Ferroelectric ceramics are broadly used in applications including actuators, sensors and information storage. An understanding of the microstructual evolution and domain dynamics is vital for predicting the performance and reliability of such devices. The underlying mechanism responsible for ferroelectric constitutive response is ferroelectric domain wall motion, domain switching and the interactions of domain walls with other material defects. In this work, a combined theoretical and numerical modeling framework is developed to investigate the nucleation and growth of domains in a single crystal of ferroelectric material. The phase-field approach, applying the material electrical polarization as the order parameter, is used as the theoretical modeling framework to allow for a detailed accounting of the electromechanical processes. The finite element method is used for the numerical solution technique. In order to obtain a better understanding of the energetics of fracture within the phase-field setting, the J-integral is modified to include the energies associated with the order parameter. Also, the J- integral is applied to determine the crack-tip energy release rate for common sets of electromechanical crack-face boundary conditions. The calculations confirm that only true equilibrium states exhibit path-independence of J, and that domain structures near crack tips may be responsible for allowing positive energy release rate during purely electrical loading. The small deformation assumption is prevalent in the phase-field modeling approach, and is used in the previously described calculations. The analysis of large deformations will introduce the concept of Maxwell stresses, which are assumed to be higher order effects that can be neglected in the small deformation theory. However, in order to investigate the material response of soft dielectric elastomers undergoing large mechanical deformation and electric field, which are employed in electrically driven actuator devices, manipulators and energy harvesters, a finite deformation theory is incorporated in the phase-field model. To describe the material free energy, compressible Neo-Hookean and Gent models are used. The Jaumann rate of the polarization is used as the objective polarization rate to make the description of the dissipation frame indifferent. To illustrate the theory, electromechanical instabilities in composite materials with different inclusions will be studied using the finite element methods. / text

Thesis (M.Sc.Eng.) / Dielectric elastomers (DEs) have attracted significant attention in recent years and have been found to provide excellent overall performance in actuation-based application. This thesis will introduce the fundamentals of DEs, derive the field and finite element equations for simulating its deformation, and then focus on numerically studying electromechanical instabilities, in particular electrostatically driven creep and the effect of pre-stretch on surface (creasing) instabilities. First, a nonlinear, dynamic finite element model coupled with a finite deformation viscoelastic constitutive law is utilized to study the inhomogeneous deformation and instabilities resulting from the application of a constant voltage to dielectric elastomers. Theoretical studies are performed of two problems that have been experimentally observed, i.e. electromechanical snap-through instability and bursting drops in a dielectric elastomer. In general, increasing the viscoelastic relaxation time leads to an increase in time needed to nucleate the electromechanical instability. However, it is found that the time needed to nucleate the instability of these two cases scales with the relaxation time. Second, the effect of pre-stretch on the performance of dielectric elastomers is studied. Two cases are studied, the electromechanical snap-through instability under equibiaxial pre-stress, and a strip under uniaxial pre-stretch. It is found that prestress markedly increases the stability of the elastomers, while pre-stretch increases the critical field for electro-creasing instability. / 2031-01-01

