In silico optimization of actuation performance in dielectric elastomercomposites via integrated finite element modeling and deep learning

Dielectric elastomers(DEs)require balanced electric actuation performance and mechanical integrity under applied voltages.Incorporating high dielectric particles as fillers provides extensive design space to optimize concentration,morphology,and distribution for improved actuation performance and material modulus.This study presents an integrated framework combining finite element modeling(FEM)and deep learning to optimize the microstructure of DE composites.FEM first calculates actuation performance and the effective modulus across varied filler combinations,with these data used to train a convolutional neural network(CNN).Integrating the CNN into a multi-objective genetic algorithm generates designs with enhanced actuation performance and material modulus compared to the conventional optimization approach based on FEM approach within the same time.This framework harnesses artificial intelligence to navigate vast design possibilities,enabling optimized microstructures for high-performance DE composites.

Performance Investigation of Cone Dielectric Elastomer Actuator Using Taguchi Method

Dielectric elastomer actuator （DEA） show promise for mechatronic applications due to the advantages of dielectric elastomer, such as lightweight, flexible, low cost, high strain, etc, and many configurations of DEAs have been demonstrated. As a kind of linear actuator, cone DEAs are studied in some laboratory prototypes due to easy manufacturing, however, their performance have not been exploited fully. Based on the working principle of DEA, a four-bar linkage mechanism is designed to provide negative stiffness preload, which can increase displacement output of actuator （outer diameter 100 mm） to 17 mm. Three cone actuating units are assembled in parallel to enhance the maximum force output to 5.07 N. Loading experiments of actuator in forward and backward strokes are performed, the experimental results show that backward stroke has stronger actuating capability than forward stroke, accordingly application of actuator is recommended. Four factors rather than applied voltage, i.e., number of actuating units, pre-stretch ratio, inner diameter, and outer diameter, are determined as influencing factors for Taguchi method. Then the performance objectives of actuator, i.e., displacement output, maximum force output, and maximum work in backward stroke, are investigated based on L9（34） Taguchi orthogonal design. The mean signal-to-noise （S/N） ratio based on the larger-the-better criterion is calculated according to the acquired displacement and force output. Analytical results show that outer diameter has the most significant influence on displacement output, and maximum force out and work output are influenced most by number of actuating units. Inner diameter also has an important effect on the performance objectives of actuator, while pre-stretch ratio has the least influence. The proposed performance investigation is helpful for the design and application of cone actuator in mechatronic system.

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.

Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion

The time-dependent electro-viscoelastic performance of a circular dielectric elastomer(DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices.

Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

Dielectric elastomer(DE) is suitable in soft transducers for broad applications,among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices call for an efficient and reliable method to analyze the dynamic response of DE. This remains to be a challenge since the resultant vibration equation of DE, for example, the vibration of a DE balloon considered here is highly nonlinear with higher-order power terms and time-dependent coefficients. Previous efforts toward this goal use largely the numerical integration method with the simple harmonic balance method as a supplement. The numerical integration and the simple harmonic balance method are inefficient for large parametric analysis or with difficulty in improving the solution accuracy. To overcome the weakness of these two methods,we describe formulations of the incremental harmonic balance(IHB) method for periodic forced solutions of such a unique system. Combined with an arc-length continuation technique, the proposed strategy can capture the whole solution branches, both stable and unstable, automatically with any desired accuracy.

On the ratio of expectation crossings of random-excited dielectric elastomer balloon

The ratio of expectation crossings of dielectric elastomer balloon excited by random pressure is analytically evaluated in this letter. The Mooney-Rivlin model is adopted to describe the constitutive relation while the random pressure is described by Gaussian white noise. Through a specific transformation, the stochastic differential equations for the total energy and phase are derived. With the application of the stochastic averaging, the system total energy is then approximated by a one-dimensional diffusion pro-cess. Solving the associated Fokker-Planck-Kolmogorov （FPK） equation yields the stationary probability density of the system total energy. The ratio of expectation crossings is then derived based on the joint stationary probability density of stretch ratio and its ratio of change. The efficacy and accuracy of the proposed procedure are verified by comparing with the results from Monte Carlo simulation （MCS）.

