When subjected to a high electric field, dielectrics deform. For a hard dielectric, voltage-induced deformation is usually small, and the potential for deformation is determined by its breakdown voltage. If a dielectric is soft, the voltage-induced deformation is significantly large. The potential for deformation is determined by the breakdown voltage together with electromechanical instability and snap-through instability. Based on the theoretical researches conducted by Zhao and Suo [Phys. Rev. Lett. 104, 178302 (2010)] and Li et al. [Int. J. Smart Nano Mater. 2(2), 59-67 (2011)], taking the dielectric elastomer soft material as research object, we introduce three kinds of material limits: strain-stiffening, polarization saturation, and breakdown voltage. The effect of material limits on voltage-induced deformation is analyzed. Also investigated is the influence of pre-stretch and material parameters on the deformation. For a specific soft dielectric material under certain pre-stretch, the theoretical maximum electrical actuation deformation can be determined.

1.
R.
Pelrine
,
R.
Kornbluh
,
Q. B.
Pei
, and
J.
Joseph
, “
High-speed electrically actuated elastomers with strain greater than 100%
,”
Science
287
,
836
839
(
2000
).
2.
Z. G.
Suo
, “
Theory of dielectric elastomers
,”
Acta Mech. Solidia Sinica
,
23
,
549
578
(
2010
).
3.
P.
Brochu
and
Q. B.
Pei
, “
Advances in dielectric elastomers for actuators and artificial muscles
,”
Macromol. Rapid. Commun.
31
,
10
36
(
2010
).
4.
A.
O’Halloran
,
F.
O’Malley
, and
P.
McHugh
, “
A review on dielectric elastomer actuators, technology, applications, and challenges
,”
J. Appl. Phys.
104
,
071101
(
2008
).
5.
L. W.
Liu
,
Z.
Zhang
,
Y. J.
Liu
, and
J. S.
Leng
, “
Stability of dielectric elastomer/carbon nanotube composites coupling electrostriction and polarization
,”
Appl. Phys. Lett.
(submitted).
6.
M.
Zhenyi
,
J. I.
Scheinbeim
,
J. W.
Lee
, and
B. A.
Newman
, “
High field electrostrictive response of polymers
,”
J. Polym. Sci. B
32
,
2721
2731
(
1994
).
7.
R. E.
Pelrine
,
R. D.
Kornbluh
, and
J. P.
Joseph
. “
Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation
,”
Sens. Actuators, A
64
,
77
85
(
1998
).
8.
C.
Keplinger
,
M.
Kaltenbrunner
,
N.
Arnold
, and
S.
Bauer
, “
Röntgen’s electrode-free elastomer actuators without electromechanical pull-in instability
,”
Proc. Natl. Acad. Sci. U.S.A.
107
,
4505
4510
(
2010
).
9.
Z. G.
Suo
,
X. H.
Zhao
, and
W. H.
Greene
, “
A nonlinear field theory of deformable dielectrics
,”
J. Mech. Phys. Solids
56
,
476
486
(
2008
).
10.
X. H.
Zhao
and
Z. G.
Suo
, “
Method to analyze electromechanical stability of dielectric elastomers
,”
Appl. Phys. Lett.
91
,
061921
(
2007
).
11.
X. H.
Zhao
,
W.
Hong
, and
Z. G.
Suo
, “
Electromechanical coexistent states and hysteresis in dielectric elastomers
,”
Phys. Rev. B
76
,
134113
(
2007
).
12.
J. X.
Zhou
,
W.
Hong
,
X. H.
Zhao
,
Z.
Zhang
, and
Z. G.
Suo
, “
Propagation of instability in dielectric elastomers
,”
Int. J. Solids Struct.
45
,
3739
3750
(
2008
).
13.
A. N.
Norrisa
, “
Comments on “Method to analyze electromechanical stability of dielectric elastomers,”
Appl. Phys. Lett.
92
,
026101
(
2007
).
14.
Y. J.
Liu
,
L. W.
Liu
,
Z.
Zhang
,
L.
Shi
, and
J. S.
Leng
, “
Comment on “Method to analyze electromechanical stability of dielectric elastomers,”
Appl. Phys. Lett.
93
,
106101
(
2008
).
15.
R.
Díaz-Calleja
,
E.
Riande
, and
M. J.
Sanchis
, “
On electromechanical stability of dielectric elastomers
,”
Appl. Phys. Lett.
93
,
101902
(
2008
).
16.
Y. J.
Liu
,
L. W.
Liu
,
S. H.
Sun
,
L.
Shi
, and
J. S.
Leng
, “
Comment “On electromechanical stability of dielectric elastomers,”
Appl. Phys. Lett.
94
,
096101
(
2009
).
17.
S. A.
Koh
,
X. H.
Zhao
, and
Z. G.
Suo
, “
Maximal energy that can be converted by a dielectric elastomer generator
,”
Appl. Phys. Lett.
94
,
262902
(
2009
).
18.
Y. J.
Liu
,
L. W.
Liu
,
Z.
Zhang
,
Y.
