We investigate the ture electromechanical stability of dielectric elastomer actuators by considering the competition between Maxwell and mechanical stresses. Existing researches based on the positive defiiteness of the nominal Hessian matrix addressed only the initial load routie stability, i.e., Born stability, in the absence of prestresses. We generalize this method to account for electromechanical stability at any prestress state. For large enough prestresses, we demonstatre that the previous method for Born stability may lead to predcitions that deviate considerably from the true results. The true method for electromechanical stablity can help the factual design of actuators constructed from dielectric elastomers.
A layer of dielectric elastomer can be voltage actuated to behave as actuators, but needs to avoid the electromechanical instability of excessively thin down accompanied with electric breakdown. We develop a true method to analyze the electromechanical stability of dielectric elastomers by adopting the positive definiteness of the true tangential modulus matrix, and demonstrate that the previous method is only valid for the special case of zero prestress. Our new method is applicable for arbitrary prestress cases including zero prestress, with predictions consistent with available experimental…
Dielectric elastomers (DEs) that couple deformation and electrostatics have the potential for use in soft sensors and actuators with applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. However, currently available DEs are limited by weak electromechanical coupling and require large electric fields for significant actuation. In this work, a statistical mechanics-based model of DE chains is applied to elucidate the role of a polymer network architecture in the performance of the bulk material. Given a polymer network composed of chains that are cross-lin…
We present a new finite deformation, dynamic finite element model that incorporates surface tension to capture elastocapillary effects on the electromechanical deformation of dielectric elastomers. We demonstrate the significant effect that surface tension can have on the deformation of dielectric elastomers through three numerical examples: (1) surface tension effects on the deformation of single finite elements with homogeneous and inhomogeneous boundary conditions; (2) surface tension effects on instabilities in constrained dielectric elastomer films, and (3) surface tension effects on burs…
Dielectric elastomers have recently been proposed for various biologically-relevant applications, in which they may operate in fluidic environments where surface tension effects may have a significant effect on their stability and reliability. Here, we present a theoretical analysis coupled with computational modeling for a generalized electromechanical analysis of surface stability in dielectric elastomers accounting for surface tension effects. For mechanically deformed elastomers, significant increases in critical strain and instability wavelength are observed for small elastocapillary numb…
Pull-in (or electro-mechanical) instability occurs when a drastic decrease in the thickness of a dielectric elastomer results in electrical breakdown, which limits the applications of dielectric devices. Here we derive the criteria for determining the pull-in instability of dielectrics actuated by different loading methods: voltage-control, charge-control, fixed pre-stress and fixed pre-stretch, by analyzing the free energy of the actuated systems. The Hessian criterion identifies a maximum in the loading curve beyond which the elastomer will stretch rapidly and lose stability, and can be seen…
Macroscale robotic systems have demonstrated great capabilities of high speed, precise, and agile functions. However, the ability of soft robots to perform complex tasks, especially in centimeter and millimeter scale, remains limited due to the unavailability of fast, energy-efficient soft actuators that can programmably change shape. Here, we combine desirable characteristics from two distinct active materials: fast and efficient actuation from dielectric elastomers and facile shape programmability from liquid crystal elastomers into a single shape changing electrical actuator. Uniaxially ali…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each plane parallel to the major surfaces will expand or contract to a different extent. Here we study the voltage-induced bending response of a functionally graded dielectric plate on the basis of the nonlinear theory of electro-elasticity, when both the elastic shear modulus and the electric permittivity change with the thickness coordinate. The theory is illustra…
Plasticized poly(vinyl chloride) (PVC) is a jelly-like soft dielectric material that attracted substantial interest recently as a new type of electro-active polymers. Under electric fields of several hundred Volt/mm, PVC gels undergo large deformations. These gels can be used as artificial muscles and other soft robotic devices, with striking deformation behavior that is quite different from conventional dielectric elastomers. Here, we present a simple model for the electro-activity of PVC gels, and show a non-linear effect of free ions on its dielectric behaviors. It is found that their parti…
