Wrinkling is a common phenomenon in natural and engineering film structures. The wrinkles influence the geometry and dynamic response of these structures. In this work, we investigate the wrinkling of a stretched thin film containing engineered microstructures and its derived functionality on controlling the propagation of bending waves. The underlying mechanism is revealed and the effect of wrinkles on the bandgap of bending waves is systematically evaluated via numerical simulations based on the Bloch wave theory. We show that wrinkles with a customized wavelength can be triggered in the microstructured film due to the mismatched deformation in the film. The bandgap of the wrinkled film can be finely tuned via applied stretching, resulting in the controllable propagation of bending waves in thin films. Our work provides fundamental insights into wave propagation in wrinkled films and potential applications for dynamic control of the wave propagation in engineering film structures.

References

References
1.
Savin
,
T.
,
Kurpios
,
N. A.
,
Shyer
,
A. E.
,
Florescu
,
P.
,
Liang
,
H.
,
Mahadevan
,
L.
, and
Tabin
,
C. J.
,
2011
, “
On the Growth and Form of the Gut
,”
Nature
,
476
(
7358
), pp.
57
62
.
2.
Wong
,
Y. W.
, and
Pellegrino
,
S.
,
2006
, “
Wrinkled Membranes Part I: Experiments
,”
J. Mech. Mater. Struct.
,
1
(
1
), pp.
3
25
.
3.
Li
,
B.
,
Cao
,
Y.-P.
,
Feng
,
X.-Q.
, and
Gao
,
H.
,
2012
, “
Mechanics of Morphological Instabilities and Surface Wrinkling in Soft Materials: A Review
,”
Soft Matter
,
8
(
21
), pp.
5728
5745
.
4.
Rogers
,
J. A.
,
Someya
,
T.
, and
Huang
,
Y.
,
2010
, “
Materials and Mechanics for Stretchable Electronics
,”
Science
,
327
(
5973
), pp.
1603
1607
.
5.
Singamaneni
,
S.
, and
Tsukruk
,
V. V.
,
2010
, “
Buckling Instabilities in Periodic Composite Polymeric Materials
,”
Soft Matter
,
6
(
22
), pp.
5681
5692
.
6.
Croll
,
A. B.
, and
Crosby
,
A. J.
,
2012
, “
Pattern Driven Stress Localization in Thin Diblock Copolymer Films
,”
Macromolecules
,
45
(
9
), pp.
4001
4006
.
7.
Harris
,
J. M.
,
Huh
,
J. Y.
,
Semler
,
M. R.
,
Ihle
,
T.
,
Stafford
,
C. M.
,
Hudson
,
S. D.
,
Fagan
,
J. A.
, and
Hobbie
,
E. K.
,
2013
, “
Elasticity and Rigidity Percolation in Flexible Carbon Nanotube Films on PDMS Substrates
,”
Soft Matter
,
9
(
48
), pp.
11568
11575
.
8.
Cerda
,
E.
, and
Mahadevan
,
L.
,
2003
, “
Geometry and Physics of Wrinkling
,”
Phys. Rev. Lett.
,
90
(
7
), p.
074302
.
9.
Massabò
,
R.
, and
Gambarotta
,
L.
,
2007
, “
Wrinkling of Plane Isotropic Biological Membranes
,”
ASME J. Appl. Mech.
,
74
(
3
), pp.
550
559
.
10.
Johnson
,
L.
,
Young
,
R.
,
Montgomery
,
E.
, and
Alhorn
,
D.
,
2011
, “
Status of Solar Sail Technology Within NASA
,”
Adv. Space Res.
,
48
(
11
), pp.
1687
1694
.
11.
Wong
,
Y. W.
, and
Pellegrino
,
S.
,
2006
, “
Wrinkled Membranes Part II: Analytical Models
,”
J. Mech. Mater. Struct.
,
1
(
1
), pp.
27
61
.
12.
Lin
,
S.
,
Mao
,
Y.
