Abstract

This work presents the dynamic modeling and analysis of a particle-reinforced and pre-stressed electro-magneto-viscoelastic plate actuator. The actuator belongs to a smart actuator category and is made of an electro-magneto-active polymer filled with a particular volume fraction of suitable fillers. An energy-based electro-magneto-viscoelastic model is developed to predict the actuator response and interrogate the impact of particle reinforcement on the dynamic oscillations of a pre-stressed condition of the actuator. An Euler–Lagrange equation of motion is implemented to deduce the governing dynamic equation of the actuator. The findings of the model solutions provide preliminary insights on the alteration of the nonlinear behavior of the actuator driven by DC and AC dynamic modes of actuation. It is observed that the enrichment in the particle reinforcement characterized by the amount of fillers strengthens the polymer and depleted the associated level of deformation. Also, the depletion in the intensity of oscillation and enhancement in the frequency of excitation is perceived with an increase in the particle reinforcement. In addition, the time-history response, Poincare plots, and phase diagrams are also plotted to assess the stability, periodicity, beating phenomenon, and resonant behavior of the actuator. In general, the current study provides initial steps toward the modern actuator designs for various futuristic applications in the engineering and medical field.

References

1.
Alameh
,
Z.
,
Yang
,
S.
,
Deng
,
Q.
, and
Sharma
,
P.
,
2018
, “
Emergent Magnetoelectricity in Soft Materials, Instability, and Wireless Energy Harvesting
,”
Soft. Matter
,
14
(
28
), pp.
5856
5868
.
2.
Kumar
,
D.
, and
Sarangi
,
S.
,
2018
, “
Instability Analysis of an Electro-Magneto-Elastic Actuator: A Continuum Mechanics Approach
,”
AIP Adv.
,
8
(
11
), p.
115314
.
3.
Amiri-Hezaveh
,
A.
,
Karimi
,
P.
, and
Ostoja-Starzewski
,
M.
,
2019
, “
Stress Field Formulation of Linear Electro-Magneto-Elastic Materials
,”
Math. Mech. Solids
,
24
(
12
), pp.
3806
3822
.
4.
Kumar
,
D.
, and
Sarangi
,
S.
,
2019
, “
Electro-Magnetostriction Under Large Deformation: Modeling With Experimental Validation
,”
Mech. Mater.
,
128
, pp.
1
10
.
5.
Kumar
,
D.
,
Sarangi
,
S.
, and
Saxena
,
P.
,
2020
, “
Universal Relations in Coupled Electro-Magneto-Elasticity
,”
Mech. Mater.
,
143
, p.
103308
.
6.
Bar-Cohen
,
Y.
,
2001
, “
Electroactive Polymers as Artificial Muscles-Reality and Challenges
,”
19th AIAA Applied Aerodynamics Conference
,
Anaheim, CA
,
June 11–14
, p. 1492.
7.
Kumar
,
D.
,
Ghosh
,
S.
,
Roy
,
S.
, and
Santapuri
,
S.
,
2021
, “
Modeling and Analysis of an Electro-Pneumatic Braided Muscle Actuator
,”
J. Intel. Mater. Syst. 23 Struct.
,
32
(
4
), pp.
399
409
.
8.
Keplinger
,
C.
,
Sun
,
J.-Y.
,
Foo
,
C. C.
,
Rothemund
,
P.
,
Whitesides
,
G. M.
, and
Suo
,
Z.
,
2013
, “
Stretchable, Transparent, Ionic Conductors
,”
Science
,
341
(
6149
), pp.
984
987
.
9.
Carpi
,
F.
,
Frediani
,
G.
,
Turco
,
S.
, and
De Rossi
,
D.
,
2011
, “
Bioinspired Tunable Lens With Muscle-Like Electroactive Elastomers
,”
Adv. Funct. Mater.
,
21
(
21
), pp.
4152
4158
.
10.
Khurana
,
A.
,
Kumar
,
A.
,
Raut
,
S. K.
,
Sharma
,
A. K.
, and
Joglekar
,
M. M.
,
2021
, “
Effect of Viscoelasticity on the Nonlinear Dynamic Behavior of Dielectric Elastomer Minimum Energy Structures
,”
Int. J. Solids. Struct.
,
208
, pp.
141
153
.
11.
Mori
,
T.
, and
Tanaka
,
K.
,
1973
, “
Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,”
Acta. Metall.
,
21
(
5
), pp.
571
574
.
12.
Long
,
Y.
