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Research Papers

Computational Model of Hydrostatically Coupled Dielectric Elastomer Actuators

[+] Author and Article Information
Huiming Wang

Department of Engineering Mechanics,  Zhejiang University, Hangzhou 310027, P.R. China;School of Engineering and Applied Sciences,  Kavli Institute for Nanobio Science and Technology,  Harvard University, Cambridge, MA 02138

Shengqiang Cai

School of Engineering and Applied Sciences,  Kavli Institute for Nanobio Science and Technology,  Harvard University, Cambridge, MA 02138

Federico Carpi

Interdepartmental Research Centre “E. Piaggio,”School of Engineering,  University of Pisa, Pisa 56100, Italy;  Technology & Life Institute, Pisa 56100, Italy e-mail: f.carpi@ing.unipi.it

Zhigang Suo

School of Engineering and Applied Sciences,  Kavli Institute for Nanobio Science and Technology,  Harvard University, Cambridge, MA 02138 e-mail: suo@seas.harvard.edu

J. Appl. Mech 79(3), 031008 (Apr 05, 2012) (8 pages) doi:10.1115/1.4005885 History: Received July 02, 2011; Revised October 13, 2011; Posted February 13, 2012; Published April 04, 2012; Online April 05, 2012

A hydrostatically coupled dielectric elastomer (HCDE) actuator consists of two membranes of a dielectric elastomer, clamped with rigid circular rings. Confined between the membranes is a fixed volume of a fluid, which couples the movements of the two membranes when a voltage or a force is applied. This paper presents a computational model of the actuator, assuming that the membranes are neo-Hookean, capable of large and axisymmetric deformation. The voltage-induced deformation is described by the model of ideal dielectric elastomer. The force is applied by pressing a rigid flat punch onto one of the membranes over an area of contact. The computational predictions agree well with experimental data. The model can be used to explore nonlinear behavior of the HCDE actuators.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sectional views of a HCDE actuator. Two membranes of a dielectric elastomer are clamped by rigid circular rings. The bottom membrane is sandwiched between soft electrodes, which are connected to a voltage source. Confined in between the membranes is a certain volume of a fluid. (a) When the voltage is off, the actuator is in the rest state. (b) When the voltage in on, the bottom membrane expands in area and moves downward, pulling the top membrane down through the coupling fluid.

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Figure 2

Experiment to characterize the HCDE actuator. (a) While the actuator is in the rest state, a rigid flat punch is brought to touch the top membrane with negligible force. (b) When the bottom membrane is subject to voltage, both membranes move downward. (c) While the voltage is on, the rigid punch is brought to touch the top membrane with negligible force, and the displacement of the punch defines the free stroke. (d) The voltage is turned off while the punch is fixed in position, the punch presses the top membrane over an area of contact at a certain blocking force.

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Figure 3

Schematics of states used to describe the computational model. In each state, the position of a particular material particle has been identified by a circular dot.

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Figure 4

Free-body diagrams to describe the mechanical equilibrium of a membrane. (a) In the undeformed state of the membrane, imagine an annulus, radii R and R+dR. (b) In a deformed state, the annulus becomes an axisymmetric band. The pressure on the face of the band is balanced by the longitudinal stress on the rims of the band. (c) Balance the pressure, the longitudinal stress, and the latitudinal stress in a half of the band.

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Figure 5

(a) Voltage, (b) force, and (c) pressure as functions of the apical displacement. The experimental data are extracted from Ref. [14].

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Figure 6

Distribution of various fields in the active membrane at several values of the voltage. (a) Deformed shapes of the actuator. (b) True electric field. (c) Longitudinal stretch. (d) Latitudinal stretch. (e) Longitudinal true stress. (f) Latitudinal true stress.

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Figure 7

While the voltage is off, a rigid flat punch is pressed onto the top membrane. (a) The deformed shapes of the actuator at several values of the radius of contact. (b) The normalized area of contact as a function of the normalized apical displacement.

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