Local buckling can form microcorrugations in thin films on elastomeric substrates, to yield an effective type of mechanical stretchability in otherwise rigid, brittle materials, with many application possibilities. For large area films or relatively thin substrates, however, global (Euler) buckling, as opposed to local buckling, can be observed in experiments. This paper describes analytically the mechanics of local and global buckling of one-dimensional thin films or two-dimensional thin membranes on elastomeric substrates. The critical condition separating these two buckling modes is obtained analytically, and it agrees well with experiments and numerical simulations.

1.
G. P.
Crawford
,
Flexible Flat Panel Display Technology
(
Wiley
,
New York
,
2005
).
2.
H. C.
Ko
,
M. P.
Stoykovich
,
J.
Song
,
V.
Malyarchuk
,
W. M.
Choi
,
C.-J.
Yu
,
J. B.
Geddes
,
J.
Xiao
,
S.
Wang
,
Y.
Huang
, and
J. A.
Rogers
, “
A hemispherical electronic eye camera based on compressible silicon optoelectronics
,”
Nature
(in press).
3.
V.
Lumelsky
,
M. S.
Shur
, and
S
Wagner
,
IEEE Sens. J.
1
,
41
(
2001
).
4.
T.
Someya
,
T.
Sekitani
,
S.
Iba
,
Y.
Kato
,
H.
Kawaguchi
, and
T.
Sakurai
,
Proc. Natl. Acad. Sci. U.S.A.
101
,
9966
(
2004
).
5.
A.
Nathan
,
B.
Park
,
A.
Sazonov
,
S.
Tao
,
I.
Chan
,
P.
Servati
,
K.
Karim
,
T.
Charania
,
D.
Striakhilev
,
Q.
Ma
, and
R. V. R.
Mruthy
,
Microelectron. J.
31
,
883
(
2000
).
6.
Y. Q.
Fu
,
S.
Sanjabi
,
Z. H.
Barber
,
T. W.
Clyne
,
W. M.
Huang
,
M.
Cai
,
J. K.
Luo
,
A. J.
Flewitt
, and
W. I.
Milne
,
Appl. Phys. Lett.
89
,
3
(
2006
).
7.
C.
Harrison
,
C. M.
Stafford
,
W. H.
Zhang
, and
A.
Karim
,
Appl. Phys. Lett.
85
,
4016
(
2004
).
8.
K.
Efimenko
,
M.
Rackaitis
,
E.
Manias
,
A.
Vaziri
,
L.
Mahadevan
, and
J.
Genzer
,
Nat. Mater.
4
,
293
(
2005
).
9.
A. K.
Harris
,
P.
Wild
, and
D.
Stopak
,
Science
208
,
177
(
1980
).
10.
A. I.
Teixeira
,
G. A.
Abrams
,
P. J.
Bertics
,
C. J.
Murphy
, and
P. F.
Nealey
,
J. Cell. Sci.
116
,
1881
(
2003
).
11.
X. Y.
Jiang
,
S.
Takayama
,
X. P.
Qian
,
E.
Ostuni
,
H. K.
Wu
,
N.
Bowden
,
P.
LeDuc
,
D. E.
Ingber
, and
G. M.
Whitesides
,
Langmuir
18
,
3273
(
2002
).
12.
C. M.
Stafford
,
S.
Guo
,
C.
Harrison
, and
M. Y. M.
Chiang
,
Rev. Sci. Instrum.
76
,
5
(
2005
).
13.
C. M.
Stafford
,
C.
Harrison
,
K. L.
Beers
,
A.
Karim
,
E. J.
Amis
,
M. R.
Vanlandingham
,
H. C.
Kim
,
W.
Volksen
,
R. D.
Miller
, and
E. E.
Simonyi
,
Nat. Mater.
3
,
545
(
2004
).
14.
C. M.
Stafford
,
B. D.
Vogt
,
C.
Harrison
,
D.
Julthongpiput
, and
R.
Huang
,
Macromolecules
39
,
5095
(
2006
).
15.
E. A.
Wilder
,
S.
Guo
,
S.
Lin-Gibson
,
M. J.
Fasolka
, and
C. M.
Stafford
,
Macromolecules
39
,
4138
(
2006
).
