152
, pp.
181
190
.
22.
Ren
,
C.
,
Yang
,
D.
, and
Qin
,
H.
,
2018
, “
Mechanical Performance of Multidirectional Buckling-Based Negative Stiffness Metamaterials: An Analytical and Numerical Study
,”
Materials
,
11
(
7
), p.
1078
.
23.
Hua
,
J.
,
Lei
,
H.
,
Zhang
,
Z.
,
Gao
,
C.
, and
Fang
,
D.
,
2019
, “
Multistable Cylindrical Mechanical Metastructures: Theoretical and Experimental Studies
,”
ASME J. Appl. Mech.
,
86
(
7
), p.
071007
.
24.
Gao
,
R.
,
Guo
,
S.
,
Tian
,
X.
, and
Liu
,
S.
,
2021
, “
A Negative-Stiffness Based 1D Metamaterial for Bidirectional Buffering and Energy Absorption With State Recoverable Characteristic
,”
Thin-Walled Struct.
,
169
, p.
108319
.
25.
Rafsanjani
,
A.
,
Akbarzadeh
,
A.
, and
Pasini
,
D.
,
2015
, “
Snapping Mechanical Metamaterials Under Tension
,”
Adv. Mater.
,
27
(
39
), pp.
5931
5935
.
26.
Zhao
,
J.
,
Jia
,
J.
,
He
,
X.
, and
Wang
,
H.
,
2008
, “
Post-Buckling and Snap-Through Behavior of Inclined Slender Beams
,”
ASME J. Appl. Mech.
,
75
(
4
), p.
041020
.
27.
Shan
,
S.
,
Kang
,
S. H.
,
Raney
,
J. R.
,
Wang
,
P.
,
Fang
,
L.
,
Candido
,
F.
,
Lewis
,
J. A.
, and
Bertoldi
,
K.
,
2015
, “
Multistable Architected Materials for Trapping Elastic Strain Energy
,”
Adv. Mater.
,
27
(
29
), pp.
4296
4301
.
28.
Chen
,
T.
,
Mueller
,
J.
, and
Shea
,
K.
,
2017
, “
Integrated Design and Simulation of Tunable, Multi-state Structures Fabricated Monolithically With Multi-material 3D Printing
,”
Sci. Rep.
,
7
(
1
), p.
45671
.
29.
Danso
,
L. A.
, and
Karpov
,
E. G.
,
2017
, “
Cusp Singularity-Based Bistability Criterion for Geometrically Nonlinear Structures
,”
Extreme Mech. Lett.
,
13
, pp.
135
140
.
30.
Ha
,
C. S.
,
Lakes
,
R. S.
, and
Plesha
,
M. E.
,
2018
, “
Design, Fabrication, and Analysis of Lattice Exhibiting Energy Absorption Via Snap-Through Behavior
,”
Mater. Des.
,
141
, pp.
426
437
.
31.
Liu
,
S.
,
Azad
,
A. I.
, and
Burgueño
,
R.
,
2019
, “
Architected Materials for Tailorable Shear Behavior With Energy Dissipation
,”
Extreme Mech. Lett.
,
28
, pp.
1
7
.
32.
Chen
,
B.
,
Chen
,
L.
,
Du
,
B.
,
Liu
,
H.
,
Li
,
W.
, and
Fang
,
D.
,
2021
, “
Novel Multifunctional Negative Stiffness Mechanical Metamaterial Structure: Tailored Functions of Multi-stable and Compressive Mono-stable
,”
Compos. Part B: Eng.
,
204
, p.
108501
.
33.
Tan
,
X.
,
Zhu
,
S.
,
Wang
,
B.
,
Yao
,
K.
,
Chen
,
S.
,
Xu
,
P.
,
Wang
,
L.
, and
Sun
,
Y.
,
2020
, “
Mechanical Response of Negative Stiffness Truncated-Conical Shell Systems: Experiment, Numerical Simulation and Empirical Model
,”
Compos. Part B: Eng.
,
188
, p.
107898
.
34.
Alturki
,
M.
, and
Burgueño
,
R.
,
2019
, “
Response Characterization of Multistable Shallow Domes With Cosine-Curved Profile
,”
Thin-Walled Struct.
,
140
, pp.
74
84
.
35.
Fang
,
H.
,
Chu
,
S. C. A.
,
Xia
,
Y.
, and
Wang
,
K. W.
,
2018
, “
Programmable Self-Locking Origami Mechanical Metamaterials
,”
Adv. Mater.
,
30
(
15
), p.
1706311
.
36.
Luo
,
G.
,
Fu
,
H.
,
Cheng
,
X.
,
Bai
,
K.
,
Shi
,
L.
,
He
,
X.
,
Rogers
,
J. A.
,
Huang
,
Y.
, and
Zhang
,
Y.
,
2019
, “
Mechanics of Bistable Cross-Shaped Structures Through Loading-Path Controlled 3D Assembly
,”
J. Mech. Phys. Solids
,
129
, pp.
261
277
.
37.
Mirkhalaf
,
M.
, and
Barthelat
,
F.
,
2017
, “
Design, 3D Printing and Testing of Architectured Materials With Bistable Interlocks
,”
Extreme Mech. Lett.
,
11
, pp.
1
7
.
38.
Zhu
,
S.
,
Wang
,
B.
,
Tan
,
X.
,
Hu
,
J.
,
Wang
,
L.
,
Zhou
,
Z.
, and
Chen
,
S.
,
2021
, “
A Novel Bi-material Negative Stiffness Metamaterial in Sleeve-Type Via Combining Rigidity With Softness
,”
Compos. Struct.
,
262
, p.
113381
.
39.
Hewage
,
T. A. M.
,
Alderson
,
K. L.
,
Alderson
,
A.
, and
Scarpa
,
F.
,
2016
, “
Double-Negative Mechanical Metamaterials Displaying Simultaneous Negative Stiffness and Negative Poisson’s Ratio Properties
,”
Adv. Mater.
,
28
(
46
), pp.
10323
10332
.
40.
Rafsanjani
,
A.
, and
Pasini
,
D.
,
2016
, “
Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
,”
Extreme Mech. Lett.
,
9
, pp.
291
296
.
41.
Fu
,
K.
,
Zhao
,
Z.
, and
Jin
,
L.
,
2019
, “
Programmable Granular Metamaterials for Reusable Energy Absorption
,”
Adv. Funct. Mater.
,
29
(
32
), p.
1901258
.
42.
Pan
,
F.
,
Li
,
Y.
,
Li
,
Z.
,
Yang
,
J.
,
Liu
,
B.
, and
Chen
,
Y.
,
2019
, “
3D Pixel Mechanical Metamaterials
,”
Adv. Mater.
,
31
(
25
), p.
1900548
.
43.
Zhang
,
Y.
,
Tichem
,
M.
, and
van Keulen
,
F.
,
2021
, “
A Novel Design of Multi-stable Metastructures for Energy Dissipation
,”
Mater. Des.
,
212
, p.
110234
.
44.
Deng
,
H.
,
Cheng
,
L.
,
Liang
,
X.
,
Hayduke
,
D.
, and
To
,
A. C.
,
2020
, “
Topology Optimization for Energy Dissipation Design of Lattice Structures Through Snap-Through Behavior
,”
Comput. Methods Appl. Mech. Eng.
,
358
, p.
112641
.
You do not currently have access to this content.