We utilize a nonlinear, dynamic finite element model coupled with a finite deformation viscoelastic constitutive law to study the inhomogeneous deformation and instabilities resulting from the application of a constant voltage to dielectric elastomers. The constant voltage loading is used to study electrostatically driven creep and the resulting electromechanical instabilities for two different cases that have all been experimentally observed, i.e., electromechanical snap-through instability and bursting drops in a dielectric elastomer. We find that in general, increasing the viscoelastic relaxation time leads to an increase in time needed to nucleate the electromechanical instability. However, we find for these two cases that the time needed to nucleate the instability scales with the relaxation time.

References

References
1.
Carpi
,
F.
,
Bauer
,
S.
, and
Rossi
,
D. D.
,
2010
, “
Stretching Dielectric Elastomer Performance
,”
Science
,
330
, pp.
1759
1761
.10.1126/science.1194773
2.
Brochu
,
P.
, and
Pei
,
Q.
,
2010
, “
Advances in Dielectric Elastomers for Actuators and Artificial Muscles
,”
Macromol. Rapid Commun.
,
31
, pp.
10
36
.10.1002/marc.200900425
3.
Biddiss
,
E.
, and
Chau
,
T.
,
2008
, “
Dielectric Elastomers As Actuators for Upper Limb Prosthetics: Challenges and Opportunities
,”
Med. Eng. Phys.
,
30
, pp.
403
418
.10.1016/j.medengphy.2007.05.011
4.
Bar-Cohen
,
Y.
,
2005
, “
Biomimetics: Mimicking and Inspired-by Biology
,”
Proc. SPIE
,
5759
, pp.
1
8
.10.1117/12.597436
5.
Mirfakhrai
,
T.
,
Madden
,
J. D. W.
, and
Baughman
,
R. H.
,
2007
, “
Polymer Artificial Muscles
,”
Mater. Today
,
10
(
4
), pp.
30
38
.10.1016/S1369-7021(07)70048-2
6.
O'Halloran
,
A.
,
O'Malley
,
F.
, and
McHugh
,
P.
,
2008
, “
A Review on Dielectric Elastomer Actuators, Technology, Applications, and Challenges
,”
J. Appl. Phys.
,
104
, p.
071101
.10.1063/1.2981642
7.
Zhang
,
X.
,
Wissler
,
C. L. M.
,
Jaehne
,
B.
, and
Kovacs
,
G.
,
2005
, “
Dielectric Elastomers in Actuator Technology
,”
Adv. Eng. Mater.
,
7
(
5
), pp.
361
367
.10.1002/adem.200500066
8.
Zhang
,
X. Q.
,
Wissler
,
M.
,
Jaehne
,
B.
,
Broennimann
,
R.
, and
Kovacs
,
G.
,
2004
, “
Effects of Crosslinking, Prestrain and Dielectric Filler on the Electromechanical Response of a New Silicone and Comparison With Acrylic Elastomer
,”
Proc. SPIE
,
5385
, pp.
78
86
.10.1117/12.540888
9.
Plante
,
J.-S.
, and
Dubowsky
,
S.
,
2006
, “
Large-Scale Failure Modes of Dielectric Elastomer Actuators
,”
Int. J. Solids Struct.
,
43
, pp.
7727
7751
.10.1016/j.ijsolstr.2006.03.026
10.
Keplinger
,
C.
,
Kaltenbrunner
,
M.
,
Arnold
,
N.
, and
Bauer
,
S.
,
2008
, “
Capacitive Extensometry for Transient Strain Analysis of Dielectric Elastomer Actuators
,”
Appl. Phys. Lett.
,
92
, p.
192903
.10.1063/1.2929383
11.
Hong
,
W.
,
2011
, “
Modeling Viscoelastic Dielectrics
,”
J. Mech. Phys. Solids
,
59
, pp.
637
650
.10.1016/j.jmps.2010.12.003
12.
Zhao
,
X.
,
Koh
,
S. J. A.
, and
Suo
,
Z.
,
2011
, “
Nonequilibrium Thermodynamics of Dielectric Elastomers
,”
Int. J. Appl. Mech.
,
3
(
2
), pp.
203
217
.10.1142/S1758825111000944
13.
Foo
,
C. C.
,
Cai
,
S.
,
Koh
,
S. J. A.
,
Bauer
,
S.
, and
Suo
,
Z.
,
2012
, “
Model of Dissipative Dielectric Elastomers
,”
J. Appl. Phys.
,
111
, p.
034102
.10.1063/1.3680878
14.
Wang
,
H.
,
Lei
,
M.
, and
Cai
,
S.
,
2013
, “
Viscoelastic Deformation of a Dielectric Elastomer Membrane Subject to Electromechanical Loads
,”
J. Appl. Phys.
,
113
, p.
213508
.10.1063/1.4807911
15.
Tagarielli
,
V. L.
,
Hildick-Smith
,
R.
, and
Huber
,
J. E.
,
2012
, “
Electro-Mechanical Properties and Electrostriction Response of a Rubbery Polymer for EAP Applications
,”
Int. J. Solids Struct.
,
49
, pp.
3409
3415
.10.1016/j.ijsolstr.2012.07.018
16.
Park
,
H. S.
, and
Nguyen
,
T. D.
,
2013
, “
Viscoelastic Effects on Electromechanical Instabilities in Dielectric Elastomers
,”
Soft Matter
,
9
, pp.
