A Nonlinear Model for Dielectric Elastomer Membranes

[+] Author and Article Information
Nakhiah Goulbourne, Mary Frecker

Department of Mechanical Engineering,  Pennsylvania State University, University Park, PA 16802

Eric Mockensturm

Department of Mechanical Engineering,  Pennsylvania State University, University Park, PA 16802emm10@psu.edu

J. Appl. Mech 72(6), 899-906 (Apr 21, 2005) (8 pages) doi:10.1115/1.2047597 History: Received July 21, 2004; Revised April 21, 2005

The material and geometrical nonlinearities of novel dielectric elastomer actuators make them more difficult to model than linear materials used in traditional actuators. To accurately model dielectric elastomers, a comprehensive mathematical formulation that incorporates large deformations, material nonlinearity, and electrical effects is derived using Maxwell-Faraday electrostatics and nonlinear elasticity. The analytical model is used to numerically solve for the resultant behavior of an inflatable dielectric elastomer membrane, subject to changes in various system parameters such as prestrain, external pressure, applied voltage, and the percentage electroded membrane area. The model can be used to predict acceptable ranges of motion for prescribed system specifications. The predicted trends are qualitatively supported by experimental work on fluid pumps [A. Tews, K. Pope, and A. Snyder, Proceedings SPIE, 2003)]. For a potential cardiac pump application, it is envisioned that the active dielectric elastomer membrane will function as the motive element of the device.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Actual deformed profiles (1∕2 symmetry) of an inflated membrane

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Figure 2

The nonlinear curve-fit of the experimental data for a sample of VHB 4910. The Mooney-Rivlin fit is a good approximation only to approximately 300% strain

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Figure 3

Pressure-volume curves (main graph) and volume-stretch curves (inset) for different prestretch values

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Figure 4

Pressure-volume curves for various applied voltages

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Figure 5

Comparative pressure-volume curves (main graph) for various electric fields voltages. Voltage and electric field versus the arc length from the pole to the edge of the membrane (inset)

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Figure 6

Pressure-volume curves for different electroded areas of the total membrane area (A)

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Figure 9

Hypothetical work-loop from pressure-volume curves for different voltages

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Figure 10

The blocked pressure for various initial volumes and applied voltages

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Figure 7

The % variance in volume versus the % electroded area of the membrane

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Figure 8

Stable and unstable regions of pressure-volume curves for different applied voltages



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