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1
Electromechanical instability of large deformation in
dielectric elastomers
Zhigang SuoHarvard University
Work withX. Zhao, W. Hong, J. Zhou, W. Greene
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2
l
Q
Q
Stark & GartonNature 176, 1225 (1955)
Pull-in instability
Q
l
Compliant Electrode
Dielectric Elastomer
L
A
a
Q
polarizing thinning
Pelrine, Kornbluh, Pei, JosephScience 287, 836 (2000)
Plante, Dubowsky Int. J. Solids and Structures 43, 7727 (2006)
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Theory
2P 1P
22L
33L
11L
Q
2P 1P
22L
33L
11L
Q
QLPLPDWLLLDG 2221112132121~,,~,,
DEDWsWsW
LLLG ~~
~0 222
111321
System Dielectric Weights Battery
Equilibrium condition
APs /
LE /~
AQD /~ Zhao, Suo, APL 91, 061921 (2007)
Free energy of the system
Need free-energy function DW ~,, 21
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Dielectric constant is insensitive to deformation
Kofod, Sommer-Larsen, Kornbluh, Pelrine Journal of Intelligent Material Systems and Structures 14, 787-793 (2003).
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5
2
,~,,2
2121DWDW s
32
, 23
22
2121 sW
Stretch Polarization
Material law: Ideal dielectric elastomersZhao, Hong, Suo, Physical Review B 76, 134113 (2007)
aQD
AQD ~
21
~
DD
213 /1
Dielectric behavior is liquid-like, unaffected by deformation.
Ideal electromechanical coupling is purely a geometric effect:
Choose a free energy of stretching. For example, neo-Hookean law:
incompressibility
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6
l
Q
Q
Stark & Garton, Nature 176, 1225 (1955)
Theory of pull-in instability
3/12~1
D
Q
l
3/22~1
~
/
~
DDE
mVmFmNEc /10/10/10~~~ 8
10
6
Zhao, Suo, APL 91, 061921 (2007)
22
12~
322
~, DDW
0~,
DWs
DDWE ~~,~
63.0cQ
polarizing thinning
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Pre-stretch increases actuation strain
2P 1P
22L
33L
11L
Q
2P 1P
22L
33L
11L
Q
Experiment: Pelrine, Kornbluh, Pei, JosephScience 287, 836 (2000).
Theory: Zhao, SuoAPL 91, 061921 (2007)
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8
l
Q
Q
Theory: Zhao, Hong, SuoPhysical Review B 76, 134113 (2007)
Coexistent states: flat and wrinkledExperiment: Plante, Dubowsky, Int. J. Solids and Structures 43, 7727 (2006)
Qthick thin
Top viewCross section
Coexistent states polarizing
thinning
stiffening
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Stiffening due to extension limit
l
Q
Q
Q
Zhao, Hong, Suo, Physical Review B 76, 134113 (2007).
...9
2013
21 2I
nIWs
Stiffening as each polymer chain approaches its fully stretched length (e.g., Arruda-Boyce model)
: small-strain shear modulusn: number of monomers per chain
23
22
21 I
Zhao, Hong, SuoPhysical Review B 76, 134113 (2007)
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FEM: inhomogeneous deformation
Thick State
Transition
Thin State
Thick State
Transition
Thin State
Zhou, Hong, Zhao, Zhang, Suo, IJSS, 2007
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Summary
• Ideal dielectric elastomers: dielectric behavior is liquid like, unaffected by deformation.
• Pull-in instability: coupling large deformation and electric charge.
• Pre-stretch increases actuation strain.• Co-existent states: stiffening due to extension limit.
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Game plan
• Inhomogeneous deformation.• Quantitative comparison with experiments.• Effect of viscosity on instability.• Nonideal electromechanical coupling.• Adding other effects (solvents, ions, enzymes
…): Soft Active Materials (SAMs)
http://imechanica.org/node/2280