On the dynamic electromechanical loading of dielectric elastomer membranes

Dielectric elastomer actuators (DEAs) have received considerable attention recently due to large voltage-induced strains, which can be over 100%. Previously, a large deformation quasi-static model that describes the out-of-plane deformations of clamped diaphragms was derived. The numerical model results compare well with quasi-static experimental results for the same configuration. With relevance to dynamic applications, the time-varying response of initially planar dielectric elastomer membranes configured for out-of-plane deformations has not been reported until now. In this paper, an experimental investigation and analysis of the dynamic response of a dielectric elastomer membrane is reported. The experiments were conducted with prestretched DEAs fabricated from 0.5 mm thick polyacrylate films and carbon grease electrodes. The experiments covered the electromechanical spectrum by investigating membrane response due to (i) a time-varying voltage input and (ii) a time-varying pressure input, resulting in a combined electromechanical loading state in both cases. For the time-varying voltage experiments, the membrane had a prestretch of three and was passively inflated to various predetermined states, and then actuated. The pole strains incurred during the inflation were as high as 25.6%, corresponding to slightly less than a hemispherical state. On actuation, the membrane would inflate further, causing a maximum additional strain of 9.5%. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum polar strain of 28%. The results from these experiments reveal that the response of the membrane is a departure from the classical dynamic response of continuum membrane structures. The dynamic response of the membrane is that of a damped system with specific deformation shapes reminiscent of the classical membrane mode shapes but without same-phase oscillation, that is to say all parts of the system do not pass through the equilibrium configuration at the same time. Of particular interest is the ability to excite these deformations through a varying electrical load at constant mechanical pressure.     

Experimental investigation of side force control on cone-cylinder slender bodies with flexible micro balloon actuators

Side forces on slender bodies of revolution at medium to high angles of attack (AOA > 30°) has been known from a large number of investigations. Asymmetric vortex pairs over a slender body are believed to be the principle cause of the side forces. Under some flight conditions, this side force may be as large as the normal force acting on the slender body. In this paper, experimental results are presented for side force control on a cone-cylinder slender body by using microfabricated balloon actuators. The micro balloon actuators are made of polydimethylsiloxane (PDMS) elastomer by using micro molding techniques. They can be packaged on curve surfaces of a cone-cylinder slender body. As actuator is actuated, the micro balloon actuator inflates about 1.2 mm vertically, which is about 2.4% of the cylinder diameter D (=50 mm) of the cone-cylinder slender body. Micro balloon actuators are actuated at different roll angles of a cone-cylinder slender body. Aerodynamic force measurement results indicate the effects of micro balloon actuators vary at different actuation locations on the cone-cylinder slender body. The side forces can be significantly reduced if the actuators are actuated in the weak vortex side (the side corresponding to the asymmetric vortex which is far from the surface) and actuation angles are located at about 50–60° (the actuation angle here is measured from stagnation line of the incidence plane toward weak vortex side direction). Significant changes are noticed from the surface pressure, as well as leeside vortex flow field, measurement. Micro balloon actuators change nose shapes of the slender body which decide adverse-pressure-gradient values and directly influence the origin of the separation lines and characteristics of the separated vortices over the leeside surface.     

The electro-mechanical response of elastomer membranes coated with ultra-thin metal electrodes

This paper presents experimental and theoretical analyses of the electro-mechanical response of metal/elastomer multilayers. A novel test has been devised to determine the relationship between the mechanical response of clamped elastomer membranes, coated on both sides with metal electrodes, and an applied electric field. The load-deflection response of the multilayers subjected to different voltages was measured using an instrumented spherical indenter having dimensions comparable to the freestanding span. The measurements are used with closed-form solutions for membrane deflection to determine the effective plane-strain modulus of cracked multilayers and electrically induced in-plane strains. The experiments demonstrate that: (i) electrically induced strains vary with the square of the electric field, as expected from electrostatic models of parallel plate capacitors, (ii) the transverse stiffness of membranes can be controlled using applied electric fields, (iii) analytical models accurately predict the relationship between electrode crack spacing, layer properties and effective moduli. Finally, we estimate the toughness of the sub-micron metal electrodes, using cracking models that relate crack spacing, imposed strain and the energy release rate governing channel crack formation.     

