A numerical framework for modeling anisotropic dielectric elastomers

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.

Electromechanical instability (EMI) is one of most common failure modes for dielectric elastomers (DEs). It has been reported that pre-stretching a DE sample can suppress EMI due to strain stiffening taking place for larger strains and a higher elastic modulus are achieved at high stretch ratios when a voltage is applied to the material. In this work, the influence of equi-biaxial stretch on DE secant modulus was studied using VHB 4910 and silicone rubber (SR) composites containing barium titanate (BaTiO3, BT) particles and also dopamine coated BT (DP-BT) particles. The investigation of equi-biaxial deformation and EMI failure for VHB 4910 was undertaken by introducing a voltage-stretch function. The results showed that EMI was suppressed by equi-biaxial pre-stretch for all the DEs fabricated and tested. The stiffening properties of the DE materials were also studied with respect to the secant modulus. Furthermore, a voltage-induced strain of above 200% was achieved for the polyacrylate film by applying a pre-stretch ratio of 2.0 without EMI occurring. However, a maximum voltage-induced strain in the polyacrylate film of 78% was obtained by the SR/20 wt% DP-BT composite for a lower applied pre-stretch ratio of 1.6 and again EMI was eliminated.

Dielectric elastomers are novel soft smart material that could deform sustainably when subjected to external electric field. That makes dielectric elastomers promising materials for actuators. In this paper, a spring-roll actuator that would bend when a high voltage is applied was fabricated based on dielectric elastomer. Using such actuators as active parts, the flexible grippers and inchworm-inspired crawling robots were manufactured, which demonstrated some examples of applications in soft robotics. To guide the parameters design of dielectric elastomer based spring-roll bending actuators, the theoretical model of such actuators was established based on thermodynamic theories. The initial deformation and electrical induced bending angle of actuators were formulated. The failure of actuators was also analyzed considering some typical failure modes like electromechanical instability, electrical breakdown, loss of tension and maximum tolerant stretch. Thus the allowable region of actuators was determined. Then the bending angle-voltage relations and failure voltages of actuators with different parameters, including stretches of the dielectric elastomer film, number of active layers, and dimensions of spring, were investigated. The influences of each parameter on the actuator performances were discussed, providing meaningful guidance to the optical design of the spring-roll bending actuators.

Electromechanical instability in anisotropic dielectric elastomers

Shear Locking Free Finite Elements for Thick Plates on Elastic Foundations In this study, the analysis of thick plates resting on elastic foundation is investigated by using four-noded (PBQ4) and eight-noded (PBQ8) quadrilateral finite elements based on Mindlin plate theory and by taking into account transverse shear deformations. In order to avoid shear locking problem in case of small thicknesses, selective reduced integration technique is used in addition to full integration technique for the evaluation of the stiffness matrices of both elements. Various loading and boundary conditions are considered and a reference example is solved for comparison. It is concluded that the results obtained by using PBQ4 and PBQ8 elements are both satisfactory for thicker plates. However selective reduced integration technique is more reliable for thinner plates.

Dielectric elastomer is a kind of typical electro-active polymer material. Under external electric field it can produce large electrostriction deformation and possesses the advantages of high elastic energy density, super short response time, high efficiency, and so on. It is widely used in the artificial muscles, facial expressions, actuators, energy harvesters, sensors, robots and Braille display devices, and also shows huge application potential in the aerospace and intelligent bionic areas. We built the free energy of the dielectric elastomer electrical-mechanical coupling system and investigated its constitutive relation and stability behavior. Then we calculated the elastomer’s critical deformation suffering from the voltage. If electrical breakdown, electromechanical instability and snap-through instability can be avoided, the large electrostriction deformation can induce adiabatic temperature change and isothermal entropy change of the dielectric elastomer. We used the entropy-temperature or electric displacement-electric field plane to describe the temperature change and entropy change of dielectric elastomer undergoing large electrostriction deformation. With the influence of temperature, we developed a temperature and deformation coupling thermodynamical free energy model to calculate the electric field induced variation of temperature and entropy in dielectric elastomers. The results should offer great help in guiding the design and fabrication of excellent actuators featuring soft dielectric elastomers.