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

The dielectric elastomer(DE)is an important intelligent soft material widely used in soft actuators,and the dynamic response of the DE is highly nonlinear due to the material properties.In the DE,electrostriction denotes the deformation-dependent permittivity.In the present study,we formulate the nonlinear dynamic governing equations of the DE membrane considering the electrostriction effect.The free vibration and parametric excitation of the DE membrane with different geometric sizes are calculated.The free vibration bifurcations induced by the initial location and the voltage are both discussed according to an energy-based approach.The amplitude-frequency characteristics and bifurcation diagrams of parametric excitation are also given.The results show that electrostriction decreases the free vibration amplitude and increases the frequency,but it has less influence on the parametric excitation oscillation frequency and decreases the parametric excitation amplitude except when the membrane resonates.The initial location and the applied voltage can induce the snap-through instability of the free vibration.A large geometric size will lead to a much lower resonance frequency.The resonance amplitudes increase while the resonance frequencies decrease with the increase in the applied voltage.The critical voltage of snap-through instability for the parametric excitation is larger than that for the free vibration one.

Snap-through path in a bistable dielectric elastomer actuator

The dielectric elastomer(DE)has attracted significant attention due to its desired features,including large deformation,fast response,and high energy density.However,for a DE actuator(DEA)utilizing a snap-through deformation mode,most existing theoretical models fail to predict its deformation path.This paper develops a new finite element method(FEM)based on the three-parameter Gent-Gent model suitable for capturing strain-stiffening behaviors.The simulation results are verified by experiments,indicating that the FEM can accurately characterize the snap-through path of a DE.The method proposed in this paper provides theoretical guidance and inspiration for designing and applying DEs and bistable electroactive actuators.

Analytical models for circular and spherical dielectric elastomers

In order to imitate skin characteristics, a dielectric elastomer (DE) membrane coated with flexible electrodes is applied with high voltage, which can lead to wrinkles and other phenomena. To develop soft-actuated air vehicles and other equipment, lightweight gas is pumped into a DE spherical shell to generate controllable flight movements. According to experimental phenomena and data, the calculation models of phase transitions on circular DE films are built. Meanwhile, the deformation characteristics of different DE (acrylic polymer and rubber) spherical actuators combined with helium are compared. The peak pressure inside a rubber balloon is greater than that of a VHB (acrylic polymer) balloon shell, but the limit stretch of rubber is much smaller. By taking advantages of this phenomenon, large deformations of a VHB spherical shell can be realized at an actuated state. Moreover, multi-layer spherical DE shells can achieve larger voltage-induced volume change than monolayer ones. The research indicates that pre-stretching is one of the key factors to induce phase transitions between flat, wrinkled and bulging regions on circular DE films, and the internal pressure determines the electromechanical performance of balloon actuators.

Experimental investigation on electromechanical deformation of dielectric elastomers under different temperatures

Under an applied voltage, dielectric elastomers （DEs） produce an actuation strain that is nonlinear, partly because of the material properties. In this study, an experimental characterization is conducted to evaluate how the ambient temperature and pre-stretch affected the actuation performance. For DEs with a pre-stretch of 2 × 2, an increase of temperature from -10° to 80° results in a variation in the actuation strain of more than 1700%. Low pre-stretched DEs are more susceptible to temperature change; while highly pre-stretched DEs are relatively insensitive to temperature, because in this case the energy conversion was dominated by mechanical stretching, rather than thermal conduction, during the actuation.

Phase transitions of dielectric elastomers in a circular frame

In order to imitate biological addesion performance nd skin properties,phase transitions on dielectric elastomers(D E)with high voltages are studied.The states of flat,rinkled and bulging on the circular active area which is coated w th electrodes verify the theoretical prediction of phase transitions and failure phenomena.When the DE membrane is subjected to a radial force and increasing voltage,four experimental phenomena are discovered before electric breakdown:The active region expands,and the thin membrane is still flat till breakdown;bulging forms instead of a fa t area on the membrane;wrinkes and bulging coexist;and the active aea is completely wrinlded there are two types of phase transitions between the fa t andwrinded regions in a membrane:Wrinkles form in small regions,and te n propagate at the expense of t e flat area until he entire active part becomes wrinded;b o t the wrinded a d flat regions move interchangeably on a membrane with ramping voltage till breakdown.It is found that when Aere is no prestretch of a DE membrane,bulging w ill occur with te increasing voltage.Wrinkles commonly appear at large prestretch and,terefore,the prestetched ratio significantly affects electomechanical phase tansitions.

