Elastic dielectrics

1
Elastic dielectrics

• Zhigang Suo
• suo_at_seas.harvard.edu
• Room 309, Pierce Hall

Battery
Dielectric Elastomer
Compliant Electrode
Reference State
Current State
2
Dielectric elastomer actuators

• Large deformation
• Compact
• Lightweight
• Low cost
• Low-temperature fabrication

Kofod, Wirges, Paajanen, Bauer APL 90, 081916,
2007
3
Parallel-plate capacitor
P
battery
electrode
vacuum
electrode
P
force
Electric field
e0, permittivity of vacuum
Electric displacement field
stress field
Maxwell stress
4
An atom in an electric field
- - - - - - - - - - - -
battery
Hydrogen atom

• External electric field displaces positive and
  negative charges somewhat.
• Polarization Induce more change on the
  electrodes.
• Deformation Distort the shape of the atom.

5
A dipole in an electric field
- - - - - - - - - - - -
battery
Polar molecules

• External electric field reorients dipoles.
• Polarization Induce more change on the
  electrodes.
• Deformation Distort the shape of the sample.

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thinning or thickening?
Subject to an electric field, many polymers thin,
but many ceramics thicken.
Cheng, Zhang, MRS Bulletin 33, 183 (2008).
7
Thermodynamics of elastic dielectrics
Suo, Zhao, Greene, J. Mech. Phys. Solids 56, 467
(2008)
Reference State
Current State
For elastic dielectrics, work fully converts to
free energy
Free-energy density
Equations of state
8
Ideal dielectric elastomers
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
Zhao, Hong, Suo, Physical Review B 76, 134113
(2007)
9
Dielectric constant is insensitive to stretch
Kofod, Sommer-Larsen, Kornbluh, Pelrine Journal
of Intelligent Material Systems and Structures
14, 787-793 (2003).
10
Theory of pull-in instability
polarizing
thinning
F
Stark Garton, Nature 176, 1225 (1955)
Zhao, Suo, APL 91, 061921 (2007)
11
Pre-stretch increases actuation strain
Experiment Pelrine, Kornbluh, Pei,
Joseph Science 287, 836 (2000).
Theory Zhao, Suo APL 91, 061921 (2007)
12
Coexistent states
stiffening
thinning
polarizing
F
thick
thin
Top view
Coexistent states flat and wrinkled
Experiment Plante, Dubowsky, Int. J. Solids
and Structures 43, 7727 (2006)
Theory Zhao, Hong, Suo Physical Review B 76,
134113 (2007)