1. 1 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

2. 2 Stark & Garton, Nature 176, 1225 (1955) Theory of pull-in instability Zhao, Suo, APL 91, 061921 (2007)  polarizing thinning

3. 3 Free energy System Dielectric Weights Battery

4. 4 Free energy minimized at a state of equilibrium Equations of state Critical condition for onset of instability Zhao, Suo, APL 91, 061921 (2007)

5. 5 Pre-stretch increases deformation of actuation Experiment: Pelrine, Kornbluh, Pei, Joseph Science 287, 836 (2000). Theory: Zhao, Suo APL 91, 061921 (2007)

6. 6 Interpretation: Zhao, Hong, Suo Physical Review B 76, 134113 (2007) Coexistent states: flat and wrinkled Observation: Plante, Dubowsky, Int. J. Solids and Structures 43, 7727 (2006) thickthin  Top view Cross section Coexistent states polarizing thinning stiffening

7. 7 When stretched, a polymer stiffens n links Langevin Gauss released stretched fully stretched

8. 8 Stiffening due to extension limit Zhao, Hong, Suo, Physical Review B 76, 134113 (2007). Stiffening as each polymer chain approaches its fully stretched length (e.g., Arruda-Boyce model)  : small-strain shear modulus n: number of monomers per chain Zhao, Hong, Suo Physical Review B 76, 134113 (2007)

9. 9 FEM: inhomogeneous deformation Thick State Transition Thin State Thick State Transition Thin State Zhou, Hong, Zhao, Zhang, Suo, IJSS, 2007

10. 10 Failure Modes RuptureLoss of Tension Electrical BreakdownElectromechanical Instability + – + – + – + – + – + – + – + – stableunstable or + – + – + – + – + – + – + – + – + – + –

11. 11 Pei, Pelrine, Stanford, Kornbluh, Rosenthal, Meijer, Full Proc. SPIE 4698, 246 (2002) Allowable states of a transducer Moscardo, Zhao, Suo, Lapusta JAP 104, 093503 (2008) allowable states

12. 12 Energy harvesting Generate electricity from walkingGenerate electricity from waves Pelrine, Kornbluh…

13. 13 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. 14 A “practical” design 2 J/g Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009)

15. 15 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