Constitutive relation of viscoelastic dielectric elastomer

In this paper, we present a modified model describing the constitutive relation of viscoelas-tic dielectric elastomer （DE）. The uniform uniaxial tension-recovery experiment was carried out at different stretching rates. Based on Yeoh hyper-elastic model, model-fitting approach is put forward to obtain the relationship between parameters of Yeoh model and stretching rate, thus the modified model was obtained. From the approximate relationship between harmonic motion and uniform reciprocating motion, the stress-strain curve in the recovery process was also identified through the hysteresis between stress and strain. The modified model, with concise form and evident physical concept, can describe the strong nonlinear behavior between deformation and mechanical stress of the material in a common stretching rate range （from 0.01s^-1 to 0.8s^-1 at least）. The accuracy and reliability of the modified model was examined.

Electromechanical phase transition of a dielectric elastomer tube under internal pressure of constant mass

The electromechanical phase transition for a dielectric elastomer （DE） tube has been demonstrated in recent experiments, where it is found that the unbulged phase gradually changed into bulged phase. Previous theoretical works only studied the transition process under pressure control condition, which is not consistent with the real experimental condition. This paper focuses on more complex features of the electromechanical phase transition under internal pressure of constant mass. We derive the equilibrium equations and the condition for coexistent states for a DE tube under an internal pressure, a voltage through the thickness and an axial force. We find that under mass control condition the voltage needed to maintain the phase transition increases as the process proceeds. We analyze the entire process of electromechanical phase transition and find that the evolution of configurations is also different from that for pressure control condition.

Recent progress in the development of dielectric elastomer materials and their multilayer actuators

Dielectric elastomers(DEs)have emerged as one of the most promising artificial muscle technologies,due to their exceptional properties such as large actuation strain,fast response,high energy density,and flexible processibility for various configurations.Over the past two decades,researchers have been working on developing DE materials with improved properties and exploring innovative applications of dielectric elastomer actuators(DEAs).This review article focuses on two main topics:recent material innovation of DEs and development of multilayer stacking processes for DEAs,which are important to promoting commercialization of DEs.It begins by explaining the working principle of a DEA.Then,recently developed strategies for preparing new DE materials are introduced,including reducing mechanical stiffness,increasing dielectric permittivity,suppressing viscoelasticity loss,and mitigating electromechanical instability without pre-stretching.In the next section,different multilayer stacking methods for fabricating multilayer DEAs are discussed,including conventional dry stacking,wet stacking,a novel dry stacking method,and micro-fabrication-enabled stacking techniques.This review provides a comprehensive and up-to-date overview of recent developments in high-performance DE materials and multilayer stacking methods.It highlights the progress made in the field and also discusses potential future directions for further advancements.

The rate dependence of the dielectric strength of dielectric elastomers

Elastomers are widely used in electronics and electrical devices,either as insulators or transducers.The insulation and actuation performance of elastomers are highly suscepti-ble to their dielectric strength.Among the factors that influ-encethedielectricstrength ofelastomers,material viscoelasticity is an important factor that needs further inves-tigation.Since the material viscoelasticity is often character-ized by rate-dependent behaviors,we present two different sample configurations to experimentally examine the electrical and mechanical rate dependence of the dielectric strength of VHB 4905 elastomers.At pre-stretch ratio of 4,the improve-ment of the dielectric strength is about 30%from voltage ramp of 50 V/s to 800 V/s.Particularly,with an in-house biaxial test platform,the effect of the stretching rate on the dielectric strength is examined for the first time.The improvement of the dielectric strength is about 35%from stretching rate of 0.1 mm/s to 5 mm/s.Moreover,a dielectric strength predictor based on configurational stress is adopted to describe the experimental data.According to the predictor,the loading rate affects the dielectric strength of the elastomer mainly by influencing the evolution of the inelastic deformation.