We investigate elastic wave propagation in finitely deformed dielectric elastomers in the presence of an electrostatic field. To analyze the propagation of both longitudinal (P-) and transverse (S-) waves, we utilize compressible material models. We derive explicit expressions of the generalized acoustic tensor and phase velocities of elastic waves for the ideal and enriched dielectric elastomer models. We analyze the slowness curves of the elastic wave propagation, and find the P-S-mode disentangling phenomenon. In particular, P- and S- waves are separated by the application of an electric fi…
A predicting model for soft Dielectric Elastomer Generators (DEGs) must consider a realistic model of the electromechanical behaviour of the elastomer filling, the variable capacitor and of the electrical circuit connecting all elements of the device. In this paper such an objective is achieved by proposing a complete framework for reliable simulations of soft energy harvesters. In particular, a simple electrical circuit is realised by connecting the capacitor, stretched periodically by a source of mechanical work, in parallel with a battery through a diode and with an electrical load consumin…
Thin dielectric elastomers with compliant electrodes exhibit various types of instability under the action of electromechanical loading. Guided by the thermodynamically-based formulation of Fosdick and Tang (J. Elasticity 88, 255-297, 2007), here we provide an energetic perspective on the stability of dielectric elastomers and we highlight the fundamental energetic divide between voltage control and charge control. By using the concept of energy relaxation, we describe wrinkling for neo-Hookean ideal elastomers, and we show that in voltage control wrinkling is stable as long as the tension-ext…
Dielectric elastomers (DEs) are a type of multifunctional materials with salient features that are very attractive in developing soft, lightweight, and small-scale transducers and robotics. This paper reviews the mechanics of soft DE structures, focusing on their dynamic responses, including vibrations and waves in typical structures. The basic formulations of nonlinear electroelasticity are briefly summarized by following the descriptions of Dorfmann and Ogden. The recent advances in the study on linearized dynamic problems of DE plates and shells are then outlined according to the geometric …
This paper is concerned with the optimisation of the actuation response of electro-elastic, rank-two laminates obtained laminating a core rank-one composite with a soft phase which constitutes the shell. The analysis is performed for two classes of composites that are subjected to traction-free boundary-value problems. The results are compared with those computed in a previous study where the optimisation was carried out at small strains. The non-linear approach allows a better estimation of the geometric layout of the reference configuration to enhance the maximum stretch or shear strain at t…
We propose a protocol to model accurately the electromechanical behavior of dielectric elastomer membranes using experimental data of stress-stretch and voltage-stretch tests. We show how the relationship between electric displacement and electric field can be established in a rational manner from this data. Our approach demonstrates that the ideal dielectric model, prescribing linearity in the purely electric constitutive equation, is quite accurate at low-to-moderate values of the electric field and that, in this range, the dielectric permittivity constant of the material can be deduced from…
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental version. We first study the static finite bending deformation of the slab. We then derive the three-dimensional equations for the onset of small-amplitude wrinkles superimposed upon the finite bending. We use the surface impedance matrix method to build a robust numerical procedure for solving the resulting dispersion equations and determining the wrinkled sh…
We provide a clear energetic insight into the catastrophic nature of the so-called creasing and pull-in instabilities in soft electro-active elastomers. These phenomena are ubiquitous for thin electro-elastic plates and are a major obstacle to the development of giant actuators; yet they are not completely understood nor modelled accurately. Here, in complete agreement with experiments, we give a simple formula to predict the voltage thresholds for these instability patterns and model their shape, and show that equilibrium is impossible beyond their onset. Our analysis is fully analytical, doe…
In this paper we describe a stretchable solid-state electronic switching material that operates at high voltage potentials, as well as a switch material benchmarking technique that utilizes a modular dielectric elastomer (artificial muscle) ring oscillator. The solid-state switching material was integrated into our oscillator, which self-started after 16s and performed 5 oscillations at a frequency of 1.05Hz with 3.25kV DC input. Our materials-by-design approach for the nickel filled polydimethysiloxane (Ni-PDMS) based switch has resulted in significant improvements over previous carbon-grease…