Mechanical energy and electrical energy can be converted to each other by using a dielectric elastomer transducer. Large voltage-induced deformation has been a major challenge in the practical applications. The voltage-induced deformation of dielectric elastomer is restricted by electromechanical instability (EMI) and electric breakdown. We study the loading path effect of dielectric elastomer and introduce various methods to achieve giant deformation in dielectric elastomer and demonstrate the principles of operation in experiments. We use a computational model to analyze the operation of DE generators and actuators to guide the experiment. In actuator mode, we get three designing parameters to vary the actuation response of the device, and realize giant deformation with appropriate parameter group. In the generator mode, energy flows in a device with inhomogeneous deformation is demonstrated.

With the development of tire mechanics and computer technology, tire deformation, rolling resistance, and temperature distribution under rolling conditions may be predicted accurately through finite element analysis (FEA). Deep knowledge of tire fracture and failure behavior may also be obtained by FEA. During the past years, an in‐house finite element program has been developed in our research laboratory which can analyze the tire deformation, stress, and strain under the static inflation and footprint load conditions and can predict the tire rolling resistance and temperature distribution as well. This paper gives a brief description of the mathematical and mechanical foundations of the developed FEA code and the computing procedures, emphasizing the tire material loss model and the calculation procedure of strain energy release rate in tire fracture analysis. Two characteristics of the presented model compared with the published literature are the three‐dimensional anisotropic properties included in the loss model of cord‐rubber materials and a new VCCT (Virtual Crack Closure Technique), which is simple and physically direct, saves on the amount of computation, and is developed to compute the fields of strain energy release rates (Serrs) in the crack front to analyze tire fracture behavior.

In the definition of Noll, a body is uniform if all points are made of the same material. As shown by Noll himself and by Epstein and Maugin, uniformity makes the Helmholtz free energy depend on the material point exclusively through a tensor field, called uniformity tensor or implant tensor or material isomorphism. Uniformity is therefore a particular case of inhomogeneity. In turn, uniformity includes homogeneity as a particular case: indeed, homogeneity is attained when the uniformity tensor happens to be integrable. This work focuses on the non-linear large-deformation behaviour of uniform dielectric elastomers. Building on the foundational works of Toupin, Eringen and others, this work integrates continuum mechanics with electrostatics to develop a finite element framework for analysing uniform dielectric elastomers. This framework allows for considering the inherent inhomogeneity in materials exhibiting non-linear electromechanical coupling such as electro-active polymers. The inhomogeneity is assumed to be self-driven, i.e., not implied by the second law of thermodynamics: rather, it depends on the torsion of the connection (covariant derivative) induced by the uniformity tensor. A MATLAB®-based finite element solver is developed and applied to the simulation of an electromechanical beam-type actuator. The solver is robust and capable of addressing various simulation scenarios. Numerical simulations demonstrate the significant impact of material uniformity on actuator performance. This research provides a tool for future applications in dielectric elastomers, particularly in sensors, actuators and bio-inspired robotics.

The shape and size of a satellite adapter ring are optimized in this paper using particle swarm optimization and an in-house finite element program. For a realistic high-fidelity modeling of the adapter ring, a commercial preprocessor is used. However, optimization of a high-fidelity model inevitably involves longer computation time; therefore, parallelization is essential to shorten the total elapsed time. Furthermore, fitness evaluation time by the finite element simulation differs from case to case, which unavoidably causes idling of some of parallel computing resources. To overcome the inefficiency induced by the irregularities of individual fitness evaluation, an asynchronous parallel swarm algorithm is developed and applied to the structural optimization of the adapter ring with 19 design variables. The adapter ring’s total mass is reduced to 33.4 kg from 35.9 kg within 202 min. The asynchronous version also performs almost twice better compared with the synchronous one. The methodology proposed in this paper offers an attractive advantage for complex structural design, both in aspect of computational time and global search.

