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Research Papers

Electromechanical Instability of Dielectric Elastomer Actuators With Active and Inactive Electric Regions

[+] Author and Article Information
Atul Kumar Sharma

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
e-mail: asharma4@me.iitr.ac.in

Pramod Kumar

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India

A. Singh

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India

D. M. Joglekar

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
e-mail: dhanashri.joglekar.fme@iitr.ac.in

M. M. Joglekar

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
e-mail: mmj81fme@iitr.ac.in

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 19, 2019; final manuscript received February 28, 2019; published online March 19, 2019. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 86(6), 061008 (Mar 19, 2019) (11 pages) Paper No: JAM-19-1030; doi: 10.1115/1.4042996 History: Received January 19, 2019; Accepted February 28, 2019

Electrically driven dielectric elastomers (DEs) suffer from an electromechanical instability (EMI) when the applied potential difference reaches a critical value. A majority of the past investigations address the mechanics of this operational instability by restricting the kinematics to homogeneous deformations. However, a DE membrane comprising both active and inactive electric regions undergoes inhomogeneous deformation, thus necessitating the solution of a complex boundary value problem. This paper reports the numerical and experimental investigation of such DE actuators with a particular emphasis on the EMI in quasistatic mode of actuation. The numerical simulations are performed using an in-house finite element framework developed based on the field theory of deformable dielectrics. Experiments are performed on the commercially available acrylic elastomer (VHB 4910) at varying levels of prestretch and proportions of the active to inactive areas. In particular, two salient features associated with the electromechanical response are addressed: the effect of the flexible boundary constraint and the locus of the dielectric breakdown point. To highlight the influence of the flexible boundary constraint, the estimates of the threshold value of potential difference on the onset of electromechanical instability are compared with the experimental observations and with those obtained using the lumped parameter models reported previously. Additionally, a locus of localized thinning, near the boundary of the active electric region, is identified using the numerical simulations and ascertained through the experimental observations. Finally, an approach based on the Airy stress function is suggested to justify the phenomenon of localized thinning leading to the dielectric breakdown.

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Figures

Grahic Jump Location
Fig. 1

An arbitrary continuum dielectric body in undeformed and deformed states

Grahic Jump Location
Fig. 2

(a) Schematic of a dielectric elastomer in the reference state. (b) Prestretched DE actuator with clamped boundaries and square-shaped electrodes (LAP × LAP) deposited on the top and bottom surfaces.

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Fig. 3

A representative specimen used for experimentation

Grahic Jump Location
Fig. 4

(a) Schematic and (b) FE mesh of the (1/8)th symmetric model of DEA used in finite element simulations

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Fig. 5

Electromechanical response of the dielectric elastomer actuator for varying proportions of active to inactive area and the applied prestretch: (a) λP = 2.0, (b) λP = 2.5, and (c) λP = 3.0., finite element analysis; o, experiment.

Grahic Jump Location
Fig. 6

Evolution of the total thickness stretch at the breakdown point with the applied potential difference for (a) λP = 2.0, (b) λP = 2.5, and (c) λP = 3.0

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Fig. 7

(a) and (b) Experimental evidences of the location of the breakdown point. (c) Contour plot of the top surface of the DE actuator obtained from the FE analysis [λP = 2.0, Φ = 6 kV].

Grahic Jump Location
Fig. 8

(a) Beam configuration, dimensions, material, and geometric parameters. (b) Variation of the point of maximum deformation with the slenderness ratio of the beam (the slenderness ratio pertaining to λP = 2 is marked by X). (c) Deformation profile for thin (d = 1 mm) and thick (d = 20 mm) beams obtained using the Airy function method and FE analysis.

Grahic Jump Location
Fig. 9

Schematic of a homogeneously deforming dielectric elastomer in the (a) reference state, (b) prestretched state, and (c) actuated state

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