, and
Shanks
,
R. A.
,
1996
, “
Pp–Elastomer–Filler Hybrids. I. Processing, Microstructure, and Mechanical Properties
,”
J. Appl. Polym. Sci.
,
61
(
11
), pp.
1877
1885
.
13.
Bartczak
,
Z.
,
Argon
,
A.
,
Cohen
,
R.
, and
Weinberg
,
M.
,
1999
, “
Toughness Mechanism in Semi-Crystalline Polymer Blends: II. High-Density Polyethylene Toughened With Calcium Carbonate Filler Particles
,”
Polymer
,
40
(
9
), pp.
2347
2365
.
14.
Sangerano
,
M.
,
Pallaro
,
E.
,
Roppolo
,
I.
, and
Rizza
,
G.
,
2009
, “
UV-Cured Epoxy Coating Reinforced With Sepiolite As Inorganic Filler
,”
J. Mater. Sci.
,
44
(
12
), pp.
3165
3171
.
15.
Lee
,
H. S.
,
Phung
,
H.
,
Lee
,
D. -H.
,
Kim
,
U. K.
,
Nguyen
,
C. T.
,
Moon
,
H.
,
Koo
,
J. C.
,
Choi
,
H. R.
,
2014
, “
Design Analysis and Fabrication of Arrayed Tactile Display Based on Dielectric Elastomer Actuator
,”
Sens. Actuators., A.
,
205
, pp.
191
198
.
16.
Xia
,
F.
,
Tadigadapa
,
S.
, and
Zhang
,
Q.
,
2006
, “
Electroactive Polymer Based Microfluidic Pump
,”
Sens. Actuators. A.
,
125
(
2
), pp.
346
352
.
17.
Jee
,
J.
, and
Choi
,
J.-W.
,
2017
, “
Smart Loudspeaker Arrays for Self-Coordination and User Tracking
,”
International Conference on Multimedia Modeling
,
Reykjavik, Iceland
,
Jan. 4–6
, Springer, pp. 343–355.
18.
Antonietti
,
M.
,
Neese
,
M.
,
Blum
,
G.
, and
Kremer
,
F.
,
1996
, “
Dielectric and Mechanic Relaxation in Polyelectrolyte-Supported Bilayer Stacks: A Model for the Dynamics of Membranes?
,”
Langmuir
,
12
(
18
), pp.
4436
4441
.
19.
Ho
,
S.
, and
Mittal
,
G. S.
,
1996
, “
Electroporation of Cell Membranes: A Review
,”
Crit. Rev. Biotechnol.
,
16
(
4
), pp.
349
362
.
20.
Zhu
,
J.
,
Cai
,
S.
, and
Suo
,
Z.
,
2010
, “
Resonant Behavior of a Membrane of a Dielectric Elastomer
,”
Int. J. Solids. Struct.
,
47
(
24
), pp.
3254
3262
.
21.
Xu
,
B.-X.
,
Mueller
,
R.
,
Theis
,
A.
,
Klassen
,
M.
, and
Gross
,
D.
,
2012
, “
Dynamic Analysis of Dielectric Elastomer Actuators
,”
Appl. Phys. Lett.
,
100
(
11
), p.
112903
.
22.
Joglekar
,
M. M.
,
2015
, “
Dynamic-Instability Parameters of Dielectric Elastomer Actuators With Equal Biaxial Prestress
,”
AIAA. J.
,
53
(
10
), pp.
3129
3133
.
23.
Zhu
,
J.
,
2015
, “
Instability in Nonlinear Oscillation of Dielectric Elastomers
,”
ASME J. Appl. Mech.
,
82
(
6
), p.
061001
.
24.
Sharma
,
A. K.
,
Bajpayee
,
S.
,
Joglekar
,
D. M.
, and
Joglekar
,
M. M.
,
2017
, “
Dynamic Instability of Dielectric Elastomer Actuators Subjected to Unequal Biaxial Prestress
,”
Smart Mater. Struct.
,
26
(
11
), p.
115019
.
25.
Sharma
,
A. K.
,
Arora
,
N.
, and
Joglekar
,
M. M.
,
2018
, “
DC Dynamic Pull-in Instability of a Dielectric Elastomer Balloon: An Energy-Based Approach
,”
Proc. R. Soc. A. Math. Phys. Eng. Sci.
,
474
(
2211
), p.
20170900
.
26.
Arora
,
N.
,
Kumar
,
P.
, and
Joglekar
,
M. M.
,
2018
, “
A Modulated Voltage Waveform for Enhancing the Travel Range of Dielectric Elastomer Actuators
,”
ASME J. Appl. Mech.