,
Radovitzky
,
R.
, and
Zhao
,
X.
,
2017
, “
Instabilities in Confined Elastic Layers Under Tension: Fringe, Fingering and Cavitation
,”
J. Mech. Phys. Solids
,
106
, pp.
229
256
.
13.
Cerda
,
E.
,
Ravi-Chandar
,
K.
, and
Mahadevan
,
L.
,
2002
, “
Wrinkling of an Elastic Sheet Under Tension
,”
Nature
,
419
(
6907
), pp.
579
580
.
14.
Nayyar
,
V.
,
Ravi-Chandar
,
K.
, and
Huang
,
R.
,
2011
, “
Stretch-Induced Stress Patterns and Wrinkles in Hyperelastic Thin Sheets
,”
Int. J. Solids Struct.
,
48
(
25–26
), pp.
3471
3483
.
15.
Wang
,
B.
,
Ghanta
,
P.
,
Vinnikova
,
S.
,
Bao
,
S.
,
Liang
,
J.
,
Lu
,
H.
, and
Wang
,
S.
,
2017
, “
Wrinkling of Tympanic Membrane Under Unbalanced Pressure
,”
ASME J. Appl. Mech.
,
84
(
4
), p.
041002
.
16.
Kim
,
T. H.
,
Choi
,
W. M.
,
Kim
,
D. H.
,
Meitl
,
M. A.
,
Menard
,
E.
,
Jiang
,
H.
,
Carlisle
,
J. A.
, and
Rogers
,
J. A.
,
2008
, “
Printable, Flexible, and Stretchable Forms of Ultrananocrystalline Diamond With Applications in Thermal Management
,”
Adv. Mater.
,
20
(
11
), pp.
2171
2176
.
17.
Cao
,
Y.-P.
,
Li
,
B.
, and
Feng
,
X.-Q.
,
2012
, “
Surface Wrinkling and Folding of Core-Shell Soft Cylinders
,”
Soft Matter
,
8
(
2
), pp.
556
562
.
18.
Chan
,
H. F.
,
Zhao
,
R.
,
Parada
,
G. A.
,
Meng
,
H.
,
Leong
,
K. W.
,
Griffith
,
L. G.
, and
Zhao
,
X.
,
2018
, “
Folding Artificial Mucosa With Cell-Laden Hydrogels Guided by Mechanics Models
,”
Proc. Natl. Acad. Sci.
,
115
(
29
), pp.
7503
7508
.
19.
Terwagne
,
D.
,
Brojan
,
M.
, and
Reis
,
P. M.
,
2014
, “
Smart Morphable Surfaces for Aerodynamic Drag Control
,”
Adv. Mater.
,
26
(
38
), pp.
6608
6611
.
20.
Reis
,
P. M.
,
2015
, “
A Perspective on the Revival of Structural (In) Stability With Novel Opportunities for Function: From Buckliphobia to Buckliphilia
,”
ASME J. Appl. Mech.
,
82
(
11
), p.
111001
.
21.
Yan
,
D.
,
Zhang
,
K.
,
Peng
,
F.
, and
Hu
,
G.
,
2014
, “
Tailoring the Wrinkle Pattern of a Microstructured Membrane
,”
Appl. Phys. Lett.
,
105
(
7
), p.
071905
.
22.
Yan
,
D.
,
Zhang
,
K.
, and
Hu
,
G.
,
2016
, “
Wrinkling of Structured Thin Films Via Contrasted Materials
,”
Soft Matter
,
12
(
17
), pp.
3937
3942
.
23.
Yan
,
D.
,
Huangfu
,
D.
,
Zhang
,
K.
, and
Hu
,
G.
,
2016
, “
Wrinkling of the Membrane With Square Rigid Elements
,”
EPL
,
116
(
2
), p.
24005
.
24.
Bowden
,
N.
,
Brittain
,
S.