Electromechanical transducers based on elastomer capacitors are presently considered for many soft actuation applications, due to their large reversible deformation in response to electric field induced electrostatic pressure. The high operating voltage of such devices is currently a large drawback, hindering their use in applications such as biomedical devices and biomimetic robots, however, they could be improved with a careful design of their material properties. The main targets for improving their properties are increasing the relative permittivity of the active material, while maintaining high electric breakdown strength and low stiffness, which would lead to enhanced electrostatic storage ability and hence, reduced operating voltage. Improvement of the functional properties is possible through the use of nanocomposites. These exploit the high surface-to-volume ratio of the nanoscale filler, resulting in large effects on macroscale properties. This thesis explores several strategies for nanomaterials design. The resulting nanocomposites are fully characterized with respect to their electrical and mechanical properties, by use of dielectric spectroscopy, tensile mechanical analysis, and electric breakdown tests. First, nanocomposites consisting of high permittivity rutile TiO2 nanoparticles dispersed in thermoplastic block copolymer SEBS (poly-styrene-coethylene-co-butylene-co-styrene) are shown to exhibit permittivity increases of up to 3.7 times, leading to 5.6 times improvement in electrostatic energy density, but with a trade-off in mechanical properties (an 8-fold increase in stiffness). The variation in both electrical and mechanical properties still allows for electromechanical improvement, such that a 27 % reduction of the electric field is found compared to the pure elastomer. Second, it is shown that the use of nanofiller conductive particles (carbon black (CB)) can lead to a strong increase of relative permittivity through percolation, however, with detrimental side effects. These are due to localized enhancement of the electric field within the composite, which leads to sharp reductions in electric field strength. Hence, the increase in permittivity does not make up for the reduction in breakdown strength in relation to stored electrical energy, which may prohibit their practical use. Third, a completely new approach for increasing the relative permittivity and electrostatic energy density of a polymer based on 'molecular composites' is presented, relying on chemically grafting soft π-conjugated macromolecules to a flexible elastomer backbone. Polarization caused by charge displacement along the conjugated backbone is found to induce a large and controlled permittivity enhancement (470 % over the elastomer matrix), while chemical bonding, encapsulates the PANI chains manifesting in hardly any reduction in electric breakdown strength, and hence resulting in a large increase in stored electrostatic energy. This is shown to lead to an improvement in the sensitivity of the measured electromechanical response (83 % reduction of the driving electric field) as well as in the maximum actuation strain (250 %). These results represent a large step forward in the understanding of the strategies which can be employed to obtain high permittivity polymer materials with practical use for electro-elastomer actuation. / Die Palette von elektro-mechanischen Aktuatoren, basierend auf dem Prinzip weicher dehnbarer Kondensatoren, scheint besonders für Anwendungen in der Medizin und für biomimetische Applikationen unbegrenzt. Diese Wandler zeichnen sich sowohl durch hohe Reversibilität bei großer mechanischer Deformation als auch durch ihre Flexibilität aus, wobei die mechanischen Deformationen durch elektrische Felder induziert werden. Die Notwendigkeit von hoher elektrischer Spannung zur Erzeugung dieser mechanischen Deformationen verzögert jedoch die technisch einfache und breite Markteinführung dieser Technologie. Diesem Problem kann durch eine gezielte Materialmodifikation begegnet werden. Eine Modifikation hat das Ziel, die relative Permittivität zu erhöhen, wobei die Flexibilität und die hohe elektrische Durchbruchsfeldstärke beibehalten werden sollten. Durch eine Materialmodifikation kann die Energiedichte des Materials bedeutend erhöht und somit die notwendige Betriebsspannung des Aktuators herabgesetzt werden. Eine Verbesserung der funktionalen Materialeigenschaften kann durch die Verwendung von Nanokompositen erzielt werden, welche die fundamentalen Eigenschaften der Nanopartikel, d.h. ein gutes Verhältnis von Oberfläche zu Volumen nutzen, um eine gezielte makroskopische Materialmodifikation zu bewirken. Diese Arbeit behandelt die Anwendung innovativer Strategien für die Erzeugung von Nanomaterialien mit hoher Permittivität. Die so erzeugten Materialien und deren relevante Aktuatorkenngrößen werden durch elektrische und mechanische Experimente vollständig erfasst. Mittels der klassischen Mischansätze zur Erzeugung von Kompositmaterialen mit hoher Permittivität konnte durch nichtleitendes Titaniumdioxid TiO2 (Rutile) in einem Thermoplastischen-Block-Co-Polymer SEBS (poly-styrene-co-ethylene-cobutylene-co-styrene) die Permittivität bereits um 370 % erhöht und die elektrische Energiedichte um 570 % gesteigert werden. Diese Veränderungen führten jedoch zu einem signifikanten Anstieg der Steifigkeit des Materials. Aufgrund der positiven Rückkopplung von elektrischen und mechanischen Eigenschaften des Kompositmaterials ermöglicht bereits dieser einfache Ansatz eine Verbesserung der Aktuation, bei einer 27 %-igen Reduktion der Aktuatorbetriebsspannung. Eine direkte Verwendung von leitfähigen Nanopartikeln kann ebenso zu einem Anstieg der relativen Permittivität beitragen, wobei jedoch die Leitfähigkeit dieser Nanopartikel bedeutende Wechselwirkungen verursacht, welche somit die Energiedichte des Materials negativ beeinflusst und die praktische Verwendung dieses Kompositsystems ausschließt. Als ein völlig neuer Ansatz zur Steigerung der relativen Permittivität und Energiedichte und abweichend vom klassischen Mischverfahren, wird die Herstellung eines "Molekularen Komposits", basierend auf einem chemischen Propfverfahren, präsentiert. In diesem Ansatz wird ein π-konjugiertes leitfähiges Polymer (PANI) an die Hauptkette des Elastomers der Polymermatrix gebunden. Die daraus resultierende Ladungsverteilung entlang der Elastomerhauptkette bewirkt eine 470 %-ige Steigerung der Permittivität des "Molekularen Komposits" im Vergleich zur Permittivität des unbehandelten Elastomermaterials. Aufgrund der Verkapselung der chemischen Bindungen der PANI-Kette entstehen kaum negative Rückwirkungen auf die elektrischen und mechanischen Eigenschaften des so erzeugten Komposits. Diese Materialeigenschaften resultieren in einem signifikanten Anstieg der Energiedichte des Materials. Das mittels dieses Verfahrens erzeugte Komposit zeigt sowohl eine Steigerung der Sensitivität der elektromechanischen Antwort (Reduktion des elektrischen Felds um 83 %) als auch eine bedeutende Steigerung der maximalen Aktuation (250 %). Die Ergebnisse und Ideen dieser Arbeit stellen einen wesentlichen Sprung im Verständnis zur Permittivitätssteigerung in Polymermaterialien dar und werden deshalb in der Erforschung und Entwicklung von Elastomeraktuatoren Beachtung finden.