Jiao
,
S. H.
Sun
, and
J. S.
Leng
, “
Analysis and manufacture of an energy harvester based on a Mooney-Rivlin–type dielectric elastomer
,”
Europhys. Lett.
90
,
36004
(
2010
).
19.
Y. J.
Liu
,
L. W.
Liu
,
J. S.
Leng
,
K.
Yu
, and
S. H.
Sun
, “
Electromechanical stability of dielectric elastomer
,”
Appl. Phys. Lett.
94
,
211901
(
2009
).
20.
Y. J.
Liu
,
L. W.
Liu
,
K.
Yu
,
S. H.
Sun
, and
J. S.
Leng
, “
An investigation on Electromechanical stability of dielectric elastomer undergoing large deformation
,”
Smart Mater. Struct.
18
,
095040
(
2009
).
21.
X. H.
Zhao
and
Z. G.
Suo
, “
Method to analyze programmable deformation of dielectric elastomer layers
,”
Appl. Phys. Lett.
93
,
251902
(
2008
).
22.
X. H.
Zhao
and
Z. G.
Suo
, “
Electromechanical instability in semicrystalline polymers
,”
Appl. Phys. Lett.
95
,
031904
(
2009
).
23.
X. H.
Kong
,
Y. B.
Li
,
L. W.
Liu
, and
X. D.
He
, “
Electromechanical stability of semi-crystalline polymer
,”
Thin Solid Films
519
(
15
),
5017
5021
(
2011
).
24.
W.
Hong
,
X. H.
Zhao
, and
Z. G.
Suo
, “
Formation of creases on the surfaces of elastomers and gels
,”
Appl. Phys. Lett.
95
,
111901
(
2009
).
25.
X. H.
Zhao
and
Z. G.
Suo
, “
Theory of dielectric elastomers capable of giant deformation of actuation
,”
Phys. Rev. Lett.
104
,
178302
(
2010
).
26.
Z. G.
Suo
and
J.
Zhu
, “
Dielectric elastomers of interpenetrating networks
,”
Appl. Phys. Lett.
95
,
232909
(
2009
).
27.
M.
Moscardo
,
X. H.
Zhao
,
Z. G.
Suo
, and
Y.
Lapusta
, “
On designing dielectric elastomer actuators
,”
J. Appl. Phys.
104
,
093503
(
2008
).
28.
L. W.
Liu
,
Z.
Zhang
,
Y. J.
Liu
, and
J. S.
Leng
, “
Failure modes of folded dielectric elastomer actuator
,”
Sci. China Ser. G
(in press).
29.
X. H.
Zhao
and
Z. G.
Suo
, “
Electrostriction in elastic dielectrics undergoing large deformation
,”
J. Appl. Phys.
104
,
123530
(
2008
).
30.
T. H.
He
,
X. H.
Zhao
, and
Z. G.
Suo
, “
Equilibrium and stability of dielectric elastomer membranes undergoing inhomogeneous deformation
,”
J. Appl. Phys.
106
,
083522
(
2009
).
31.
Y. J.
Liu
,
L. W.
Liu
,
Z.
Zhang
, and
J. S.
Leng
, “
Dielectric elastomer film actuators: Characterization, experiment and analysis
,”
Smart Mater. Struct.
18
,
095024
(
2009
).
32.
Y. J.
Liu
,
L. W.
Liu
,
S. H.
Sun
, and
J. S.
Leng
, “
Electromechanical stability of Mooney-Rivlin-type dielectric elastomer with nonlinear variable dielectric constant
,”
Polym. Int.
59
,
371
377
(
2010
).
33.
J.
Zhu
,
S. Q.
Cai
, and
Z. G.
Suo
, “
Nonlinear oscillation of a dielectric elastomer balloon
,”
Polym. Int.
59
,
378
383
(
2010
).
34.
F.
Carpi
,
S.
Raspopovic
,
G.
Frediani
, and
D.
Rossi
, “
Real-time control of dielectric elastomer actuators via bioelectric and biomechanical signals
,”
Polym. Int.
59
,
422
429
(
2010
).
35.
Y. J.
Liu
,
L. W.
Liu
,
S. H.
Sun
, and
J. S.
Leng
, “
Stability analysis of dielectric elastomer film actuator
,”
Sci. China. Ser. E
52
(
9
),
2715
2723
(
2009
).
36.
T. H.
He
,
L. L.
Cui
,
C.
Chen
, and
Z. G.
Suo
, “
Nonlinear deformation analysis of a dielectric elastomer membrane-spring system
,”
Smart Mater. Struct.
19
,
085017
(
2010
).
37.
X. H.
Zhao
,
S. A.
Koh
, and
Z. G.
Suo
, “
Nonequilibrium thermodynamics of dielectric elastomers
,”
Int. J. Appl. Mech.
3
,
203
217
(
2011
).
38.
L. W.
Liu
,
Y. J.
Liu
,
Z.
Zhang
,
B.
Li
, and
J. S.
Leng
, “
Electromechanical stability of electro-active silicone filled with high permittivity particles undergoing large deformation
,”
Smart Mater. Struct.
19
,
115025
(
2010
).
39.
J.
