Recent studies on periodic metamaterial systems have shown that remarkable properties adaptivity and versatility are often the products of exploiting internal, coexisting metastable states. Motivated by this concept, this research develops and explores a local-global design framework wherein macroscopic system-level properties are sought according to a strategic periodic constituent composition and assembly. To this end and taking inspiration from recent insights in studies of multiphase composite materials and cytoskeletal actin networks, this study develops adaptable metastable modules that are assembled into modular metastructures, such that the latter are invested with synergistic features due to the strategic module development and integration. Using this approach, it is seen that modularity creates an accessible pathway to exploit metastable states for programmable metastructure adaptivity, including a near-continuous variation of mechanical properties or stable topologies and adjustable hysteresis. A model is developed to understand the source of the synergistic characteristics, and theoretical findings are found to be in good agreement with experimental results. Important design-based questions are raised regarding the modular metastructure concept, and a genetic algorithm (GA) routine is developed to elucidate the sensitivities of the properties variation with respect to the statistics amongst assembled module design variables. To obtain target multifunctionality and adaptivity, the routine discovers that particular degrees and types of modular heterogeneity are required. Future realizations of modular metastructures are discussed to illustrate the extensibility of the design concept and broad application base.

References

1.
Wagg
,
D.
,
Bond
,
I.
,
Weaver
,
P.
, and
Friswell
,
M.
,
2007
,
Adaptive Structures: Engineering Applications
,
Wiley
,
Chichester, UK
.
2.
Shim
,
J.
,
Shan
,
S.
,
Košmrlj
,
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
.
3.
Schenk
,
M.
, and
Guest
,
S. D.
,
2013
, “
Geometry of Miura-Folded Metamaterials
,”
Proc. Natl. Acad. Sci.
,
110
(
9
), pp.
3276
3281
.
4.
Crivaro
,
A.
,
Sheridan
,
R.
,
Frecker
,
M.
,
Simpson
,
T. W.
, and
von Lockette
,
P.
,
2014
, “
Bistable Compliant Mechanisms Using Magneto Active Elastomer Actuation
,”
ASME
Paper No. DETC2014-35007.
5.
Nicolaou
,
Z. G.
, and
Motter
,
A. E.
,
2012
, “
Mechanical Metamaterials With Negative Compressibility Transitions
,”
Nat. Mater.
,
11
(
7
), pp.
608
613
.
6.
Celli
,
P.
, and
Gonella
,
S.
,
2015
, “
Tunable Directivity in Metamaterials With Reconfigurable Cell Symmetry
,”
Appl. Phys. Lett.
,
106
(
9
), p.
091905
.
7.
Fuchi
,
K.
,
Buskohl
,
P. R.
,
Joo
,
J. J.
,
Reich
,
G. W.
, and
Vaia
,
R. A.
,
2015
, “
Resonance Tuning of RF Devices Through Origami Folding
,”
20th International Conference on Composite Materials
, Copenhagen, Denmark, pp.
1
10
.
8.
Florijn
,
B.
,
Coulais
,
C.
, and
van Hecke
,
M.
,
2014
, “
Programmable Mechanical Metamaterials
,”
Phys. Rev. Lett.
,
113
(
17
), p.
175503
.
9.
Silverberg
,
J. L.
,
Na
,
J. H.
,
Evans
,
A. A.
,
Liu
,
B.
,
Hull
,
T. C.
,
Santangelo
,
C. D.
,
Lang
,
R. J.
, and
Hayward
,
R. C.
, and
Cohen
,
I.
,
2015
, “
Origami Structures With a Critical Transition to Bistability Arising From Hidden Degrees Of Freedom
,”
Nat. Mater.
,
14
(
4
), pp.
389
393
.
10.
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
.
11.
Wang
,
P.
,
Casadei
,
F.
,
Shan
,
S.
,
Weaver
,
J. C.
, and
Bertoldi
,
K.
,
2014
, “
Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials
,”
Phys. Rev. Lett.
,
113
(
1
), p.
014301
.
12.
Kuder
,
I. K.
,
Arrieta
,
A. F.
,
Rathier
,
W. E.
, and
Ermanni
,
P.
,
2013
, “
Variable Stiffness Material and Structural Concepts for Morphing Applications
,”
Prog. Aerosp. Sci.
,
63
, pp.
33
55
.
13.
Dai
,
F.
,
Li
,
H.
, and
Du
,
S.
,
2013
, “
A Multi-Stable Lattice Structures and Its Snap-Through Behavior Among Multiple States
,”
Compos. Struct.
,
97
, pp.
56
63
.
14.
Daynes
,
S.
,
Trask
,
R. S.
, and
Weaver
,
P. M.
,
2014
, “
Bio-Inspired Structural Bistability Employing Elastomeric Origami for Morphing Applications
,”
Smart Mater. Struct.
,
23
(
12
), p.
125011
.
15.
Bowen
,
L.
,
Springsteen
,
K.
,
Feldstein
,
H.
,
Frecker
,
M.
,
Simpson
,
T. W.
, and
von Lockette
,
P.
