# Electrostatic modeling of dielectric elastomer membrane actuators

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.
Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

Keywords:

ISBN:

Date of Publication: