Dielectric Elastomer Tube Research Articles

Energy harvesting with dielectric elastomer tubes: active and (responsive materials-based) passive approaches

Mechanical to electrical energy conversion is a well-established energy transduction approach. However, cases in which a mechanical energy source is not available call for new approaches to harvest electrical energy. In the present study, we demonstrate energy harvesting in soft dielectric elastomer (DE) tubes. Broadly, energy harvesting is obtained through inflation of the tube, electrical charging of the DE layer, and deflation, which results in a decrease in capacitance and an increase in voltage. We propose two methods to mechanically charge (or inflate) the system: (1) active, in which the tube is inflated through the application of mechanical pressure, and (2) passive, in which a passive cylindrical component placed inside the DE tube deforms radially in response to an environmental stimulus such as thermal excitation or water uptake and inflates the DE tube. To demonstrate passive charging, we consider gels as the passive component and employ well-known models with the properties of the commonly employed DE VHB 4910 to simulate the mechanical response of the system and estimate the harvested electrical energy. Our findings reveal that energy-densities in the order of ∼10–50 mJ cm–3 can be harvested. The proposed approach and the inclusion of a passive component to mechanically charge the system opens new opportunities to generate energy in environments lacking traditional mechanical energy sources.

Semi-analytical modeling of electro-strictive behavior in dielectric elastomer tube actuators

Dielectric elastomer tube actuators (DETAs) facilitate versatile soft robotic motions when activated by electric fields. However, optimizing their performance necessitates understanding complex deformation behaviors under different electrical loading patterns. While prior analytical models provide valuable insights, many rely on assumptions like infinite-length and uniform conditions, limiting their ability to capture experimentally-observed nonuniform deformations. This paper presents a semi-analytical approach permitting both radial and longitudinal electrostatic effects by modeling a dielectric tube of effectively infinite-length. It also incorporates the crucial compression-torsion behavior for soft actuator designs. We validate the model against finite element simulations, achieving excellent agreement. Our efficient technique successfully predicts intricate deformation phenomena in DETAs under combined electrical, mechanical, and geometric effects. Results show the model effectively captures axial and twisting deformations, overcoming limitations of linear twist angle assumptions. This analytical framework offers a powerful tool for optimizing next-generation soft actuators across diverse cutting-edge engineering and robotic applications.

Bulging of dielectric elastomer tubes considering residual stress and viscoelasticity

This paper investigates the impacts of residual stress and viscoelasticity on the bifurcation and post-bifurcation behaviors of dielectric elastomer tube actuator (DETA) with finite thickness. A theoretical model with residual stress is developed to analyze the electromechanical (EM) behavior of a DETA under a combined effect of voltage, internal pressure, and axial force loadings. A mathematical derivation of the bifurcation condition for the DETA under EM coupling loadings is presented, and a coexistence phase transition condition for steady bugle propagation is established. The effects of voltage, axial force, and residual stress on the bifurcation and coexistence phase transition conditions are studied. To validate the theoretical predictions, finite element (FE) simulations are performed on a closed-ended DETA subjected to the EM loadings. The results reveal a competitive relationship between the localized bugling and electric breakdown (EB). The large residual stress can inhibit the localized bugling and enhance the stability of the tube. Additionally, we explore the bifurcation behavior of the viscoelastic DETA, revealing that the viscoelastic effect significantly influences the critical pressure of bifurcation and the loading/unloading paths. It is observed that snap-back instability can occur during the unloading process under high loading rates or voltages. This work provides valuable insights into the finite deformation and bifurcation behaviors of the DETA under complex EM coupling loadings.

Snap-through instability in rotating dielectric elastomer tubes

Dielectric elastomers (DEs) have been widely used in soft robotics, high-performance actuators, and bioengineering. However, they may suffer from more failure modes than pure elastic elastomers when undergoing rotational motion. In this paper, we present a theoretical analysis of the finite deformation of rotating DE tubes, addressing the challenges associated with rotational motion in DEs. Our study focuses on the combined influence of a radial electric field and an axial pre-stretch. We numerically calculate three different materials, including neo-Hookean, Gent, and Ogden models, for rotating DE tubes and find that the snap-through instability caused by rotation occurs only in tubes with the Ogden model, resulting in dramatic deformation. Moreover, we study the effects of geometric dimensions and external loads and reveal the competition mechanism between the snap-through instability and electrical breakdown of DE tubes under external voltage. Significantly, our work presents practical thresholds that offer comprehensive guidance for designing and controlling of rotating DE tubes, preventing electrical breakdown during rapid deformation through the adjustment of external loads. This study provides novel insights and practical recommendations for the field of nonlinear deformation in rotating DE tubes.