,
2015
, “
Development and Validation of a Dynamic Model of Magneto-Active Elastomer Actuation of the Origami Waterbomb Base
,”
J. Mech. Robots
,
7
(
1
), p.
011010
.
16.
Li
,
S.
, and
Wang
,
K. W.
,
2015
, “
Fluidic Origami With Embedded Pressure Dependent Multi-Stability: A Plant Inspired Innovation
,”
J. R. Soc. Interface
,
12
(
111
), p.
20150639
.
17.
Wu
,
Z.
,
Harne
,
R. L.
, and
Wang
,
K. W.
,
2015
, “
Exploring a Modular Adaptive Metastructure Concept Inspired by Muscle's Cross-Bridge
,”
J. Intell. Mater. Syst. Struct.
, (online).
18.
Lakes
,
R. S.
, and
Drugan
,
W. J.
,
2002
, “
Dramatically Stiffer Elastic Composite Materials Due to a Negative Stiffness Phase?
,”
J. Mech. Phys. Solids
,
50
(
5
), pp.
979
1009
.
19.
Fritzen
,
F.
, and
Kochmann
,
D. M.
,
2014
, “
Material Instability-Induced Extreme Damping in Composites: A Computational Study
,”
Int. J. Solids Struct.
,
51
, pp.
4101
4112
.
20.
Caruel
,
M.
,
Allain
,
J. M.
, and
Truskinovsky
,
L.
,
2013
, “
Muscle as a Metamaterial Operating Near a Critical Point
,”
Phys. Rev. Lett.
,
110
(
24
), p.
248103
.
21.
Schenk
,
M.
, and
Guest
,
S. D.
,
2014
, “
On Zero Stiffness
,”
Proc. Inst. Mech. Eng., Part C
,
228
(
10
), pp.
1701
1714
.
22.
Puglisi
,
G.
, and
Truskinovsky
,
L.
,
2002
, “
A Mechanism of Transformational Plasticity
,”
Continuum Mech. Thermodyn.
,
14
(
5
), pp.
437
457
.
23.
Holst
,
G. L.
,
Teichert
,
G. H.
, and
Jensen
,
B. D.
,
2011
, “
Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
133
(
5
), p.
051002
.
24.
Chen
,
Y. H.
, and
Lan
,
C. C.
,
2012
, “
An Adjustable Constant-Force Mechanism for Adaptive End-Effector Operations
,”
ASME J. Mech. Des.
,
134
(
3
), p.
031005
.
25.
Kovacic
,
I.
, and
Brennan
,
M. J.
, eds.,
2011
,
The Duffing Equation: Nonlinear Oscillators and Their Behaviour
,
Wiley
,
Chichester, UK
.
26.
Barbarino
,
S.
,
Saavedra Flores
,
E. I.
,
Ajaj
,
R. M.
,
Dayyani
,
I.
, and
Friswell
,
M. I.
,
2014
, “
A Review on Shape Memory Alloys With Applications to Morphing Aircraft
,”
Smart Mater. Struct.
,
23
(
6
), p.
063001
.
27.
Kidambi
,
N.
,
Harne
,
R. L.
, and
Wang
,
K. W.
,
2016
, “
Adaptation of Energy Dissipation in a Mechanical Metastable Module Excited Near Resonance
,”
ASME J. Vib. Acoust.
,
138
, p.
011001
.
28.
Romeo
,
F.
,
Sigalov
,
G.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2015
, “
Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Numerical Study
,”
ASME J. Comput. Nonlinear Dyn.
,
10
, p.
011007
.
29.
Biggs
,
N. L.
,
1979
, “
The Roots of Combinatorics
,”
Hist. Math.
,
6
(
2
), pp.
109
136
.
30.
Antoniadis
,
I.
,
Chronopoulos
,
D.
,
Spitas
,
V.
, and
Koulocheris
,
D.
,
2015
, “
Hyper-Damping Peroperties of a Stiff and Stable Linear Oscillator With a Negative Stiffness Element
,”
J. Sound Vib.
,
346
, pp.
37
52
.
31.
Haupt
,
R. L.
, and
Haupt
,
S. E.
,
1998
,
Practical Genetic Algorithms
,
Wiley
,
Hoboken, NJ
.
32.
Freund
,
R. J.
,
Wilson
,
W. J.
, and
Mohr
,
D. L.
,
2010
,
Statistical Methods
,
Academic Press
,
Burlington, MA
.
33.
Schaeffer
,
M.
, and
Ruzzene
,
M.
,
2015
, “
Wave Propagation in Multistable Magneto-Elastic Lattices
,”
Int. J. Solids Struct.
,
56–57
, pp.
78
95
.
34.
Tipton
,
C. R.
,
Han
,
E.
, and
Mullin
,
T.
,
2012
, “
Magneto-Elastic Buckling of a Soft Cellular Solid
,”
Soft Matter
,
8
(
26
), pp.
6880
6883
.
35.
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
.
36.
Rafsanjani
,
A.
,
Akbarzadeh
,
A.
, and
Pasini
,
D.
,
2015
, “
Snapping Mechanical Metamaterials Under Tension
,”
Adv. Mater.
,
27
(
39
), pp.
5931
5935
.
You do not currently have access to this content.