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Electromechanical instability
Zhigang SuoHarvard University
2:00 pm – 2:45 pm, 11 January 2010, Monday
PhD Winter SchoolDielectric Elastomer Transducers
Monte Verita, Ascona, Switzerland, 11-16 January 2010http://www.empa.ch/eap-winterschool
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2
l
Q
Q
Stark & Garton, Nature 176, 1225 (1955)
Theory of pull-in instability
3/12~
1
D
Q
l
3/22~
1~
/
~
DDE
mVmF
mNEc /10
/10
/10~~
~ 810
6
Zhao, Suo, APL 91, 061921 (2007)
2
~32
2~,
2212 D
DW
0
~,
DW
s D
DWE ~
~,~
63.0cQ
polarizing thinning
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Free energy
2P 1P
22L
33L
11L
Q
2P 1P
22L
33L
11L
Q
QLPLPDWLLLDG 2221112132121
~,,
~,,
System Dielectric Weights Battery
1L3L
2L
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Free energy minimized at a state of equilibrium
DD
WD
D
WWD
D
WWW
DED
Ws
Ws
WLLL
G
~~
~~
~~2
121
21
~~~
22
2
11
2
2121
22
2
2222
2
2212
1
2
222
111321
D
DWE
DWs
DWs ~
~,,~
,~,,
,~,, 21
2
212
1
211
0
~~~
~
~
det
2
2
2
2
1
22
2
22
2
21
21
2
21
2
21
2
D
W
D
W
D
WD
WWWD
WWW
Equations of state
Critical condition for onset of instability
Zhao, Suo, APL 91, 061921 (2007)
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Pre-stretch
increases deformation of actuation
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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6
l
Q
Q
Interpretation: Zhao, Hong, SuoPhysical Review B 76, 134113 (2007)
Coexistent states: flat and wrinkledObservation: Plante, Dubowsky, Int. J. Solids and Structures 43, 7727 (2006)
Qthick thin
Top viewCross section
Coexistent states polarizing
thinning
stiffening
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When stretched, a polymer stiffens
nb
bn
b
n links
PP
PP
P
n
Langevin
Gauss
released
stretched
fully stretched
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Stiffening due to extension limit
l
Q
Q
Q
Zhao, Hong, Suo, Physical Review B 76, 134113 (2007).
...9
20
13
2
1 2In
IWs
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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Failure ModesFailure Modes
Rupture Loss of Tension
Electrical Breakdown Electromechanical Instability
+
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–stable unstable
R 01 s or 02 s
+
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
BDEE
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11Pei, Pelrine, Stanford, Kornbluh, Rosenthal, Meijer, Full
Proc. SPIE 4698, 246 (2002)
Allowable states of a transducer
Moscardo, Zhao, Suo, LapustaJAP 104, 093503 (2008)
allowable states
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Energy harvesting
Generate electricity from walking Generate electricity from waves
Pelrine, Kornbluh…
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Maximal energy that can be converted by a dielectric elastomer
R
LT
EB
E=0
EMI
Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009)
6 J/g, Elastomer (theory)0.4 J/g, Elastomer (experiment)0.01 J/g ceramics
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A “practical” design
2 J/g
Q
Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009)
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Summary
• Pull-in instability: coupling large deformation and electric charge.
• Pre-stretch increases actuation strain.• Co-existent states: stiffening due to
extension limit.• Allowable states: as defined by various
modes of failure