This Letter proposes a design strategy leveraging tunable structural defects in multi-stable mechanical metamaterials for manipulating the propagation of the supported transition waves toward the endowment of a multi-phase patterning capability. The defect reversibly adjusts the on-site potential in order to affect the motion of the transition waves which traverse it, either prohibiting wave transmission (i.e., stabilization) or permitting transmission of specific modes, possibly converting one mode into another. Thus, the defect is able to control the occurrence and distribution of the structural phases and realize the desired phase patterns. Although the metamaterial model for our analytical and numerical study is a one-dimensional (1D) architecture comprising tri-stable elements, the proposed method is shown to apply to 2D architectures and is amenable to elements possessing more than three stable states, demonstrating greater flexibility in metamaterial design than current approaches. The proposed method expands the configuration space of phase-transforming metamaterials, which contributes to efforts aimed at re-programmable mechanical/dynamic performance.
REFERENCES
1.
R. W.
Balluffi
,
S.
Allen
, and
W. C.
Carter
, Kinetics of Materials
, 1st ed
. (
John Wiley & Sons, Inc
., 2005
), ISBN: 9780471246893.2.
G. S. D.
Beach
,
M.
Tsoi
, and
J. L.
Erskine
, “
Current-induced domain wall motion
,” J. Magn. Magn. Mater.
320
, 1272
–1281
(2008
).3.
G.
Tatara
,
H.
Kohno
, and
J.
Shibata
, “
Microscopic approach to current-driven domain wall dynamics
,” Phys. Rep
468
, 213
–301
(2008
).4.
D. C.
Ralph
and
M. D.
Stiles
, “
Spin transfer torques
,” J. Magn. Magn. Mater.
320
, 1190
–1216
(2008
).5.
S. S. P.
Parkin
,
M.
Hayashi
, and
L.
Thomas
, “
Magnetic domain-wall racetrack memory
,” Science
320
, 190
–194
(2008
).6.
S.
Cho
,
S.
Kim
,
J. H.
Kim
,
J.
Zhao
,
J.
Seok
,
D. H.
Keum
,
J.
Baik
,
D.-H.
Choe
,
K. J.
Chang
, and
K.
Suenaga
, “
Phase patterning for Ohmic homojunction contact in MoTe2
,” Science
349
, 625
–628
(2015
).7.
F.
Zheng
,
D.
Guo
,
L.
Huang
,
L. W.
Wong
,
X.
Chen
,
C.
Wang
,
Y.
Cai
,
N.
Wang
,
C.-S.
Lee
, and
S. P.
Lau
, “
Sub-nanometer electron beam phase patterning in 2D materials
,” Adv. Sci.
9
, 2200702
(2022
).8.
J. R.
Raney
,
N.
Nadkarni
,
C.
Daraio
,
D. M.
Kochmann
,
J. A.
Lewis
, and
K.
Bertoldi
, “
Stable propagation of mechanical signals in soft media using stored elastic energy
,” Proc. Natl. Acad. Sci. U. S. A.
113
, 9722
–9727
(2016
).9.
A.
Zareei
,
B.
Deng
, and
K.
Bertoldi
, “
Harnessing transition waves to realize deployable structures
,” Proc. Natl. Acad. Sci. U. S. A.
117
, 4015
–4020
(2020
).10.
B.
Deng
,
M.
Zanaty
,
A. E.
Forte
, and
K.
Bertoldi
, “
Topological solitons make metamaterials crawl
,” Phys. Rev. Appl.
17
, 014004
(2022
).11.
D.
Melancon
,
A. E.
Forte
,
L. M.
Kamp
,
B.
Gorissen
, and
K.
Bertoldi
, “
Inflatable origami: Multimodal deformation via multistability
,” Adv. Funct. Mater.
32
, 2201891
(2022
).12.
C.
Merrigan
,
C.
Nisoli
, and
Y.
Shokef
, “
Topologically protected steady cycles in an icelike mechanical metamaterial
,” Phys. Rev. Res.
3
, 023174
(2021
).13.
M.
Hwang
and
A.
Arrieta
, “
Topological wave energy harvesting in bistable lattices
,” Smart Mater. Struct.
31
, 015021
(2022
).14.
M. J.
Frazier
and
D. M.
Kochmann
, “
Atomimetic mechanical structures with nonlinear topological domain evolution kinetics
,” Adv. Mater.
29
, 1605800
(2017
).15.
R.