Zhu
,
S. Q.
Cai
, and
Z. G.
Suo
, “
Resonant behavior of a membrane of a dielectric elastomer
,”
Int. J. Solids Struct.
47
,
3254
3262
(
2010
).
40.
S. A.
Koh
,
C.
Keplinger
,
T. F.
Li
,
S.
Bauer
, and
Z. G.
Suo
, “
Dielectric elastomer generators: How much energy can be converted
,”
IEEE/ASME Trans. Mech.
16
,
33
41
(
2011
).
41.
R.
Díaz-Calleja
,
E.
Riande
, and
M. J.
Sanchis
, “
Effect of an electric field on the bifurcation of a biaxially stretched incompressible slab rubber
,”
Eur. Phys. J. E
30
,
417
426
(
2009
).
42.
B.
Li
,
L. W.
Liu
, and
Z. G.
Suo
, “
Extension limit, polarization saturation, and snap-through instability of dielectric elastomers
,”
Int. J. Smart Nano Mater.
2
(
2
),
59
67
(
2011
).
43.
J.
Zhu
,
T. F.
Li
,
S. Q.
Cai
, and
Z. G.
Suo
, “
Snap-through expansion of a gas bubble in an elastomer
,”
J. Adhes.
87
,
466
481
(
2011
).
44.
J.
Zhu
,
H.
Stoyanov
,
G.
Kofod
, and
Z. G.
Suo
, “
Large deformation and electromechanical instability of a dielectric elastomer tube actuator
,”
J. Appl. Phys.
108
,
074113
(
2010
).
45.
Z.
Zhang
,
L. W.
Liu
,
Y. J.
Liu
,
J. S.
Leng
, and
S. Y.
Du
, “
Effect of mechanical force field on the electromechanical stability of dielectric elastomers
,”
Sci. China Ser. G
55
(
1
),
94
101
(
2011
).
46.
B. X.
Xu
,
R.
Mueller
,
M.
Classen
, and
D.
Gross
, “
On electromechanical stability analysis of dielectric elastomer actuators
,”
Appl. Phys. Lett.
97
,
162908
(
2010
).
47.
B.
Li
,
H. L.
Chen
,
J. H.
Qiang
,
S. L.
Hu
,
Z. C.
Zhu
, and
Y. Q.
Wang
, “
Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation
,”
J. Phys. D: Appl. Phys.
44
,
155301
(
2011
).
48.
W.
Hong
, “
Modeling viscoelastic dielectrics
,”
J. Mech. Phys. Solids
59
,
637
650
(
2011
).
49.
L. W.
Liu
,
Y. J.
Liu
,
B.
Li
,
K.
Yang
,
T. F.
Li
, and
J. S.
Leng
, “
Thermo-electro-mechanical stability of dielectric elastomers
,”
Smart Mater. Struct.
20
,
075004
(
2011
).
50.
J. S.
Leng
,
Z.
Zhang
,
L. W.
Liu
,
Y. J.
Liu
, and
S. Y.
Du
, “
Thermodynamics and thermo-electro-mechanical stability of dielectric elastomers composite
,”
Sci. China Ser. G
41
(
11
),
1
17
(
2011
).
51.
L. W.
Liu
,
Y. J.
Liu
,
J. S.
Leng
, and
K. T.
Lau
, “
Electromechanical stability of compressible dielectric elastomer actuators
,”
Smart Mater. Struct.
20
,
115015
(
2011
).
52.
H. M.
Wang
,
S. Q.
Cai
,
F.
Carpi
, and
Z. G.
Suo
,
J. Appl. Mech.
79
,
031008
(
2012
).
53.
C.
Keplinger
,
T. F.
Li
,
R.
Baumgartner
,
Z. G.
Suo
, and
S.
Bauer
, “
Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation
,”
Soft Matter
8
,
285
288
(
2012
).
54.
L. W.
Liu
,
Y. J.
Liu
,
B.
Li
, and
J. S.
Leng
, “
Theoretical investigation on polar dielectric with large electrocaloric effect as cooling devices
,”
Appl. Phys. Lett.
99
,
181908
(
2011
).
55.
S. A.
Koh
,
T. F.
Li
,
J. X.
Zhou
,
X. H.
Zhao
,
W.
Hong
,
J.
Zhu
, and
Z. G.
Suo
, “
Mechanisms of large actuation strain in dielectric elastomers
,”
J. Polym. Sci. Part B: Polym. Phys.
49
,
504
515
(
2011
).
56.
A. N.
Gent
, “
A new constitutive relation for rubber
,”
Rubber Chen. Technol.
69
,
59
61
(
1996
).
57.
L. W.
Liu
,
Y. J.
Liu
,
X. J.
Luo
,
B.
Li
, and
J. S.
Leng
, “
Electromechanical instability and snap-through instability of dielectric elastomers undergoing polarization saturation
,”
Mech. Mater.
(in press).
58.
J. S.
Plante
and
S.
Dubowsky
, “
Large-scale failure modes of dielectric elastomer actuators
,”
Int. J. Solids Struct.
43
,
7727
7751
(
2006
).
You do not currently have access to this content.