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Electromechanical instability. Zhigang Suo Harvard University 2:00 pm – 2:45 pm, 11 January 2010, Monday PhD Winter School Dielectric Elastomer Transducers Monte Verita, Ascona, Switzerland, 11-16 January 2010 http://www.empa.ch/eap-winterschool. Theory of pull-in instability. polarizing.

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electromechanical instability

Electromechanical instability

Zhigang Suo

Harvard University

2:00 pm – 2:45 pm, 11 January 2010, Monday

PhD Winter School

Dielectric Elastomer Transducers

Monte Verita, Ascona, Switzerland, 11-16 January 2010

http://www.empa.ch/eap-winterschool

theory of pull in instability
Theory of pull-in instability

polarizing

thinning

F

Stark & Garton, Nature 176, 1225 (1955)

Zhao, Suo, APL 91, 061921 (2007)

free energy
Free energy

System Dielectric Weights Battery

free energy minimized at a state of equilibrium
Free energy minimized at astate of equilibrium

Equations of state

Critical condition for onset of instability

Zhao, Suo, APL 91, 061921 (2007)

pre stretch increases deformation of actuation
Pre-stretch increases deformation of actuation

Theory: Zhao, Suo

APL 91, 061921 (2007)

Experiment: Pelrine, Kornbluh, Pei, Joseph

Science 287, 836 (2000).

coexistent states

Cross section

stiffening

Coexistent states

thinning

polarizing

F

thick

thin

Top view

Coexistent states: flat and wrinkled

Observation: Plante, Dubowsky,

Int. J. Solids and Structures43, 7727 (2006)

Interpretation: Zhao, Hong, Suo

Physical Review B 76, 134113 (2007)

slide7

When stretched, a polymer stiffens

n links

released

Langevin

Gauss

stretched

fully stretched

slide8

Stiffening due to extension limit

Stiffening as each polymer chain approaches its fully stretched length

(e.g., Arruda-Boyce model)

m: small-strain shear modulus

n: number of monomers per chain

Zhao, Hong, Suo, Physical Review B 76, 134113 (2007).

Zhao, Hong, Suo

Physical Review B 76, 134113 (2007)

slide9

FEM: inhomogeneous deformation

Thin State

Transition

Thick State

Thick State

Transition

Thin State

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

failure modes

or

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

stable

unstable

Failure Modes

Rupture

Loss of Tension

Electrical Breakdown

Electromechanical Instability

slide11

Allowable states of atransducer

allowable states

Pei, Pelrine, Stanford, Kornbluh, Rosenthal, Meijer, Full

Proc. SPIE 4698, 246 (2002)

Moscardo, Zhao, Suo, Lapusta

JAP 104, 093503 (2008)

energy harvesting
Energy harvesting

Generate electricity from walking

Generate electricity from waves

Pelrine, Kornbluh…

maximal energy that can be converted by a dielectric elastomer
Maximal energy that can be converted by a dielectric elastomer

6 J/g, Elastomer (theory)

0.4 J/g, Elastomer (experiment)

0.01 J/g ceramics

E=0

EMI

R

EB

LT

Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009)

a practical design
A “practical” design

2 J/g

Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009)

summary
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
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