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Research Papers

Voltage-Induced Wrinkling in a Constrained Annular Dielectric Elastomer Film

[+] Author and Article Information
Kai Li

Department of Civil Engineering,
Anhui Jianzhu University,
Hefei 230601, Anhui, China;
Department of Mechanical and
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093

Wanfang Wu, Ziyang Jiang

Department of Mechanical and
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093

Shengqiang Cai

Department of Mechanical and
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: shqcai@ucsd.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 17, 2017; final manuscript received November 4, 2017; published online November 22, 2017. Editor: Yonggang Huang.

J. Appl. Mech 85(1), 011007 (Nov 22, 2017) (10 pages) Paper No: JAM-17-1580; doi: 10.1115/1.4038427 History: Received October 17, 2017; Revised November 04, 2017

Wrinkles can be often observed in dielectric elastomer (DE) films when they are subjected to electrical voltage and mechanical forces. In the applications of DEs, wrinkle formation is often regarded as an indication of system failure. However, in some scenarios, wrinkling in DE does not necessarily result in material failure and can be even controllable. Although tremendous efforts have been made to analyze and calculate a variety of deformation modes in DE structures and devices, a model which is capable of analyzing wrinkling phenomena including the critical electromechanical conditions for the onset of wrinkles and wrinkle morphology in DE structures is currently unavailable. In this paper, we experimentally demonstrate controllable wrinkling in annular DE films with the central part being mechanically constrained. By changing the ratio between the inner radius and outer radius of the annular films, wrinkles with different wavelength can be induced in the films when externally applied voltage exceeds a critical value. To analyze wrinkling phenomena in DE films, we formulate a linear plate theory of DE films subjected to electromechanical loadings. Using the model, we successfully predict the wavelength of the voltage-induced wrinkles in annular DE films. The model developed in this paper can be used to design voltage-induced wrinkling in DE structures for different engineering applications.

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Figures

Grahic Jump Location
Fig. 1

Experimental photos of voltage-induced wrinkles in a constrained annular DE film with different ratios between the inner radius A and outer radius B: (a) A/B = 0.6, (b) A/B = 0.7, and (c) A/B = 0.8. The wavenumber of wrinkling mode increases with increasing radius ratio.

Grahic Jump Location
Fig. 2

Schematics of an annular DE film constrained by an inner circular rigid plate. The inner radius and outer radius of the annular DE film without deformation are denoted by A and B, respectively. In the experiment, an electrical voltage Φ is applied across the thickness of the DE film. Three different states of the annular DE film are sketched: (a) undeformed state, (b) deformed state without wrinkles, and (c) wrinkled state.

Grahic Jump Location
Fig. 3

Distributions of radial stretch and hoop stretch in a constrained annular DE film for several different voltages and ratios between its inner radius A and outer radius B: (a) and (b) A/B = 0.1, (c) and (d) A/B = 0.6, and (e) and (f) A/B = 0.9. The highest voltages in the figures correspond to the critical voltage of inducing pull-in instability in the DE film.

Grahic Jump Location
Fig. 4

Dependence of the critical voltage of inducing pull-in instability of the annular DE film on the ratio between its inner radius and outer radius. When the ratio between inner radius and outer radius approaches zero, the annular film becomes a free-standing film; when the ratio approaches one, the deformation state of the film is pure-shear.

Grahic Jump Location
Fig. 5

Distributions of radial stress and hoop stress in the DE film without wrinkles, for several voltages and radius ratios: (a) and (b) A/B = 0.1, (c) and (d) A/B = 0.6, and (e) and (f) A/B = 0.9. The radial stress in the film is tensile, while the hoop stress is compressive. The compressive hoop stress may wrinkle the DE film.

Grahic Jump Location
Fig. 6

Dependence of critical voltage for inducing wrinkling instability on the thickness of the DE film, for several radius ratios and wrinkling modes: (a) A/B = 0.1, (b) A/B = 0.3, (c) A/B = 0.5, and (d) A/B = 0.7. For larger film thickness, the voltage for inducing pull-in instability is smaller than the voltage for inducing wrinkling in the film.

Grahic Jump Location
Fig. 7

Dependence of the wavenumber of the critical wrinkling mode on the radius ratio for two different film thicknesses H/B = 0.02 and 0.005. The three dots are experimental results from Fig. 1.

Grahic Jump Location
Fig. 8

A phase diagram of a constrained annular DE film with thickness H/B = 0.02. Depending on the ratio between the inner radius and outer radius of the film and the magnitude of applied voltage, the film may stay in a flat and stable phase, wrinkling phase, or pull-in instability phase. The boundary between the flat phase and wrinkling phase of the DE film is given by the dependence of critical voltage for wrinkling on its radius ratio A/B. For the annular DE film with the radius ratio: A/B = 0.4, the required voltage to induce wrinkles in the film is the lowest.

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