,
Evans
,
A. G.
,
Hutchinson
,
J. W.
, and
Whitesides
,
G. M.
,
1998
, “
Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer
,”
Nature
,
393
(
6681
), pp.
146
149
.
25.
Huang
,
Z. Y.
,
Hong
,
W.
, and
Suo
,
Z.
,
2005
, “
Nonlinear Analyses of Wrinkles in a Film Bonded to a Compliant Substrate
,”
J. Mech. Phys. Solids
,
53
(
9
), pp.
2101
2118
.
26.
Huang
,
R.
, and
Im
,
S. H.
,
2006
, “
Dynamics of Wrinkle Growth and Coarsening in Stressed Thin Films
,”
Phys. Rev. E
,
74
(
2
), p.
026214
.
27.
Rudykh
,
S.
, and
Boyce
,
M. C.
,
2014
, “
Transforming Wave Propagation in Layered Media Via Instability-Induced Interfacial Wrinkling
,”
Phys. Rev. Lett.
,
112
(
3
), p.
034301
.
28.
Li
,
G.-Y.
,
Zheng
,
Y.
,
Cao
,
Y.
,
Feng
,
X.-Q.
, and
Zhang
,
W.
,
2016
, “
Controlling Elastic Wave Propagation in a Soft Bilayer System Via Wrinkling-Induced Stress Patterns
,”
Soft Matter
,
12
(
18
), pp.
4204
4213
.
29.
Zheng
,
Y.
,
Li
,
G.-Y.
,
Cao
,
Y.
, and
Feng
,
X.-Q.
,
2017
, “
Wrinkling of a Stiff Film Resting on a Fiber-Filled Soft Substrate and Its Potential Application as Tunable Metamaterials
,”
Extreme Mech. Lett.
,
11
, pp.
121
127
.
30.
Hossain
,
N. M. A.
,
Jenkins
,
C. H.
,
Woo
,
K.
, and
Igawa
,
H.
,
2006
, “
Transverse Vibration Analysis for Partly Wrinkled Membranes
,”
J. Spacecr. Rockets
,
43
(
3
), pp.
626
637
.
31.
Luo
,
Y.
,
Xing
,
J.
,
Niu
,
Y.
,
Li
,
M.
, and
Kang
,
Z.
,
2017
, “
Wrinkle-Free Design of Thin Membrane Structures Using Stress-Based Topology Optimization
,”
J. Mech. Phys. Solids
,
102
, pp.
277
293
.
32.
Freeland
,
R. E.
,
Bilyeu
,
G. D.
,
Veal
,
G. R.
,
Steiner
,
M. D.
, and
Carson
,
D. E.
,
1997
, “
Large Inflatable Deployable Antenna Flight Experiment Results
,”
Acta. Astronaut.
,
41
(
4–10
), pp.
267
277
.
33.
Scarpa
,
F.
,
Ouisse
,
M.
,
Collet
,
M.
, and
Saito
,
K.
,
2013
, “
Kirigami Auxetic Pyramidal Core: Mechanical Properties and Wave Propagation Analysis in Damped Lattice
,”
ASME J. Vib. Acoust.
,
135
(
4
), p.
041001
.
34.
Ouisse
,
M.
,
Collet
,
M.
, and
Scarpa
,
F.
,
2016
, “
A Piezo-Shunted Kirigami Auxetic Lattice for Adaptive Elastic Wave Filtering
,”
Smart Mater. Struct.
,
25
(
11
), pp.
115016
.
35.
Wong
,
Y. W.
, and
Pellegrino
,
S.
,
2006
, “
Wrinkled Membranes Part III: Numerical Simulations
,”
J. Mech. Mater. Struct.
,
1
(
1
), pp.
63
95
.
36.
Åberg
,
M.
, and
Gudmundson
,
P.
,
1997
, “
The Usage of Standard Finite Element Codes for Computation of Dispersion Relations in Materials With Periodic Microstructure
,”
J. Acoust. Soc. Am.
,
102
(
4
), pp.
2007
2013
.
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