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Research Papers

Electrostatically Driven Creep in Viscoelastic Dielectric Elastomers

[+] Author and Article Information
Jin Wang

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215

Thao D. Nguyen

Department of Mechanical Engineering,
The Johns Hopkins University,
Baltimore, MD 21218

Harold S. Park

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215
e-mail: parkhs@bu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 20, 2013; final manuscript received November 4, 2013; accepted manuscript posted November 11, 2013; published online December 10, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051006 (Dec 10, 2013) (5 pages) Paper No: JAM-13-1437; doi: 10.1115/1.4025999 History: Received October 20, 2013; Revised November 04, 2013; Accepted November 11, 2013

We utilize a nonlinear, dynamic finite element model coupled with a finite deformation viscoelastic constitutive law to study the inhomogeneous deformation and instabilities resulting from the application of a constant voltage to dielectric elastomers. The constant voltage loading is used to study electrostatically driven creep and the resulting electromechanical instabilities for two different cases that have all been experimentally observed, i.e., electromechanical snap-through instability and bursting drops in a dielectric elastomer. We find that in general, increasing the viscoelastic relaxation time leads to an increase in time needed to nucleate the electromechanical instability. However, we find for these two cases that the time needed to nucleate the instability scales with the relaxation time.

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Figures

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Fig. 1

Schematic of the two problems considered, with mechanical and electrostatic boundary conditions shown. (a) Single finite element for electromechanical snap-through problem. (b) Quarter symmetry model for bursting drop in a DE. Note that all schematics are shown in two dimensions as all z displacements are set to zero in this work to mimic a plane strain problem.

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Fig. 2

Illustration of different stages of electromechanical snap-through instability. (a) Undeformed configuration. (b) Prior to snap-through instability. (c) Final configuration after snap-through instability has occurred. _D_VEC is the magnitude of the displacement vector.

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Fig. 3

Time evolution of thickness-direction stretch λy for an applied normalized voltage of Φ = 0.7, or smaller than the critical voltage needed to cause the snap-through instability, for different viscosities η. (a) Not time normalized. (b) Normalized by the viscoelastic relaxation time τr.

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Fig. 4

Time evolution of thickness-direction stretch λy for a constant normalized voltage of Φ = 0.8, or above the critical voltage needed to cause snap-through instability, for different viscosities η. (a) Not time normalized. (b) Normalized by the viscoelastic relaxation time τr.

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Fig. 5

Illustration of electrostatically driven crack initiation and propagation in a DE containing a conductive drop. Note the formation and propagation of a crack from the top of the hole. _D_VEC is the magnitude of the displacement vector.

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Fig. 6

(a) Crack propagation distance Δy as a function of time for different shear viscosities η. (b) Crack propagation distance Δy as a function of normalized time.

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