Dielectric elastomer actuators (DEAs) are compliant capacitors, which are able to transduce electrical into mechanical energy and vice versa. As they may be applied in different surrounding conditions and in applications with alternating excitations, it is necessary to investigate both, the thermal behavior and the in fluence of the temperature change during operation. Due to mechanical and electrical loss mechanisms during the energy transfer, the DEA is subjected to an intrinsic heating. In detail, the dielectric material, which has viscoelastic properties, shows a mechanical hysteresis under varying mechanical loads. This behavior leads to a viscoelastic loss of energy in the polymer layer, resulting in a heating of the structure. The non-ideal conduction of the electrode provokes a resistive loss when charging and discharging the electrode layer. Operation with frequencies in the kilohertz-range leads to remarkable local heat dissipation. The viscoelastic material behavior and the resistivity are assumed to be dependent on the temperature and/or on the strain of the material. By this, a back-coupling from the thermal field to the mechanical field or the electrical field is observed. In order to provide a thermal equilibrium, also the convective cooling { the structure is subjected to { has to be considered. Depending on the frequency and the type of electrical driving signal and mechanical load, viscoelastic and resistive heating provide different contributions during the dynamic process. In the present study we capture the described effects within our modeling approach. For a given dielectric elastomer actuator, numerical investigations are performed for a given electrical load.

Entirely soft robots with animal-like behavior and integrated artificial nervous systems will open up totally new perspectives and applications. To produce them we must integrate control and actuation in the same soft structure. Soft actuators (e.g. pneumatic, and hydraulic) exist but electronics are hard and stiff and remotely located. We present novel soft, electronicsfree dielectric elastomer oscillators, able to drive bioinspired robots. As a demonstrator we present a robot that mimics the crawling motion of the caterpillar, with integrated artificial nervous system, soft actuators and without any conventional stiff electronic parts. Supplied with an external DC voltage, the robot autonomously generates all signals necessary to drive its dielectric elastomer actuators, and translates an in-plane electromechanical oscillation into a crawling locomotion movement. Thereby, all functional and supporting parts are made of polymer materials and carbon. Besides the basic design of this first electronic-free, biomimetic robot we present prospects to control the general behavior of such robots. The absence of conventional stiff electronics and the exclusive use of polymeric materials will provide a large step towards real animal-like robots, compliant human machine interfaces and a new class of distributed, neuron-like internal control for robotic systems.

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