1 Electromechanical instability Zhigang Suo Harvard University 2:00 pm – 2:45 pm, 11 January 2010, Monday PhD Winter School Dielectric Elastomer Transducers.

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Presentation transcript:

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, January

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

3 Free energy System Dielectric Weights Battery

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

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

6 Interpretation: Zhao, Hong, Suo Physical Review B 76, (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 When stretched, a polymer stiffens n links Langevin Gauss released stretched fully stretched

8 Stiffening due to extension limit Zhao, Hong, Suo, Physical Review B 76, (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, (2007)

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

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

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

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

13 Maximal energy that can be converted by a dielectric elastomer R LT EB E=0 EMI Koh, Zhao, Suo, Appl. Phys. Lett. 94, (2009) 6 J/g, Elastomer (theory) 0.4 J/g, Elastomer (experiment) 0.01 J/g ceramics

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

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