1

Electromechanical instability of large deformation in

dielectric elastomers

Zhigang SuoHarvard University

Work withX. Zhao, W. Hong, J. Zhou, W. Greene

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)

3

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

4

Dielectric constant is insensitive to deformation

Kofod, Sommer-Larsen, Kornbluh, Pelrine Journal of Intelligent Material Systems and Structures 14, 787-793 (2003).

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

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

7

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)

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

9

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)

10

FEM: inhomogeneous deformation

Thick State

Transition

Thin State

Thick State

Transition

Thin State

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

11

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.

12

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