This paper presents a model for the electromechanically coupled dynamic behavior of dielectric elastomer actuators (DEA). The main goal is to develop a lumped, dynamic model which can be used for the optimization of actuator design in specific applications as well as for the synthesis of high precision, model-based feedback control algorithms. A mass-biased membrane actuator with an annular geometry is chosen as a reference case to introduce the modeling concept. The mechanical model extends standard linear visco-elasticity through the introduction of a nonlinear hyperelastic Ogden element. Electromechanical coupling is implemented through the Maxwell stress concept. The DEA model is then experimentally calibrated and validated for both quasi static and dynamic loading conditions. It can be shown that both mechanical preloading and electric actuation can be reproduced over a relevant range of masses and frequencies.

References

References
1.
Pelrine
,
R.
,
Kornbluh
,
R.
,
Joseph
,
J.
,
Heydt
,
R.
,
Pei
,
Q.
, and
Chiba
,
S.
,
2000
, “
High-Field Deformation of Elastomeric Dielectrics for Actuators
,”
Mater. Sci. Eng. C
,
11
(
2
), pp.
89
100
.10.1016/S0928-4931(00)00128-4
2.
Bar-Cohen
,
Y.
,
2000
, “
Electroactive Polymers as Artificial Muscles—Capabilities, Potentials and Challenges
,”
Handbook on Biomimetics
, Vol. 8, Y. Osada, ed., NTS Inc., Peachtree City, GA.
3.
Carpi
,
K.
,
Sommer-Larsen
,
R.
,
Rossi
,
P.
, and
Alici
,
D. D.
,
2011
, “
Guest Editorial Introduction to the Focused Section on Electroactive Polymer Mechatronics
,”
IEEE/ASME Trans. Mechatron.
,
16
(
1
), pp.
1
8
.10.1109/TMECH.2010.2094199
4.
Goulbourne
,
N. C.
,
Frecker
,
M. I.
, and
Mockensturm
,
E.
,
2004
, “
Electro-Elastic Modeling of a Dielectric Elastomer Diaphragm for a Prosthetic Blood Pump
,”
Proc. SPIE
,
5385
, p.
122
.10.1117/12.539818
5.
Loverich
,
J. J.
,
Kanno
,
I.
, and
Kotera
,
H.
,
2006
, “
Concepts for a New Class of All-Polymer Micropumps
,”
Lab Chip
,
6
(
9
), pp.
1147
1154
.10.1039/b605525g
6.
Carpi
,
F.
,
Menon
,
C.
, and
De Rossi
,
D.
,
2010
, “
Electroactive Elastomeric Actuator for All-Polymer Linear Peristaltic Pumps
,”
IEEE/ASME Trans. Mechatron.
,
15
(
3
), pp.
460
470
.10.1109/TMECH.2009.2028884
7.
Lotz
,
P.
,
Matysek
,
M.
, and
Schlaak
,
H. F.
,
2011
, “
Fabrication and Application of Miniaturized Dielectric Elastomer Stack Actuators
,”
IEEE/ASME Trans. Mechatron.
,
16
(
1
), pp.
58
66
.10.1109/TMECH.2010.2090164
8.
Maffli
,
L.
,
Rosset
,
S.
, and
Shea
,
H. R.
,
2013
, “
Zipping Dielectric Elastomer Actuators: Characterization, Design and Modeling
,”
Smart Mater. Struct.
,
22
(
10
), p.
104013
.10.1088/0964-1726/22/10/104013
9.
Pelrine
,
R.
,
Sommer-Larsen
,
P.
,
Kornbluh
,
R. D.
,
Heydt
,
R.
,
Kofod
,
G.
,
Pei
,
Q.
, and
Gravesen
,
P.
,
2001
, “
Applications of Dielectric Elastomer Actuators
,”
Proc. SPIE
,
4329
, pp.
335
349
.10.1117/12.432665
10.
Jhong
,
Y. Y.
,
Huang
,
C. M.
,
Hsieh
,
C. C.
, and
Fu
,
C. C.
,
2007
, “
Improvement of Viscoelastic Effects of Dielectric Elastomer Actuator and Its Application for Valve Devices
,”
Proc. SPIE
,
6524
, p.
65241Y
.10.1117/12.715998
11.
Giousouf
,
M.
, and
Kovacs
,
G.
,
2013
, “
Dielectric Elastomer Actuators Used for Pneumatic Valve Technology
,”
Smart Mater. Struct.
,
22
(
10
), p.
104010
.10.1088/0964-1726/22/10/104010
12.
Heydt
,
R.
,
Pelrine
,
R.
,
Joseph
,
J.
,
Eckerle
,
J.
, and
Kornbluh
,
R.