,
85
(
11
), p.
111009
.
27.
Dai
,
H.
,
Zou
,
J.
, and
Wang
,
L.
,
2016
, “
Effect of Initial Stretch Ratio on the Electromechanical Responses of Dielectric Elastomer Actuators
,”
Appl. Phys. A.
,
122
(
5
), pp.
1
6
.
28.
Sheng
,
J.
,
Chen
,
H.
, and
Li
,
B.
,
2011
, “
Effect of Temperature on the Stability of Dielectric Elastomers
,”
J. Phys. D: Appl. Phys.
,
44
(
36
), p.
365406
.
29.
Yong
,
H.
,
He
,
X.
, and
Zhou
,
Y.
,
2012
, “
Electromechanical Instability in Anisotropic Dielectric Elastomers
,”
Int. J. Eng. Sci.
,
50
(
1
), pp.
144
150
.
30.
Sharma
,
A. K.
, and
Joglekar
,
M.
,
2018
, “
Effect of Anisotropy on the Dynamic Electromechanical Instability of a Dielectric Elastomer Actuator
,”
Smart Mater. Struct.
,
28
(
1
), p.
015006
.
31.
Sharma
,
A. K.
,
Sheshkar
,
N.
, and
Gupta
,
A.
,
2021
, “
Static and Dynamic Stability of Dielectric Elastomer Fiber Composites
,”
Mater. Today Proc.
,
44
, pp.
2043
2047
.
32.
Zhang
,
J.
,
Chen
,
H.
,
Sheng
,
J.
,
Liu
,
L.
,
Wang
,
Y.
, and
Jia
,
S.
,
2014
, “
Dynamic Performance of Dissipative Dielectric Elastomers Under Alternating Mechanical Load
,”
Appl. Phys. A.
,
116
(
1
), pp.
59
67
.
33.
Bai
,
Y.
,
Jiang
,
Y.
,
Chen
,
B.
,
Chiang Foo
,
C.
,
Zhou
,
Y.
,
Xiang
,
F.
,
Zhou
,
J.
,
Wang
,
H.
, and
Suo
,
Z.
,
2014
, “
Cyclic Performance of Viscoelastic Dielectric Elastomers With Solid Hydrogel Electrodes
,”
Appl. Phys. Lett.
,
104
(
6
), p.
062902
.
34.
Chiang Foo
,
C.
,
Cai
,
S.
,
Jin Adrian Koh
,
S.
,
Bauer
,
S.
, and
Suo
,
Z.
,
2012
, “
Model of Dissipative Dielectric Elastomers
,”
J. Appl. Phys.
,
111
(
3
), p.
034102
.
35.
Keplinger
,
C.
,
Kaltenbrunner
,
M.
,
Arnold
,
N.
, and
Bauer
,
S.
,
2008
, “
Capacitive Extensometry for Transient Strain Analysis of Dielectric Elastomer Actuators
,”
Appl. Phys. Lett.
,
92
(
19
), p.
192903
.
36.
Joglekar
,
M. M.
,
2014
, “
An Energy-Based Approach to Extract the Dynamic Instability Parameters of Dielectric Elastomer Actuators
,”
ASME J. Appl. Mech.
,
81
(
9
), p.
091010
.
37.
Sharma
,
A. K.
, and
Joglekar
,
M. M.
,
2019
, “
A Computationally Efficient Locking Free Numerical Framework for Modeling Visco-Hyperelastic Dielectric Elastomers
,”
Comput. Methods Appl. Mech. Eng.
,
352
, pp.
625
653
.
38.
Li
,
Y.
,
Oh
,
I.
,
Chen
,
J.
,
Zhang
,
H.
, and
Hu
,
Y.
,
2018
, “
Nonlinear Dynamic Analysis and Active Control of Visco-Hyperelastic Dielectric Elastomer Membrane
,”
Int. J. Solids Struct.
,
152
, pp.
28
38
.
39.
Eder-Goy
,
D.
,
Zhao
,
Y.
, and
Xu
,
B.-X.
,
2017
, “
Dynamic Pull-In Instability of a Prestretched Viscous Dielectric Elastomer Under Electric Loading
,”
Acta Mech.
,
228
(
12
), pp.
4293
4307
.
40.
Khurana
,
A.
,
Kumar
,
A.
,
Sharma
,
A. K.
, and
Joglekar
,
M. M.
,
2021
, “
Effect of Polymer Chains Entanglements, Crosslinks and Finite Extensibility on the Nonlinear Dynamic Oscillations of Dielectric Viscoelastomer Actuators
,”
Nonlinear Dyn.