Khajehtourian
,
M. J.
Frazier
, and
D. M.
Kochmann
, “
Multistable pendula as mechanical analogs of ferroelectricity
,” Extreme Mech. Lett.
50
, 101527
(2022
).16.
N.
Nadkarni
,
C.
Daraio
,
R.
Abeyaratne
, and
D. M.
Kochmann
, “
Universal energy transport law for dissipative and diffusive phase transitions
,” Phys. Rev. B
93
, 104109
(2016
).17.
N.
Nadkarni
,
A. F.
Arrieta
,
C.
Chong
,
D. M.
Kochmann
, and
C.
Daraio
, “
Unidirectional transition waves in bistable lattices
,” Phys. Rev. Lett.
116
, 244501
(2016
).18.
V.
Ramakrishnan
and
M. J.
Frazier
, “
Transition waves in multi-stable metamaterials with space-time modulated potentials
,” Appl. Phys. Lett.
117
, 151901
(2020
).19.
Y.
Zhou
,
B. G.-G.
Chen
,
N.
Upadhyaya
, and
V.
Vitelli
, “
Kink-antikink asymmetry and impurity interactions in topological mechanical chains
,” Phys. Rev. E
95
, 022202
(2017
).20.
M.
Hwang
and
A. F.
Arrieta
, “
Solitary waves in bistable lattices with stiffness grading: Augmenting propagation control
,” Phys. Rev. E
98
, 042205
(2018
).21.
L.
Jin
,
R.
Khajehtourian
,
J.
Mueller
,
A.
Rafsanjani
,
V.
Tournat
,
K.
Bertoldi
, and
D. M.
Kochmann
, “
Guided transition waves in multistable mechanical metamaterials
,” Proc. Natl. Acad. Sci. U. S. A.
117
, 2319
–2325
(2020
).22.
N.
Vasios
,
B.
Deng
,
B.
Gorissen
, and
K.
Bertoldi
, “
Universally bistable shells with nonzero Gaussian curvature for two-way transition waves
,” Nat. Commun.
12
, 695
(2021
).23.
Y.
Zhang
,
B.
Li
,
Q. S.
Zheng
,
G. M.
Genin
, and
C. Q.
Chen
, “
Programmable and robust static topological solitons in mechanical metamaterials
,” Nat. Commun.
10
, 5605
(2019
).24.
B.
Deng
,
S.
Yu
,
A. E.
Forte
,
V.
Tournat
, and
K.
Bertoldi
, “
Characterization, stability, and application of domain walls in flexible mechanical metamaterials
,” Proc. Natl. Acad. Sci. U. S. A.
117
, 31002
–31009
(2020
).25.
N.
Yang
,
C.-W.
Chen
,
J.
Yang
, and
J. L.
Silverberg
, “
Emergent reconfigurable mechanical metamaterial tessellations with an exponentially large number of discrete configurations
,” Mater. Des.
196
, 109143
(2020
).26.
J.
Meaud
, “
Multistable two-dimensional spring-mass lattices with tunable band gaps and wave directionality
,” J. Sound Vib.
434
, 44
–62
(2018
).27.
M. D.
Schaeffer
and
M.
Ruzzene
, “
Wave propagation in multistable magneto-elastic lattices
,” Int. J. Solids Struct.
56–57
, 78
–95
(2015
).28.
V.
Ramakrishnan
and
M. J.
Frazier
, “
Multistable metamaterial on elastic foundation enables tunable morphology for elastic wave control
,” J. Appl. Phys
127
, 225104
(2020
).29.
H.
Yasuda
,
L. M.
Korpas
, and
J. R.
Raney
, “
Transition waves and formation of domain walls in multistable mechanical metamaterials
,” Phys. Rev. Appl.
13
, 054067
(2020
).30.
A.
Colombi
,
V.
Ageeva
,
R. J.
Smith
,
A.
Clare
,
R.
Patel
,
M.
Clark
,
D.
Colquitt
,
P.
Roux
,
S.
Guenneau
, and
R. V.
Craster
, “
Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces
,” Sci. Rep.
7
, 6750
(2017
).31.
C.
Wang
,
A. F.
Vakakis
, and
S.
Tawfick
, “
Non-reciprocal frequency conversion in a two-dimensional waveguide incorporating a local nonlinear gate
,” Commun. Nonlinear Sci. Numer. Simul.
118
, 107041
(2023
).32.
Y.
Zhang
,
M.
Tichem
, and
F.
van Keulen
, “
Concept and design of a metastructure-based multi-stable surface
,” Extreme Mech. Lett.
51
, 101553
(2022
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.