Nonlinear deformation and instability of a dielectric elastomer tube actuator

The mechanical response and electromechanical instability (EMI) of a dielectric elastomer tube actuator (DETA) under the coupling loadings of voltage, internal pressure and axial force are studied in this paper. Based on the Gent model and considering the nonlinear relationship between dielectric permittivity and stretches, two different loading conditions are discussed: force tuning and voltage tuning. For the force tuning, it is found that the radius of the DETA first decreases, then increases and finally decreases due to the competition between the axial force and voltage as well as the strain-stiffening property of the Gent model under the large deformation. For the voltage tuning, the effects of axial force, internal pressure and electrostrictive coefficient on the electromechanical response are explored. The electrical breakdown (EB) during the nonlinear deformation of DETA is also analyzed. The stress distribution along the thickness of the DETA is given by the analytical solution, and the two failure modes including EMI and loss of tension for the DETA are studied with axial constraints. It is found that the EMI can be eliminated by changing the stretch in the z-direction and internal pressure, which may also lead to the failure of loss of tension. The competitive relations of the two failure modes are discussed in detail. This work can contribute to the design of DETAs with a large actuation.

Electrically-induced twist in geometrically incompatible dielectric elastomer tubes

Dielectric elastomers (DEs) are materials that experience large deformations in response to electric excitation. In this work, we introduce and investigate a DE-based bi-layer tubular design that can be used as an electrically-activated torsional actuator. Specifically, the bi-layer tube is constructed as follows: an isotropic Gent tube is twisted, inserted into another tube, and the two layers are adhered along the interface, resulting in a bi-layer with residual stress. The two layers are referred to as geometrically incompatible. Next, the bi-layer tube is subjected to an electric field and, due to deformation-induced anisotropy, experiences twist. This work begins with a summary of the governing electro-mechanical equations. The overall electrically-induced twist depends on the ratios between the radii, the stiffnesses, the lock-up stretch parameters, and the permittivities of the two layers. Thus, we employ the Gent model and follow by investigating the role of each one of these four key ratios. To illustrate the feasibility of the proposed design, three bi-layer tubes from commonly used DE materials are studied. We show that twists ranging from ∼25deg /mm to ∼130deg/mm can be achieved in response to voltages of ∼6–15 kV. The behaviors that can be obtained with commonly used DEs highlight the merit of the proposed configuration. The findings and insights from this work can be used in a wide range of applications that require a twist motion, including soft rotational robots, artificial muscles, and soft torsional actuators.

Soft dielectric elastomer tubes in an electric field

Soft dielectric elastomers with high relative permittivity, very low modulus and high electric breakdown strength have emerged as promising materials for various applications as sensors, actuators and in energy harvesting and soft robotics. We study the intricate deformation behaviour of a soft dielectric elastomer tube of finite length and closed ends, that carries a dead load, is internally pressurised by an injected fluid and has a high electric potential applied across its walls. As for soft tubes in the absence of a potential, this electro-hyperelastic problem involving very large deformations, exhibits a multitude of possibilities, including homogeneous deformation, inhomogeneous bifurcation, snap-through instabilities and post bifurcation behaviour in the form of propagation of axisymmetric bulges. We develop a coupled Finite Element procedure for the situation where the domains of the mechanical and electrostatic problems coincide. The procedure can handle volume flow rate controlled electro-elastic problems. We use it to study the many aspects of the deformation behaviour and limitations placed by competing failure mechanisms on practical utilisation of the large areal strains and axial actuations that can be produced. If electrical breakdown can be avoided by ingenious design of loading sequences, the large volume increase in the tube due to the triggering of instabilities can be harnessed and has far-reaching technological implications.

Voltage-controlled instability transitions and competitions in a finitely deformed dielectric elastomer tube

This work compares the transition and competitive mechanism between three types of instabilities of an incompressible dielectric tube: wrinkling, pull-in instability and electric breakdown. We also see how to select one type of instability mode on demand. First, we investigate the finite response and the wrinkling of a tube subject to a combination of applied radial voltage, torsion and axial force (or stretch). We use the surface impedance matrix method to determine the wrinkling threshold, and obtain the corresponding two-dimensional pattern shape of wrinkled surface. Second, we look at illustrative numerical calculations for ideal Mooney-Rivlin dielectrics and study the effects of actuation methods, electric voltage, torsion and geometrical parameters on the three types of instabilities. Results show that the deformation of the solid will influence the true electric field in the solid, and induce competitive effects between the applied voltage and the mechanical loading. We find that in addition to the expected contractile buckling, buckling may also occur in extension in an electrically actuated dielectric tube, a departure from the purely elastic wrinkling. Moreover, the electro-elastic behavior of the DE elastomer can be enhanced by introducing torsion. We also find that large stable actuation can be achieved and that the wrinkling pattern can be selected on demand in the tube by finely tuning the actuation, voltage, torsion and geometry, without encountering material failure.