,
104
, pp.
1227
1251
.
41.
Sharma
,
A. K.
,
Kumar
,
P.
,
Singh
,
A.
,
Joglekar
,
D. M.
, and
Joglekar
,
M. M.
,
2019
, “
Electromechanical Instability of Dielectric Elastomer Actuators With Active and Inactive Electric Regions
,”
ASME J. Appl. Mech.
,
86
(
6
), p.
061008
.
42.
Sharma
,
A. K.
,
2020
, “
Design of a Command-Shaping Scheme for Mitigating Residual Vibrations in Dielectric Elastomer Actuators
,”
ASME J. Appl. Mech.
,
87
(
2
), p.
021007
.
43.
Sharma
,
A. K.
,
Shmuel
,
G.
, and
Amir
,
O.
,
2021
, “
Gradient-Based Topology Optimization of Soft Dielectrics as Tunable Phononic Crystals
,”
engrXiv
.
44.
Gent
,
A. N.
,
1996
, “
A New Constitutive Relation for Rubber
,”
Rubber. Chem. Technol.
,
69
(
1
), pp.
59
61
.
45.
Zhang
,
H.
,
Wang
,
Y.
,
Godaba
,
H.
,
Khoo
,
B. C.
,
Zhang
,
Z.
, and
Zhu
,
J.
,
2017
, “
Harnessing Dielectric Breakdown of Dielectric Elastomer to Achieve Large Actuation
,”
ASME J. Appl. Mech.
,
84
(
12
), p.
121011
.
46.
Khurana
,
A.
,
Sharma
,
A. K.
, and
Joglekar
,
M.
,
2021
, “
Nonlinear Oscillations of Electrically Driven Aniso-Visco-Hyperelastic Dielectric Elastomer Minimum Energy Structures
,”
Nonlinear Dyn.
,
104
(
3
), pp.
1991
2013
.
47.
Li
,
B.
,
Chen
,
H.
, and
Zhou
,
J.
,
2013
, “
Electromechanical Stability of Dielectric Elastomer Composites With Enhanced Permittivity
,”
Compos. Part A. Appl. Sci. Manufact.
,
52
, pp.
55
61
.
48.
Brochu
,
P.
, and
Pei
,
Q.
,
2012
, “Dielectric Elastomers for Actuators and Artificial Muscles,”
Electroactivity in Polymeric Materials
,
Springer US
,
Boston, MA
, pp.
1
56
.
49.
Kashyap
,
K.
,
Sharma
,
A. K.
, and
Joglekar
,
M. M.
,
2020
, “
Nonlinear Dynamic Analysis of Aniso-Visco-Hyperelastic Dielectric Elastomer Actuators
,”
Smart Mater. Struct.
,
29
(
5
), p.
055014
.
50.
Wang
,
J.
,
Nguyen
,
T. D.
, and
Park
,
H. S.
,
2014
, “
Electrostatically Driven Creep in Viscoelastic Dielectric Elastomers
,”
ASME J. Appl. Mech.
,
81
(
5
), p.
051006
.
51.
Zou
,
J.
,
Gu
,
G.-Y.
, and
Zhu
,
L.-M.
,
2016
, “
Open-loop Control of Creep and Vibration in Dielectric Elastomer Actuators With Phenomenological Models
,”
IEEE/ASME Trans. Mechatron.
,
22
(
1
), pp.
51
58
.
52.
Zhang
,
J.
,
Chen
,
H.
,
Li
,
B.
,
McCoul
,
D.
, and
Pei
,
Q.
,
2015
, “
Coupled Nonlinear Oscillation and Stability Evolution of Viscoelastic Dielectric Elastomers
,”
Soft. Matter
,
11
(
38
), pp.
7483
7493
.
53.
Zhang
,
J.
,
Tang
,
L.
,
Li
,
B.
,
Wang
,
Y.
, and
Chen
,
H.
,
2015
, “
Modeling of the Dynamic Characteristic of Viscoelastic Dielectric Elastomer Actuators Subject to Different Conditions of Mechanical Load
,”
J. Appl. Phys.
,
117
(
8
), p.
084902
.
54.
Vatanjou
,
H.
,
Hojjat
,
Y.
, and
Karafi
,
M.
,
2019
, “
Nonlinear Dynamic Analysis of Dielectric Elastomer Minimum Energy Structures
,”
Appl. Phys. A.
,
125
(
9
), p.
583
.
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