Computer-controlled ultra high voltage amplifier for dielectric elastomer actuators

Soft robotics is a breakthrough technology to support human-robot interactions.The soft structure of a soft robot can increase safety during human and robot interactions.One of the promising soft actuators for soft robotics is dielectric elastomer actuators(DEAs).DEAs can operate silently and have an excellent energy density.The simple structure of DEAs leads to the easy fabrication of soft actuators.The simplicity combined with silent operation and high energy density make DEAs interesting for soft robotics researchers.DEAs actuation follows the Maxwell-pressure principle.The pressure produced in the DEAs actuation depends much on the voltage applied.Common DEAs requires high voltage to gain an actuation.Since the power consumption of DEAs is in the milli-Watt range,the current needed to operate the DEAs can be neglected.Several commercially available DC-DC converters can convert the volt range to the kV range.In order to get a voltage in the 2-3 kV range,the reliable DC-DC converter can be pricy for each device.This problem hinders the education of soft actuators,especially for a newcomer laboratory that works in soft electric actuators.This paper introduces an entirely do-it-yourself(DIY)Ultrahigh voltage amplifier(UHV-Amp)for education in soft robotics.UHV-Amp can amplify 12 V to at a maximum of 4 kV DC.As a demonstration,we used this UHV-Amp to test a single layer of powdered-based DEAs.The strategy to build this educational type UHV-Amp was utilizing a Cockcroft-Walton circuit structure to amplify the voltage range to the kV range.In its current state,the UHV-Amp has the potential to achieve approximately 4 kV.We created a simple platform to control the UHV-Amp from a personal computer.In near future,we expect this easy control of the UHV-Amp can contribute to the education of soft electric actuators.

Failure modeling of folded dielectric elastomer actuator

When subjected to voltage,the dielectric elastomer membrane reduces its thickness and expands its area under the resulting compressive force.This characteristic enables the dielectric elastomer actuators of different structures to be designed and fabricated.By employing the thermodynamic theory and research method proposed by Suo et al.,an equilibrium equation of folded dielectric elastomer actuator with two generalized coordinates is established.The governing equations of failure models involving electromechanical instability,zero electric field,electrical breakdown,loss of tension,and rupture by stretch are also derived.The allowable areas of folded dielectric elastomer actuators are described.These results could provide a powerful guidance to the design and performance evaluation of the dielectric elastomer actuators.

THEORY OF DIELECTRIC ELASTOMERS

In response to a stimulus, a soft material deforms, and the deformation provides a function. We call such a material a soft active material （SAM）. This review focuses on one class of soft active materials： dielectric elastomers. When a membrane of a dielectric elastomer is subject to a voltage through its thickness, the membrane reduces thickness and expands area, possibly straining over 100%. The dielectric elastomers are being developed as transducers for broad applications, including soft robots, adaptive optics, Braille displays, and electric generators. This paper reviews the theory of dielectric elastomers, developed within continuum mechanics and thermodynamics, and motivated by molecular pictures and empirical observations. The theory couples large deformation and electric potential, and describes nonlinear and nonequilibrium behavior, such as electromechanical instability and viscoelasticity. The theory enables the finite element method to simulate transducers of realistic configurations, predicts the efficiency of electromechanical energy conversion, and suggests alternative routes to achieve giant voltage-induced deformation. It is hoped that the theory will aid in the creation of materials and devices.

Advances in dielectric elastomer actuation technology

Dielectric elastomer actuators(DEAs) have attracted much interest over the past decades due to the inherent flexibility, large strain, high efficiency, high energy density, and fast response of the material, which are known as one of the most promising candidates for artificial muscle. In this paper, we first introduce the actuation principle and electromechanical modeling approaches of dielectric elastomers(DEs). Then, the performance of different DEs material and existing compliant electrodes that are widely utilized for DEAs are presented. We also highlight the compatibility of DEs, which is suitable for a variety of actuator designs and applications. Lastly, we summarize the challenges and future development in terms of electromechanical modeling, improvement of materials including compliant electrodes and dielectric elastomer, designs and applications of novel dielectric elastomer actuators.

RATE DEPENDENT STRESS-STRETCH RELATION OF DIELECTRIC ELASTOMERS SUBJECTED TO PURE SHEAR LIKE LOADING AND ELECTRIC FIELD

The performance of dielectric elastomer （DE） transducers is significantly affected by viscoelastic relaxation-induced electromechanical dissipations. This paper presents an experi- mental study to obtain the rate dependent stress-stretch relation of DE membranes （VHBTM9473） subjected to pure shear like loading and electric loading simultaneously. Stretching rate depen- dent behavior is observed. The results also show that the tensile force decreases as the voltage increases. The observations are compared with predictions by a viscoelastic model of DE. This experiment may be used for further studies of dynamic electromechanical coupling properties of DEs.