16.
N.
Bowden
,
S.
Brittain
,
A. G.
Evans
,
J. W.
Hutchinson
, and
G. M.
Whitesides
,
Nature (London)
393
,
146
(
1998
).
17.
N.
Bowden
,
W. T. S.
Huck
,
K. E.
Paul
, and
G. M.
Whitesides
,
Appl. Phys. Lett.
75
,
2557
(
1999
).
18.
W. T. S.
Huck
,
N.
Bowden
,
P.
Onck
,
T.
Pardoen
,
J. W.
Hutchinson
, and
G. M.
Whitesides
,
Langmuir
16
,
3497
(
2000
).
19.
J. S.
Sharp
and
R. A. L.
Jones
,
Adv. Mater. (Weinheim, Ger.)
14
,
799
(
2002
).
20.
P. J.
Yoo
,
K. Y.
Suh
,
S. Y.
Park
, and
H. H.
Lee
,
Adv. Mater. (Weinheim, Ger.)
14
,
1383
(
2002
).
21.
H.
Schmid
,
H.
Wolf
,
R.
Allenspach
,
H.
Riel
,
S.
Karg
,
B.
Michel
, and
E.
Delamarche
,
Adv. Funct. Mater.
13
,
145
(
2003
).
22.
M.-W.
Moon
,
S. H.
Lee
,
J.-Y.
Sun
,
K. H.
Oh
,
A.
Vaziri
, and
J. W.
Hutchinson
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
1130
(
2007
).
23.
D. Y.
Khang
,
H.
Jiang
,
Y.
Huang
, and
J. A.
Rogers
,
Science
311
,
208
(
2006
).
24.
H.
Jiang
,
D. Y.
Khang
,
J.
Song
,
Y.
Sun
,
Y.
Huang
, and
J. A.
Rogers
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
15607
(
2007
).
25.
J.
Song
,
H.
Jiang
,
Z. J.
Liu
,
D. Y.
Khang
,
Y.
Huang
,
J. A.
Rogers
,
C.
Lu
, and
C. G.
Koh
,
Int. J. Solids Struct.
45
,
3107
(
2008
).
26.
C. T.
Koh
,
Z. J.
Liu
,
D. Y.
Khang
,
J.
Song
,
C.
Lu
,
Y.
Huang
,
J. A.
Rogers
, and
C. G.
Koh
,
Appl. Phys. Lett.
91
,
133113
(
2007
).
27.
X.
Chen
and
J. W.
Hutchinson
,
J. Appl. Mech.
71
,
597
(
2004
).
28.
Z. Y.
Huang
,
W.
Hong
, and
Z.
Suo
,
J. Mech. Phys. Solids
53
,
2101
(
2005
).
29.
D. H.
Kim
,
J. H.
Ahn
,
W. M.
Choi
,
H. S.
Kim
,
T. H.
Kim
,
J.
Song
,
Y.
Huang
,
Z. J.
Liu
,
C.
Lu
, and
J. A.
Rogers
,
Science
320
,
507
(
2008
).
30.
D.
Gray
,
S. V.
Hoa
, and
S. W.
Tsai
,
Composite Materials: Design and Applications
(
CRC
,
Boca Raton, FL
,
2003
), Chap. 13, pp.
283
385
.
31.
Z. P.
Bazant
and
L.
Cedolin
,
Stability of Structures
(
Dover
,
New York
,
2003
), Chap. 1, pp.
31
32
.
32.
INSPEC
,
Properties of Silicon
(
Institution of Electrical Engineers
,
New York
,
1998
).
33.
W. M.
Choi
,
J.
Song
,
D.-Y.
Khang
,
H.
Jiang
,
Y.
Huang
, and
J. A.
Rogers
,
Nano Lett.
7
,
1655
(
2007
).
34.
J.
Song
,
H.
Jiang
,
W. M.
Choi
,
D. Y.
Khang
,
Y.
Huang
, and
J. A.
Rogers
,
J. Appl. Phys.
103
,
014303
(
2008
).
35.
S. P.
Timoshenko
and
J. M.
Gere
,
Theory of Elastic Stability
(
McGraw-Hill
,
New York
,
1961
).
You do not currently have access to this content.