,
2000
, “
Acoustical Performance of an Electrostrictive Polymer Film Loudspeaker
,”
J. Acoust. Soc. Am.
,
107
(
2
), pp.
833
839
.10.1121/1.428266
13.
Sugimoto
,
T.
,
Ando
,
A.
,
Ono
,
K.
,
Morita
,
Y.
,
Hosoda
,
K.
,
Ishii
,
D.
, and
Nakamura
,
K.
,
2013
, “
A Lightweight Push-Pull Acoustic Transducer Composed of a Pair of Dielectric Elastomer Films
,”
J. Acoust. Soc. Am.
,
134
(
5
), pp.
EL432
EL437
.10.1121/1.4824631
14.
Pelrine
,
R.
,
Kornbluh
,
R. D.
,
Pei
,
Q.
,
Stanford
,
S.
,
Oh
,
S.
,
Eckerle
,
J.
,
Full
,
R. J.
,
Rosenthal
,
M. A.
, and
Meijer
,
K.
,
2002
, “
Dielectric Elastomer Artificial Muscle Actuators: Toward Biomimetic Motion
,”
Proc. SPIE
,
4695
, pp.
126
137
.10.1117/12.475157
15.
Wingert
,
A.
,
Lichter
,
M. D.
,
Dubowsky
,
S.
, and
Hafez
,
M.
,
2002
, “
Hyper-Redundant Robot Manipulators Actuated by Optimized Binary-Dielectric Polymers
,”
Proc. SPIE
,
4695
, pp.
415
423
.10.1117/12.475189
16.
Plante
,
J. S.
,
2006
, “
Dielectric Elastomer Actuators for Binary Robotics and Mechatronics
,” Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of technology, Cambridge, MA.
17.
Zdunich
,
P.
,
Bilyk
,
D.
,
MacMaster
,
M.
,
Loewen
,
D.
,
DeLaurier
,
J.
,
Kornbluh
,
R.
,
Low
,
T.
,
Stanford
,
S.
, and
Holeman
,
D.
,
2007
, “
Development and Testing of the Mentor Flapping-Wing Micro Air Vehicle
,”
J. Aircraft
,
44
(
5
), pp.
1701
1711
.10.2514/1.28463
18.
Lau
,
G. K.
,
Lim
,
H. T.
,
Teo
,
J. Y.
, and
Chin
,
Y. W.
,
2014
, “
Lightweight Mechanical Amplifiers for Rolled Dielectric Elastomer Actuators and Their Integration With Bio-Inspired Wing Flappers
,”
Smart Mater. Struct.
,
23
(
2
), p.
025021
.10.1088/0964-1726/23/2/025021
19.
Kim
,
H.
,
Park
,
J.
,
Chuc
,
N. H.
,
Choi
,
H. R.
,
Nam
,
J. D.
,
Lee
,
Y.
, and
Koo
,
J. C.
,
2007
, “
Development of Dielectric Elastomer Driven Micro-Optical Zoom Lens System
,”
Proc. SPIE
,
6524
, p.
65241V
.10.1117/12.716872
20.
Keplinger
,
C.
,
Kaltenbrunner
,
M.
,
Arnold
,
N.
, and
Bauer
,
S.
,
2010
, “
Röntgen's Electrode-Free Elastomer Actuators Without Electromechanical Pull-In Instability
,”
Proc. Natl. Acad. Sci. U.S.A.
,
107
(
10
), pp.
4505
4510
.10.1073/pnas.0913461107
21.
Carpi
,
F.
,
Frediani
,
G.
, and
De Rossi
,
D.
,
2012
,
Bioinspired Tunable Lens Driven by Electroactive Polymer Artificial Muscles
(Biomimetic and Biohybrid Systems),
Springer
,
Berlin
, pp.
74
82
.
22.
Son
,
S. I.
,
Pugal
,
D.
,
Hwang
,
T.
,
Choi
,
H. R.
,
Koo
,
J. C.
,
Lee
,
Y.
,
Kim
,
K.
, and
Nam
,
J. D.
,
2012
, “
Electromechanically Driven Variable-Focus Lens Based on Transparent Dielectric Elastomer
,”
Appl. Opt.
,
51
(
15
), pp.
2987
2996
.10.1364/AO.51.002987
23.
Jordan
,
G.
,
McCarthy
,
D. N.
,
Schlepple
,
N. N.
,
Krissler
,
J.
,
Schroder
,
H.
, and
Kofod
,
G.
,
2011
, “
Actuated Micro-Optical Submount Using a Dielectric Elastomer Actuator
,”
IEEE/ASME Trans. Mechatron.
,
16
(
1
), pp.
98
102
.10.1109/TMECH.2010.2089991
24.
Kofod
,
G.
,
Paajanen
,
M.
, and
Bauer
,
S.
