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Electrostatic modeling of dielectric elastomer membrane actuators

by Goulbourne, Nakhiah C.S.

Abstract (Summary)
iii Electroactive polymers are being used to create next generation devices for a wide variety of applications. Dielectric elastomers are of particular interest for many biomedical applications due to their high actuation speeds and very large strains, on the order of hundreds of percent strain. The dielectric elastomer actuator is a threecomponent system consisting of a soft dielectric elastomer between two compliant electrodes. Application of a voltage causes the elastomer to increase in area and decrease in thickness. The elastomer recovers its initial configuration upon removal of the voltage. A dielectric elastomer membrane actuator is to be incorporated into the design of a prosthetic blood pump. This electroactive polymer membrane is being considered as a potential replacement for the passive diaphragm in a current left ventricular assist device. In its perceived mode of operation, the circular active membrane, clamped around the edges, will deform in response to a voltage from its initially in-plane configuration to an inflated state so as to displace blood from the adjoining blood sac; thus, mimicking the pump-like behavior of the natural heart. Using a dielectric elastomer membrane actuator eliminates the need for a separate actuation source in the pump, which will create a simpler, lighter, and more compact device. The material and geometrical nonlinearities of dielectric elastomer actuators make them more difficult to model than traditional linear actuators. In this dissertation, a large deformation electro-elastic model of dielectric elastomer membrane actuators is developed by combining Maxwell-Faraday electrostatics and nonlinear elasticity theory. Initial models assumed an elastically linear constitutive model and iv considered the electrostatic Maxwell effect as an externally applied force across the thickness [1]. Improvements to such models have been made by using nonlinear elastic models [2]. Here, taking a different approach than previously described yields a new model. The dielectric is modeled as a continuum placed in an electric field subject to external surface tractions. Taking a continuum mechanics approach, the stress in the dielectric medium is determined by a superposition of the mechanical stress due to the local elastic state and the Maxwell stress due to the electrostatic field. Based on the proposed expression for the electro-elastic stress, a large deformation model is derived using membrane theory. Since the thickness of the membrane is much smaller than the radius, and given that bending effects are negligible, it is reasonable to assume that membrane theory is applicable to active membrane inflation. Using Green’s membrane theory as a starting point [3], various researchers have obtained solutions for the quasistatic inflation of a planar elastic membrane (passive), the dynamic inflation of a planar membrane, and the inflation of viscoelastic membranes. Here, solutions for the inflation of electro-elastic membranes are presented. Specifically, this contribution has been derived by modifying Adkins and Rivlin’s theory of inflatable elastic membranes to account for material stiffening at high strains (using an Ogden model) and electrical effects [4]. The quasi-static inflation of dielectric elastomer actuators by a uniform mechanical pressure and an applied voltage are presented. The model is used to solve for the resultant membrane behavior, subject to changes in various system parameters such as prestretch, external pressure, applied voltage, and the percentage electroded area of the dielectric. A method for calculating the blocked pressure specific to inflatable active v membranes is also introduced. A hypothetical work-loop simulating cardiac diaphragm conditions is constructed and evaluated. In addition, parameter studies are conducted to explore the feasibility of optimizing the active diaphragm for pump application. The numerical quasi-static results are compared to experimental data for actuators made from 3M VHB polyacrylate films. It is shown that the theoretical model for the active inflation of hyperelastic membranes, like passive membrane inflation models [5], is sensitive to the explicit form of the assumed strain energy function. Using the best overall values for the material constants the electro-elastic model predicts the zero-voltage and voltagedependent behavior for the inflation of dielectric elastomer actuators. The correlation between the numerical results and the experimental data is good for the prestretch range considered. Finally, it is shown how the membrane design can be optimized for a single variable – the prestretch, using four different numerical optimization techniques.
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School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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