Classical electrodynamics uses a dielectric constant to describe the polarization response of electromechanical systems to changes in an electric field. We generalize that description to include a wide variety of responses to changes in the electric field, as found in most systems and applications. Electromechanical systems can be found in many physical and biological applications, such as ion transport in membranes, batteries, and dielectric elastomers. We present a unified, thermodynamically consistent, variational framework for modeling electromechanical systems as they respond to changes i…
A dielectric elastomer whose edges are held fixed will buckle, given sufficient applied voltage, resulting in a nontrivial out-of-plane deformation. We study this situation numerically using a nonlinear elastic model which decouples two of the principal electrostatic stresses acting on an elastomer: normal pressure due to the mutual attraction of oppositely charged electrodes and tangential shear ("fringing") due to repulsion of like charges at the electrode edges. These enter via physically simplified boundary conditions that are applied in a fixed reference domain using a nondimensional appr…
Dielectric elastomers are an emerging class of highly deformable electro-active materials employed for electromechanical transduction technology. For practical applications, the design of such transducers requires a model accounting for insulation of the active membrane, non-perfectly compliant behaviour of the electrodes or interaction of the transducer with a soft actuated body. To this end, a three-layer model, in which the active membrane is embedded between two soft passive layers, can be formulated. In this paper, the theory of nonlinear electro-elasticity for heterogeneous soft dielectr…
This paper presents an electromechanical analysis of the nonlinear static response and the superimposed small-amplitude wave characteristics in an infinite periodic compressible dielectric elastomer (DE) laminate subjected to electrostatic excitations and prestress in the thickness direction. The enriched Gent material model is employed to account for the effects of strain stiffening and electrostriction of the DE laminate. The theory of nonlinear electroelasticity and related linearized incremental theory are exploited to derive the governing equations of nonlinear response and the dispersion…
Soft electroactive materials can undergo large deformation subjected to either mechanical or electrical stimulus, and hence they can be excellent candidates for designing extremely flexible and adaptive structures and devices. This paper proposes a simple one-dimensional soft phononic crystal cylinder made of dielectric elastomer to show how large deformation and electric field can be used jointly to tune the longitudinal waves propagating in the PC. A series of soft electrodes are placed periodically along the dielectric elastomer cylinder, and hence the material can be regarded as uniform in…
Simplified discrete model for axisymmetric dielectric elastomer membranes with robotic applications
Hohai University（河海大学）；University of Birmingham（伯明翰大学）；Nanyang Technological University（南洋理工大学）；University of Michigan（密歇根大学）；Newcastle University（纽卡斯尔大学）
It is highly desirable to discover an electromechanical coupling that allows a dielectric material to generate curvature in response to a uniform electric field, which would add a new degree of freedom for designing actuators. Flexoelectricity, a two-way coupling between polarization and strain gradient, is a good candidate. But its applications are usually limited to the nanoscale due to its inherent size dependence. Here, an inverse flexoelectret effect in silicone elastomers is introduced to overcome this limitation. Based on this idea, a flexing actuator which can generate large curvature …
Soft materials, such as liquids, polymers, foams, gels, colloids, granular materials, and most soft biological materials, play an important role in our daily lives. From a mechanical viewpoint, soft materials can easily achieve large deformations due to their low elastic moduli; meanwhile, surface instabilities, including wrinkles, creases, folds, and ridges, among others, are often observed. In particular, soft dielectrics subject to electrical stimuli can achieve significantly large deformations that are often accompanied by instabilities. While instabilities are often thought to cause failu…
We examine the stability of a soft dielectric plate deformed by the coupled effects of a mechanical pre-stress applied on its lateral faces and an electric field applied through its thickness under charge control. The electric field is created by spraying charges on the major faces of the plate: although in practice this mode of actuation is harder to achieve than a voltage-driven deformation, here we find that it turns out to be much more stable in theory and in simulations. First we show that the electromechanical instability based on the Hessian criterion associated with the free energy of …