,
2006
, “
Self-Organized Minimum-Energy Structures for Dielectric Elastomer Actuators
,”
Appl. Phys. A
,
85
(
2
), pp.
141
143
.10.1007/s00339-006-3680-3
25.
Siu
,
S.
,
Rhode-Barbarigos
,
L.
,
Wagner
,
S.
, and
Adriaenssens
,
S.
,
2013
, “
Dynamic Relaxation Study and Experimental Verification of Dielectric-Elastomer Minimum-Energy Structures
,”
Appl. Phys. Lett.
,
103
(
17
), p.
171906
.10.1063/1.4826884
26.
Toupin
,
R. A.
,
1956
, “
The Elastic Dielectric
,”
J. Ration. Mech. Anal.
,
5
(
6
), pp.
849
915
.
27.
Dorfmann
,
A.
, and
Muhr
,
A.
, eds.,
1999
,
Constitutive Models for Rubber
,
A.A. Balkema
,
Rotterdam, The Netherlands
.
28.
Kofod
,
G.
,
2001
,
Dielectric Elastomer Actuators
,
Department of Chemistry, Technical University of Denmark
,
Copenhagen
.
29.
Dorfmann
,
A.
, and
Ogden
,
R. W.
,
2005
, “
Nonlinear Electroelasticity
,”
Acta Mech.
,
174
(
3–4
), pp.
167
183
.10.1007/s00707-004-0202-2
30.
Hodgins
,
M.
,
York
,
A.
, and
Seelecke
,
S.
,
2011
, “
Modeling and Experimental Validation of a Bi-Stable Out-of-Plane DEAP Actuator System
,”
Smart Mater. Struct.
,
20
(
9
), p.
094012
.10.1088/0964-1726/20/9/094012
31.
Koh
,
S. J. A.
,
Li
,
T.
,
Zhou
,
J.
,
Zhao
,
X.
,
Hong
,
W.
,
Zhu
,
J.
, and
Suo
,
Z.
,
2011
, “
Mechanisms of Large Actuation Strain in Dielectric Elastomers
,”
J. Polym. Sci. B
,
49
(
7
), pp.
504
515
.10.1002/polb.22223
32.
Vertechy
,
R.
,
Berselli
,
G.
,
Castelli
,
V. P.
, and
Bergamasco
,
M.
,
2013
, “
Continuum Thermo-Electro-Mechanical Model for Electrostrictive Elastomers
,”
J. Intell. Mater. Syst. Struct.
,
24
(
6
), pp.
761
778
.10.1177/1045389X12455855
33.
York
,
A.
,
Dunn
,
J.
, and
Seelecke
,
S.
,
2010
, “
Experimental Characterization of the Hysteretic and Rate-Dependent Electromechanical Behavior of Dielectric Electro-Active Polymer Actuators
,”
Smart Mater. Struct.
,
19
(
9
), p.
094014
.10.1088/0964-1726/19/9/094014
34.
Wiley,
2011
,
Properties and Behavior of Polymers
,
Wiley
,
Hoboken, NJ
.
35.
Bonet
,
J.
,
2001
, “
Large Strain Viscoelastic Constitutive Models
,”
Int. J. Solids Struct.
,
38
(
17
), pp.
2953
2968
.10.1016/S0020-7683(00)00215-8
36.
De Tommasi
,
D.
,
Puglisi
,
G.
,
Saccomandi
,
G.
, and
Zurlo
,
G.
,
2010
, “
Pull-In and Wrinkling Instabilities of Electroactive Dielectric Actuators
,”
J. Phys. D: Appl. Phys.
,
43
(
32
), p.
325501
.10.1088/0022-3727/43/32/325501
37.
Plante
,
J. S.
, and
Dubowsky
,
S.
,
2006
, “
Large-Scale Failure Modes of Dielectric Elastomer Actuators
,”
Int. J. Solids Struct.
,
43
(
25
), pp.
7727
7751
.10.1016/j.ijsolstr.2006.03.026
38.
Zhao
,
X.
, and
Suo
,
Z.
,
2007
, “
Method to Analyze Electromechanical Stability of Dielectric Elastomers
,”
Appl. Phys. Lett.
,
91
(
6
), p.
061921
.10.1063/1.2768641
39.
Kofod
,
G.
,
Sommer-Larsen
,
P.
,
Kornbluh
,
R.
, and
Pelrine
,
R.
,
2003
, “
Actuation Response of Polyacrylate Dielectric Elastomers
,”
J. Intell. Mater. Syst. Struct.
,
14
(
12
), pp.
787
793
.10.1177/104538903039260
40.
Hackl
,
C. M.
,
Tang
,
H. Y.
,
Lorenz
,
R. D.
,
Turng
,
L. S.
, and
Schroder
,
D.
,
2005
, “
A Multidomain Model of Planar Electro-Active Polymer Actuators
,”
IEEE Trans. Ind. Appl.