Prismatic bifurcations of soft dielectric tubes

Dielectric elastomer tubes are employed as actuators by radial electric stimulus. Their functionality is affected by electromechanical instabilities, whose study was mainly limited to the analysis of the free energy Hessian. In this paper, we identify a different class of instabilities—prismatic diffuse modes—by employing the linearized theory of superposed deformations on finitely strained deformable dielectrics. We develop the equations that determine the onset of such modes, and show through numerical examples that the tube may enter diffuse states before the Hessian criterion fails. Moreover, we find that loading paths that are stable according to the Hessian method, can bifurcate into diffuse modes.

Electro-mechanical coupling bifurcation and bulging propagation in a cylindrical dielectric elastomer tube

This paper explores the critical and post-bulging bifurcation of a cylindrical dielectric elastomer (DE) tube undergoing finite deformation under electro-mechanical coupling loading. Explicit expressions for the critical conditions of electro-mechanical bifurcation are derived by using a simplified mathematical method. The post-bifurcation path is comprehensively investigated by specifying the material model as ideal dielectric elastomer. In the post-bifurcation analysis, we analytically establish conditions for the phase coexistence of steady propagation and analyze the physical implications. We demonstrate a global instability under force or voltage control and a localized instability under volume or charge control. Cylindrical tube experiments have been carried out under electro-mechanical coupling loading to verify the theoretical predictions. Good agreements on the critical conditions as well as the post-bifurcation path are obtained. This work characterizes the bifurcation mechanism of rubber-like materials under complex coupling loading.

Experimental investigation of the electromechanical phase transition in a dielectric elastomer tube

A membrane of dielectric elastomer undergoes a large deformation when it is subjected to a voltage through the thickness. Due to the attributes of light weight and high energy density, dielectric elastomers are suitable for electromechanical actuators and generators. In this work, the phenomenon of electromechanical phase transition is demonstrated experimentally in a tube of dielectric elastomer subjected to an internal pressure, an axial force and a voltage. When the voltage exceeds a critical value, the homogeneous deformation becomes unstable, and the tube deforms into coexistent states of bulged and unbulged sections. At the transition voltage the unbulged sections gradually bulge up and propagate. Two stable states are observed at the end of the phase transition process: one is coexistent states of the bulged and unbulged sections; the other is the wholly bulged tube. The achieved maximum voltage-induced deformation of the tube is 2200% in area, and the electromechanical energy conversion density is estimated to be 1.13 J g−1. These results are beyond the largest values reported in the literature. A theoretical analysis based on thermodynamics is carried out to qualitatively explain the observed experimental phenomenon.

Electromechanical response and failure modes of a dielectric elastomer tube actuator with boundary constraints

As a widely used configuration for dielectric elastomer (DE) actuators, DE tube actuators (or cylindrical actuators) are also found to be susceptible to electromechanical instability (EMI), which may lead to a premature electrical breakdown (EB), and inhibit the potential actuation of DE actuators. This work investigates the electromechanical response of a DE tube actuator with and without boundary constraints to demonstrate an alternative to avoid EMI while achieving large actuation. Our simulation results based on the Gent strain energy model show that the EMI of a DE tube actuator can be eliminated, and larger actuation deformation can be achieved by applying boundary constraints. As a result of these constraints, consideration is also given to the possible mechanical buckling failure that may occur. Mechanisms of possible failure modes of constrained and unconstrained DE tube actuators, such as electromechanical instability, electrical breakdown and mechanical buckling, are elucidated. This paper should provide better theoretical guidance on how to improve the actuation performance of DE actuators, thus leading to the optimal design of DE-based devices.