In seismic areas, the application of structural dampers becomes compulsory in the design of buildings. There are various types of dampers, such as viscous elastic dampers, viscous fluid dampers, friction dampers, tune mass dampers, yielding/ metallic dampers, and magnetic dampers. All damper systems are designed to protect structural integrities, control damages, prevent injuries by absorbing earthquake energy, and reduce deformation. This paper is a part of research investigating the behaviour of the U-shaped steel damper (as one type of metallic damper) that can be applied to the buildings in seismic areas. The dampers are used as connections between the roof and supporting structure, with the two general purposes. The first is to control the displacement of roof under an earthquake, and the second is to absorb seismic energy through the plasticity of some parts in dampers. If a strong earthquake occurs, the plasticity will absorb the seismic energy; therefore, heavy damage could be avoided from the roof’s mainframes. In this paper, several models of U-shaped steel dampers are introduced. Several parameters, such as elastic stiffness, maximum strength, and energy dissipation, are determined under two conditions. Firstly, static analysis of the proposed damper under variation of U-steel plate configurations, searching the model with more significant energy dissipation. Secondly, static analysis of the unsymmetrical and symmetrical damper under different loading directions. An in-house finite element program that involves both geometrical and material nonlinearities is developed as a problem solver. A quasi-static lateral loading is given to each model until one cycle of the hysteresis curve is reached (in the displacement range between -20 mm to +20 mm). The above parameters are calculated from the hysteresis curve. From the results, the behaviour of the U-steel damper can be described as follows. Firstly, increasing the energy dissipation in the lateral direction can be done by increasing the lateral stiffness of the damper. However, it can reduce the maximum elastic deformation of the damper. Secondly, under the random direction of loading, a symmetrical shape can increase the energy dissipation of the damper.

In the current study, a rate-dependent crystal plasticity finite element method (CPFEM) was used to simulate flow stress behavior and texture evolution of a body-centered cubic (BCC) crystalline material during plastic deformation at room temperature. To account for crystallographic slip and rotation, a rate-dependent crystal constitutive law with a hardening model was incorporated into an in-house finite element program, CAMPform3D. Microstructural heterogeneity and anisotropy were handled by assigning a crystallographic orientation to each integration point of the element and determining the stiffness matrix of the individual crystal. Uniaxial tensile tests of single crystals with different crystallographic orientations were simulated to determine the material parameters in the hardening model. The texture evolution during four different deformation modes - uniaxial tension, uniaxial compression, channel die compression, and simple shear deformation - was investigated based on the comparison with experimental data available in the literature.

Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability

ABSTRACTOperation of a dielectric elastomer (DE) transducer is limited by the way it fails, and any other limits imposed by the user. For example, material rupture and dielectric breakdown are two examples of transducer failure, while tension loss is a user-imposed limit. Electromechanical instability may or may not result in transducer failure, but is often considered as a boundary to denote the onset of state transition. For a DE undergoing homogeneous deformation, constructing operational limits on work-conjugate state diagrams are rather straight-forward. However, for DE subjected to non-homogeneous deformation, the process is more complex. We present a method to plot the operational boundaries of a DE subject to non-homogeneous deformation, known commonly as the Universal Muscle Actuator or the loudspeaker configuration. Our analysis show that tension loss need not be imposed as a hard operational limit, and that there is further operational space for the transducer, post tension loss. By plotting the operational limits on work-conjugate planes, we determine an optimal inner-to-outer ring ratio and the required pre-stretches that maximize energy conversion.

Unimorph bending actuators based on dielectric elastomers (DE) are promising components for soft robotic grippers in analogy to the capabilities of the human hand. In a simple manufacturing process of the unimorph actuator, a bendable, but not stretchable passive carrier film is laminated with an active DE film, which expands in the electric field and generates a large bending deformation of the laminated composite film along its length dimension. The actuation performance in terms of the bending angle, actuator tip displacement and blocking force depends not only on the geometrical design of the unimorph actuator, but also on the properties of the used materials such as the Young’s moduli of the passive film and the elastomer film as well as the elastomer’s permittivity. To evaluate the influence of all relevant geometrical and material parameters on the actuation performance, a simple mathematical model was developed. Additionally, DE unimorph actuators were manufactured with silicone elastomer and their performance was experimentally investigated. The results of calculations are compared with those of the corresponding measurements and exhibit a high degree of quantitative agreement. Furthermore, the dependence of the actuator performance on various geometrical and material parameters (thickness of the dielectric and of the carrier film, permittivity and Young’s modulus of the dielectric) is predicted with the mathematical model. These calculations pave the way to a unimorph actuator with strongly improved performance. The key for this high performance is the simultaneous enhancement of the permittivity and the Young’s modulus of the dielectric. Thermoplastic polyurethane (TPU) fulfills these requirements and unimorph actuators based on TPU actually confirm the predicted high performance experimentally. By this way, the simple mathematical model offers a powerful and efficient tool for the optimization of unimorph actuators.