1031
1042
.10.1039/c2sm27375f
17.
Buschel
,
A.
,
Klinkel
,
S.
, and
Wagner
,
W.
,
2013
, “
Dielectric Elastomers—Numerical Modeling of Nonlinear Visco-Electroelasticity
,”
Int. J. Numer. Methods Eng.
,
93
, pp.
834
856
.10.1002/nme.4409
18.
Khan
,
K. A.
,
Wafai
,
H.
, and
Sayed
,
T. E.
,
2013
, “
A Variational Constitutive Framework for the Nonlinear Viscoelastic Response of a Dielectric Elastomer
,”
Comput. Mech.
,
52
, pp.
345
360
.10.1007/s00466-012-0815-6
19.
Pelrine
,
R.
,
Kornbluh
,
R.
,
Pei
,
Q.
, and
Joseph
,
J.
,
2000
, “
High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%
,”
Science
,
287
, pp.
836
839
.10.1126/science.287.5454.836
20.
Wang
,
Q.
,
Suo
,
Z.
, and
Zhao
,
X.
,
2012
, “
Bursting Drops in Solid Dielectrics Caused by High Voltages
,”
Nat. Commun.
,
3
, p.
1157
.10.1038/ncomms2178
21.
Zhao
,
X.
,
Hong
,
W.
, and
Suo
,
Z.
,
2007
, “
Electromechanical Hysteresis and Coexistent States in Dielectric Elastomers
,”
Phys. Rev. B
,
76
, p.
134113
.10.1103/PhysRevB.76.134113
22.
Suo
,
Z.
,
Zhao
,
X.
, and
Greene
,
W. H.
,
2008
, “
A Nonlinear Field Theory of Deformable Dielectrics
,”
J. Mech. Phys. Solids
,
56
, pp.
467
486
.10.1016/j.jmps.2007.05.021
23.
Park
,
H. S.
,
Suo
,
Z.
,
Zhou
,
J.
, and
Klein
,
P. A.
,
2012
, “
A Dynamic Finite Element Method for Inhomogeneous Deformation and Electromechanical Instability of Dielectric Elastomer Transducers
,”
Int. J. Solids Struct.
,
49
, pp.
2187
2194
.10.1016/j.ijsolstr.2012.04.031
24.
Park
,
H. S.
,
Wang
,
Q.
,
Zhao
,
X.
, and
Klein
,
P. A.
,
2013
, “
Electromechanical Instability on Dielectric Polymer Surface: Modeling and Experiment
,”
Comput. Methods Appl. Mech. Eng.
,
260
, pp.
40
49
.10.1016/j.cma.2013.03.020
25.
Suo
,
Z.
,
2010
, “
Theory of Dielectric Elastomers
,”
Acta Mech. Solida Sinica
,
23
(
6
), pp.
549
578
.10.1016/S0894-9166(11)60004-9
26.
Vu
,
D. K.
,
Steinmann
,
P.
, and
Possart
,
G.
,
2007
, “
Numerical Modelling of Non-Linear Electroelasticity
,”
Int. J. Numer. Methods Eng.
,
70
, pp.
685
704
.10.1002/nme.1902
27.
Zhao
,
X.
, and
Suo
,
Z.
,
2007
, “
Method to Analyze Electromechanical Instability of Dielectric Elastomers
,”
Appl. Phys. Lett.
,
91
, p.
061921
.10.1063/1.2768641
28.
Arruda
,
E. M.
, and
Boyce
,
M. C.
,
1993
, “
A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials
,”
J. Mech. Phys. Solids
,
41
(
2
), pp.
389
412
.10.1016/0022-5096(93)90013-6
29.
Wissler
,
M.
, and
Mazza
,
E.
,
2007
, “
Mechanical Behavior of an Acrylic Elastomer Used in Dielectric Elastomer Actuators
,”
Sensors Actuators A
,
134
, pp.
494
504
.10.1016/j.sna.2006.05.024
30.
Reese
,
S.
, and
Govindjee
,
S.
,
1998
, “
A Theory of Finite Viscoelasticity and Numerical Aspects
,”
Int. J. Solids Struct.
,
35
(
26–27
), pp.
3455
3482
.10.1016/S0020-7683(97)00217-5
31.
Hughes
,
T. J. R.
,
1987
,
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
32.
Simo
,
J. C.
,
Taylor
,
R. L.
, and
Pister
,
K. S.
,
1985
, “
Variational and Projection Methods for the Volume Constraint in Finite Deformation Elasto-Plasticity
,”
Comput. Methods Appl. Mech. Eng.
,
51
, pp.
177
208
.10.1016/0045-7825(85)90033-7
33.
Nguyen
,
T. D.
2010
, “
A Comparison of a Nonlinear and Quasilinear Viscoelastic Anisotropic Model for Fibrous Tissues
,”
Proceedings of the IUTAM Symposium on Cellular, Molecular and Tissue Mechanics
, Woods Hole, MA, June 18–21,
K.
Garikipati
and
E. M.
Arruda
, eds., Springer, New York, Vol.
16
, pp.
19
29
.10.1007/978-90-481-3348-2_2
34.
Tahoe
,
2013
, SourceForge.net, http://sourceforge.net/projects/tahoe/
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