### Wednesday, 13 October 2004 - 1:25 PM

### This presentation is part of : Active Materials

### A Mathematical Model for Dielectric Elastomer Pumps

**Nakhiah C. Goulbourne**, Eric Mockensturm, and Mary Frecker. Pennsylvania State University, State College, PA 16802
The nonlinear material and geometrical behavior of dielectric elastomer actuators are characterized in the presented model. In particular, the case of an axisymmetric, electrically linear, hyperelastic membrane is investigated. Both a Cauchy continuum approach and a variational principle of virtual work are used to derive the field equations of the electro-elastic system. An Ogden material model is used to fit the nonlinear elastic portion of the formulation; Maxwell-Faraday electrostatics describes the electrical behavior. Various system parameters are investigated, for example, prestretch, initial geometry, edge constraints, constant voltage versus constant electric field, and the percentage electroded area. The model is used to predict instability regions of the deformation range. Additionally, a procedure for calculating the blocked pressure and the work output for specific pump configurations is given. Replacing the passive diaphragm of a cardiac assist pump with an electro-active membrane will eliminate the need for separate actuation sources that are currently used in these devices. Active diaphragms can be realized by electroding a dielectric elastomer to form a compliant capacitor. As the driving element of the cardiac device, the initially flat membrane will eject blood from the fluid receptacle when it inflates under the influence of an applied voltage (field) and an external mechanical pressure.

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