modeling dielectric elastomer actuators

165 Pages·2007·2.19 MB·English

ETH Library
Modeling dielectric elastomer
actuators
Doctoral Thesis
Author(s):
Wissler, Tobias
Publication date:
2007
Permanent link:
https://doi.org/10.3929/ethz-a-005406421
Rights / license:
In Copyright - Non-Commercial Use Permitted
This page was generated automatically upon download from the ETH Zurich Research Collection.
For more information, please consult the Terms of use.
DISS. ETH NO. 17142

MODELING DIELECTRIC ELASTOMER
ACTUATORS

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY in ZURICH

for the degree of

Doctor of Sciences

presented by

MICHAEL TOBIAS WISSLER

Dipl. Werkstoff.-Ing. ETH

born 25th October 1976

citizen of Sumiswald (BE)

accepted on the recommendation of
Prof. Dr. E. Mazza, examiner
Prof. Dr. P. Ermanni, co-examiner
Prof. Dr. M. Farshad, co-examiner
Dr. G. Kovacs, co-examiner

2007

Acknowledgments

I wish to express my sincere gratitude to

(cid:190) My supervisor Prof. Dr. Edoardo Mazza, for his kind support and encouragement
during this work, the many fruitful discussions and his interest in my research
work.

(cid:190) My co-examiners, Prof. Dr. Paolo Ermanni, Prof. Dr. Mehdi Farshad and Dr.
Gabor Kovacs for carefully reviewing this thesis.

(cid:190) All my colleagues and supervisors at the laboratory for Materials and
Engineering at Empa for the good atmosphere, especially: Silvain Michel, Patrick
Lochmatter, Rui Zhang, Christian Dürager, Claudio Iseli and Lukas Kessler for
the interesting and helpful discussions concerning dielectric elastomers; Alfred
Schmidlin, Urs Hintermüller, Bernd Jähne and Kurt Gantner for technical
support; Dr. Luc Wullschleger, Christian Affolter and Bernhard Weisse for
assisting me with finite element simulations.

(cid:190) Jonas Wyrsch, Riya Bhattacharya, Patrick Grau, Marcel Birrer and Julien Egger
for writing their semester thesis on topics directly related to my research.

(cid:190) Dr. Alessandro Nava for performing the aspiration experiments.

(cid:190) The Swiss National Science Foundation (SNF) for the financial support of this
thesis (Project number: 200021-107661/1).

(cid:190) My family and my friends for their encouragement and support. This work is
dedicated to my parents.

Michael Wissler
Zürich, April 2007

Table of contents

Abstract v
Zusammenfassung vii
1 Introduction 1
1.1 General remarks .......................................................................................1
1.2 Design of dielectric elastomer actuators..................................................2
1.3 Constitutive equations..............................................................................4
1.4 Literature review on modeling of DE-actuators ......................................5
1.5 Objectives of the present work.................................................................8

2 Theoretical Background and Material Details 11
2.1 Nonlinear continuum mechanics............................................................11
2.1.1 Finite strains........................................................................................11
2.1.2 Stresses ...............................................................................................13
2.1.3 Strain energy functions and nearly incompressible materials............14
2.1.4 Quasilinear viscoelasticity..................................................................15
2.2 Optimization procedure..........................................................................16
2.3 Material details.......................................................................................17
2.3.1 Elastomers...........................................................................................17
2.3.2 Electrodes...........................................................................................18

3 Modeling Dielectric Elastomer Actuators 19
3.1 Article 1..................................................................................................19
3.2 Article 2..................................................................................................37
3.3 Article 3..................................................................................................59
3.4 Article 4..................................................................................................88
i
4 Further Verification of the Actuator Model 111
4.1 Introduction..........................................................................................111
4.2 Correction of material parameters........................................................112
4.3 Aspiration tests.....................................................................................114
4.3.1 Introduction.......................................................................................114
4.3.2 Working principle of the aspiration device......................................114
4.3.3 Description of the experiments.........................................................115
4.3.4 Experimental results.........................................................................117
4.3.5 Finite element calculations...............................................................117
4.3.6 Results...............................................................................................118
4.4 Compression tests.................................................................................120
4.4.1 Introduction.......................................................................................120
4.4.2 Experimental details.........................................................................121
4.4.3 Finite element simulations................................................................122
4.4.4 Results...............................................................................................123
4.5 Deformation state in the experiments ..................................................124
4.5.1 Introduction.......................................................................................124
4.5.2 Uniaxial tensile tests.........................................................................126
4.5.3 Circular strain test.............................................................................126
4.5.4 Aspiration test...................................................................................127
4.5.5 Compression test...............................................................................128
4.5.6 Discussion.........................................................................................129
4.6 Influence of the passive part of a spring roll activation.......................130
4.6.1 Introduction.......................................................................................130
4.6.2 Analytical model...............................................................................131
4.6.2.1 Kinematics...................................................................................132
4.6.2.2 Kinetics........................................................................................134
4.6.2.3 Electromechanical coupling.........................................................135
4.6.3 Numerical considerations.................................................................136
4.6.4 Results...............................................................................................138

ii
5 Conclusions and Outlook 140
5.1 Main contributions of the present work...............................................140
5.2 General design considerations and suggestions for future work .........142
5.2.1 Material behavior of the elastomer...................................................142
5.2.2 Geometrical design of the actuator...................................................143
5.2.3 Reliability.........................................................................................144

Bibliography 147
Curriculum Vitae 153

iii
iv
Abstract
Dielectric elastomer actuators belong to the group of so called “electroactive
polymers” and are used in active structures where large strains are required. Dielectric
elastomers have many potential applications as actuators. Models and simulation
techniques are required for the design and optimization of actuator applications in
order to determine states of stress and strain as functions of the applied voltage.
Several aspects have to be considered in the modeling and simulation of dielectric
elastomer actuators, including the constitutive model of the elastomer, the
electromechanical coupling, numerical implementation and experimental validation of
the models. So far no adequate models exist which are able to predict the actuator
behavior over a large deformation and time range.
In the present work, actuators made of an acrylic elastomer (the widely used material
VHB 4910 by 3M) are investigated. The passive mechanical response of the elastomer
is decoupled from the electromechanical problem. Electrostatic forces arise only at the
interface between the electrodes and the elastomer. The elastomer behaves as a passive
layer and there is no direct interaction between electric field and its mechanical
properties. The electromechanical coupling, an equation proposed by Pelrine et al.
(Sensors and Actuators A, 64, 1998), is evaluated by analytical and numerical
methods. The dielectric constant of VHB 4910 is determined by LCR measurements
for various prestrain levels as well as by spring roll experiments. The passive
mechanical response of the elastomer is described using a ‘quasilinear visco-
hyperelastic model’ suitable for large strains and viscoelasticity. The constitutive
model and the electromechanical coupling are implemented in finite element models
for simulating the behavior of circular actuators. A systematic experimental
characterization of circular actuators under various prestrain and voltage conditions
has been carried out. Over 40 actuators have been tested at 11 different
prestrain/voltage levels. These experimental data are essential for model definition and
validation purposes. The constitutive model is further evaluated using different
deformation configurations. Uniaxial tensile and relaxation tests, aspiration tests and
compression tests have been carried out and compared to corresponding simulations.
The mechanical model (with an optimized parameter set) is valid over a wide
deformation and time range, as shown for circular actuator tests at different prestrain
and voltage levels as well as for uniaxial, aspiration and compression tests. The
concept of quasilinear viscoelasticity was validated by uniaxial relaxation tests which
showed that the normalized stress-relaxation function is independent of the magnitude
of the deformation. For the simulation of the circular actuators, a novel finite element
v