1

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

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

3

Free energy

2P 1P

22L

33L

11L

Q

2P 1P

22L

33L

11L

Q

QLPLPDWLLLDG 2221112132121

~,,

~,,

System Dielectric Weights Battery

1L3L

2L

4

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)

5

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)

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

7

When stretched, a polymer stiffens

nb

bn

b

n links

PP

PP

P

n

Langevin

Gauss

released

stretched

fully stretched

8

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)

9

FEM: inhomogeneous deformation

Thick State

Transition

Thin State

Thick State

Transition

Thin State

Zhou, Hong, Zhao, Zhang, Suo, IJSS, 2007

10

Failure ModesFailure Modes

Rupture Loss of Tension

Electrical Breakdown Electromechanical Instability

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–stable unstable

R 01 s or 02 s

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–

+

–

BDEE

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

12

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

14

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