1. Dielectric elastomers capable of giant deformation of actuation
Zhigang Suo
Harvard University
9:00 am – 9:45 am, 12 January 2010, Tuesday
PhD Winter School
Dielectric Elastomer Transducers
Monte Verita, Ascona, Switzerland, January 2010

2. Two modes of failure Electromechanical instability Soft material
Electrical breakdown
Hard material
polarizing
thinning
polarizing F F
Stark & Garton, Nature 176, 1225 (1955)

3. The Essential Dilemma (TED)
To deform appreciably without electrical breakdown, the elastomer must be soft.
But a soft elastomer is susceptible to electromechanical instability.
How large can deformation of actuation be?

4. Experimentally observed large deformation of actuation
Zhenyi, et al. (1994), ~3%.
Pelrine, et al. (1998), low modulus, high dielectric strength, ~26%.
Pelrine, et al. (2000), pre-stress, ~100%.
Ha, et al. (2006), interpenetrating networks, ~100%.
How do we understand these experiments?
What is the theoretical limit?
How about 1000%?

5. Stress-stretch relation

6. Electromechanics
Maxwell stress
voltage
Equation of state

7. Electromechanical instability limits deformation of actuation
neo-Hookean model F
Experiment: Pelrine, Kornbluh, Joseph, Sensors & Actuators A 64, 77 (1998)
Calculation: Zhao & Suo
Appl. Phys Lett. 91, (2007)

8. Coexistent states stiffening thinning polarizing thick thin
Cross section
Top view
Coexistent states: flat and wrinkled
Observation: Plante, Dubowsky,
Int. J. Solids and Structures 43, 7727 (2006)
Interpretation: Zhao, Hong, Suo
Physical Review B 76, (2007)

9. Electrical breakdown Kofod, Plante… To measure dielectric strength,
one must suppress electromechanical instability by fixing stretch.

10. Snap-through instability may enable an elastomer to achieve giant deformation of actuation
Soft material
with a safety net
Soft material
Hard material

11. Theoretical limit of deformation of actuation
Experimental conditions voltage ramps up;
voltage stays below electrical breakdown,
Equations of state
Game: Find a material with
high dielectric strength,
suitable stress-strain curve.

12. Suitable stress-stretch curve
hard
Ear lobe
soft
Soft: enable deformation at low stress.
Hard: provide a safety net to avert excessive deformation.

13. When stretched, a polymer stiffens
n links
released
Langevin
Gauss
stretched
fully stretched

14. Arruda-Boyce model Kuhn, Grun, Kolloid-Z. 101, 248 (1942)
Arruda, Boyce, J. Mech. Phys. Solids 41, 389 (1993)

15. Change chain length
n = 5 50
500

16. Pre-stretch increases deformation of actuation
Experiment: Pelrine, Kornbluh, Pei, Joseph
Science 287, 836 (2000).
Theory: Zhao, Suo
APL 91, (2007)

17. Effect of Prestress
n = 50
Koh, unpublished work

18. Interpenetrating networks
Ha, Yuan, Pei, Pelrine, Adv. Mater. 18, 887 (2006).

19. Interpenetrating networks
Suo, Zhu. APL 95, (2009).

20. Interpenetrating networks
Short chains provide a safety net.
Long chains fill the space.

21. Dielectric gels
Zhao, unpublished work

22. Zhao, unpublished work

23. Summary Hard material is limited by by electrical breakdown
Soft material is limited by electromechanical instability
Soft-then-hard material may achieve giant deformation of actuation.