Axisymmetric wave propagation in finitely deformed dielectric elastomer tubes

Wave propagation in hollow dielectric elastomer cylinders is studied. The quasi-static deformation of the tube owing to a combination of radial electric field and mechanical loading is determined first. Two combinations are accounted for, one at which the tube is free to expand in the axial direction, and another at which the tube is axially pre-stretched and restricted from elongating. Subsequently, longitudinal axisymmetric incremental motions are superposed on the underlying state. The governing equations in the tube and in the surrounding space are formulated and a numerical procedure is used in order to solve the resulting set of equations. The fundamental mode in the frequency spectrum is determined for thin, intermediate and thick wall tubes. The influences of the tube geometry, the mechanical pre-stretch and particularly the electric bias field are examined. An important observation is the ability to manipulate the propagation of the waves by adjusting the electromechanical bias field. This infers the use of dielectric elastomers in tubular configurations as active waveguides or isolators by a proper tuning of the electrostatic stimuli.

Beam manipulating by graded photonic crystal slab made of dielectric elastomer actuators

The focusing lens and beam-steering device are implemented using two-dimensional graded photonic crystals with dielectric elastomer tube array embedded in air background. The gradient refractive index could be adjusted by varying the applied voltage on the dielectric elastomer tube so that the tube radius would change accordingly, which consequently alters the filling factor of the constituent material in photonic crystals, and the photonic dispersion band can be modulated. The finite element method is employed to simulate the electromagnetic wave propagation inside the designed device and analyze both the tunable focusing properties and beam-deflecting behavior. The implementation of the proposed device is validated within the lowest band. It is concluded that the proposed innovative device could easily accomplished the applications of focusing and steering electromagnetic fields with nonuniform applied voltage profiles.

Large conversion of energy in dielectric elastomers by electromechanical phase transition

When air is pumped in, a tubular balloon initially inflates slightly and homogeneously. A short section of the balloon then forms a bulge, which coexists with the unbulged section of the balloon. As more air is pumped in, the bulged section elongates at the expense of the unbulged section, until the entire balloon is bulged. The phenomenon is analogous to the liquid-to-vapor phase transition. Here we study the bulging transition in a dielectric elastomer tube as air is pumped into the balloon and a voltage is applied through the thickness of the membrane. We formulate the condition for coexistent budged and unbulged sections, and identify allowable states set by electrical breakdown and mechanical rupture. We find that the bulging transition dramatically amplifies electromechanical energy conversion. Energy converted in an electromechanical cycle consisting of unbulged and bulged states is thousands of times that in an electromechanical cycle consisting of only unbulged states.

Large deformation and electromechanical instability of a dielectric elastomer tube actuator

This paper theoretically analyzes a dielectric elastomer tube actuator (DETA). Subject to a voltage difference between the inner and outer surfaces, the actuator reduces in thickness and expands in length, so that the same voltage will induce an even higher electric field. This positive feedback may cause the actuator to thin down drastically, resulting in electrical breakdown. We obtain an analytical solution of the actuator undergoing finite deformation when the elastomer obeys the neo-Hookean model. The critical strain of actuation is calculated in terms of various parameters of design. We also discuss the effect of the strain-stiffening on electromechanical behavior of DETAs by using the model of freely joined links.

Linear actuation in coextruded dielectric elastomer tubes

Cylindrical fibre actuators have been constructed by a coextrusion method using a thermoplastic polyurethane wall and a conductive grease filler. These actuators may be operated as single fibres or bundled together as actuating ropes. Key results include the validation of Carpi’s wall pressure model [F. Carpi, D.D. Rossi, Dielectric elastomer cylindrical actuators: electromechanical modelling and experimental evaluation, Mater. Sci. Eng. C-Biomimetic Supramol. Syst. 24 (2004) 555–562] and the proof-of-concept demonstration of a technique that can be used for producing inexpensive dielectric elastomer actuators on an industrial scale.

Dielectric elastomer based prototype fiber actuators

Dielectric elastomer based prototype fiber actuators have been developed and evaluated. The work is motivated by the tremendous potential offered by the current multicomponent fiber forming technologies as a means to fabricate fiber actuators. To explore the potential, prototype fiber actuators have been fabricated using commercially available dielectric elastomer tubes and by applying appropriate compliant electrodes to inner cavity and outer walls of these tubes. The force and displacement generated by such actuators have been studied as a function of applied electric field under different prestrained conditions. In order to introduce anisotropy in the fiber behavior, two types of prestrains (uniaxial and uniform) were applied. Actuation strains of 7 and 18% were recorded for silicone tubes in the axial and radial directions, respectively. Polyurethane tubes produced significantly higher blocking force compared to silicone tubes. The results demonstrate significant influence of applied prestrain on actuation strains and blocking force measured under isometric condition.