,
41
(
5
), pp.
1142
1148
.10.1109/TIA.2005.853384
41.
Wissler
,
M.
, and
Mazza
,
E.
,
2005
, “
Modeling of a Pre-Strained Circular Actuator Made of Dielectric Elastomers
,”
Sens. Actuators, A
,
120
(
1
), pp.
184
192
.10.1016/j.sna.2004.11.015
42.
Kaal
,
W.
, and
Herold
,
S.
,
2011
, “
Electroactive Polymer Actuators in Dynamic Applications
,”
IEEE/ASME Trans. Mechatron.
,
16
(
1
), pp.
24
32
.10.1109/TMECH.2010.2089529
43.
Sarban
,
R.
,
Lassen
,
B.
, and
Willatzen
,
M.
,
2012
, “
Dynamic Electromechanical Modeling of Dielectric Elastomer Actuators With Metallic Electrodes
,”
IEEE/ASME Trans. Mechatron.
,
17
(
5
), pp.
960
967
.10.1109/TMECH.2011.2150239
44.
Berselli
,
G.
,
Vertechy
,
R.
,
Babič
,
M.
, and
Castelli
,
V. P.
,
2012
, “
Dynamic Modeling and Experimental Evaluation of a Constant-Force Dielectric Elastomer Actuator
,”
J. Intell. Mater. Syst. Struct.
,
24
(
6
), pp.
779
791
.10.1177/1045389X12457251
45.
Iskandarani
,
Y.
, and
Karimi
,
H. R.
,
2013
, “
Dynamic Characterization for the Dielectric Electroactive Polymer Fundamental Sheet
,”
Int. J. Adv. Manuf. Technol.
,
66
(
9–12
), pp.
1457
1466
.10.1007/s00170-012-4423-6
46.
Rizzello
,
G.
,
Naso
,
D.
,
York
,
A.
, and
Seelecke
,
S.
,
2013
, “
A Nonlinear Electro-Mechanical Model for an Annular Dielectric Elastomer Actuator With a Biasing Mass
,” VDI Mechatronik 2013, Aachen, Germany, Mar. 6–8.
47.
Moretti
,
G.
,
Fontana
,
M.
, and
Vertechy
,
R.
,
2013
, “
Modeling and Control of Lozenge-Shaped Dielectric Elastomer Generators
,”
ASME
Paper No. SMASIS2013-3258.10.1115/SMASIS2013-3258
48.
McMeeking
,
R. M.
, and
Landis
,
C. M.
,
2005
, “
Electrostatic Forces and Stored Energy for Deformable Dielectric Materials
,”
ASME J. Appl. Mech.
,
72
(
4
), pp.
581
590
.10.1115/1.1940661
49.
Rudykh
,
S.
,
Bhattacharya
,
K.
, and
deBotton
,
G.
,
2012
, “
Snap-Through Actuation of Thick-Wall Electroactive Balloons
,”
Int. J. Non-Linear Mech.
,
47
(
2
), pp.
206
209
.10.1016/j.ijnonlinmec.2011.05.006
50.
Hodgins
,
M.
,
York
,
A.
, and
Seelecke
,
S.
,
2013
, “
Experimental Comparison of Bias Elements for Out-of-Plane DEAP Actuator System
,”
Smart Mater. Struct.
,
22
(
9
), p.
094016
.10.1088/0964-1726/22/9/094016
51.
Rizzello
,
G.
,
Naso
,
D.
,
York
,
A.
, and
Seelecke
,
S.
,
2013
, “
Modeling and Position Control of an Electromechanical Actuator Based on a Mass-Spring-Biased EAP System
,” IEEE
18th Conference on Emerging Technologies and Factory Automation
(
ETFA
), Cagliari, Italy, Sept. 10–13.10.1109/ETFA.2013.6648039
52.
Stratton
,
J. A.
,
1941
,
Electromagnetic Theory
,
McGraw-Hill
, New York.
53.
Coleman
,
T.
,
Branch
,
M. A.
, and
Grace
,
A.
,
1999
, “
Optimization Toolbox: For Use With Matlab,” User's Guide for Matlab 5, Ver. 2
, Release II, The MathWorks Inc., Natick, MA.
54.
Suo
,
Z.
,
2010
, “
Theory of Dielectric Elastomers
,”
Acta Mech. Solida Sin.
,
23
(
6
), pp.
549
578
.10.1016/S0894-9166(11)60004-9
55.
Jang
,
J.
,
Sun
,
C.
, and
Mizutani
,
E.
,
1997
,
Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
56.
Ljung
,
L.
,
1988
, “
System Identification Toolbox:, For Use With Matlab
,” User's Guide, Ver. 6., The MathWorks Inc., Natick, MA.
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