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.

     

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 experimental study to obtain the rate dependent stress-stretch relation of DE membranes(VHB TM 9473) subjected to pure shear like loading and electric loading simultaneously.Stretching rate dependent 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.     

基于可逆畴变的压电圆环多层致动器应变响应研究

压电致动器在现代工业中发挥着非常重要的作用。然而，目前应用的压电致动器均是基于线性压电效应，最大应变一般只有0.1-0.15%，实现大的致动应变一直是该领域学者追求的目标。本文中，我们提出了两种经过特殊设计的基于可逆非180°电畴翻转的PZT圆环多层致动器，一种是径向极化、部分电极（RPPE）的4层圆环，另一种是周期性正交极化（POP）的4层圆环，以期能够实现大的致动应变，而且圆环构型层数增加时也不容易发生失稳等问题。实验结果表明，在相同的驱动电场（2kV/mm，0.1Hz）下，4层RPPE最大致动应变为0.27%，约为普通PZT圆环的2倍，但表面变形很不均匀。相比之下，4层的POP圆环致动器的最大输出应变为0.36%，是普通PZT圆环的2.7倍。这两种致动器的致动应变都是随着频率的增加而减小， RPPE致动器在超过1Hz后稳定在0.19%， POP致动器在超过5Hz后稳定在0.2%。而且， POP圆环致动器重复性能很好，经过2万次致动循环后致动应变几乎不变。这种POP PZT多层圆环致动器具有结构稳定、输出应变大等优点，在致动领域具有很好的应用前景。     

基于可逆畴变的压电圆环多层致动器应变响应研究

压电致动器在现代工业中发挥着非常重要的作用。然而,目前应用的压电致动器均是基于线性压电效应,最大应变一般只有0.1-0.15%,实现大的致动应变一直是该领域学者追求的目标。本文中,我们提出了两种经过特殊设计的基于可逆非180°电畴翻转的PZT圆环多层致动器,一种是径向极化、部分电极（RPPE）的4层圆环,另一种是周期性正交极化（POP）的4层圆环,以期能够实现大的致动应变,而且圆环构型层数增加时也不容易发生失稳等问题。实验结果表明,在相同的驱动电场（2kV/mm,0.1Hz）下,4层RPPE最大致动应变为0.27%,约为普通PZT圆环的2倍,但表面变形很不均匀。相比之下,4层的POP圆环致动器的最大输出应变为0.36%,是普通PZT圆环的2.7倍。这两种致动器的致动应变都是随着频率的增加而减小, RPPE致动器在超过1Hz后稳定在0.19%, POP致动器在超过5Hz后稳定在0.2%。而且, POP圆环致动器重复性能很好,经过2万次致动循环后致动应变几乎不变。这种POP PZT多层圆环致动器具有结构稳定、输出应变大等优点,在致动领域具有很好的应用前景。     

Dynamic response of tubular dielectric elastomer transducers

In this paper, a numerical model for the dynamic response of tubular dielectric elastomer transducers is presented and validated with experimental results for the first time. Dielectric elastomers (DE) are soft polymer based smart materials that can be potentially employed in applications such as actuation, sensing and energy harvesting (Kornbluh, 2004, Carpi et al., 2005, Waki et al., 2008). In our previous work, the quasi-static response of tubular DE transducers was studied (Goulbourne et al., 2007, Son and Goulbourne, 2009). Here, a numerical model is developed to predict the dynamic response of tubular DE transducers. Inertia effects are included in our previous static model which yields a system of partial differential equations. The results of the dynamic response of the tubular DE transducers are obtained by numerically solving the simplified partial different equations using a finite difference scheme. The capacitance change induced by the dynamic deformation of the tubular DE is also calculated by a simple electrostatic model, illustrating dynamic passive sensing.Several tubular DE transducer samples (VHB 4905 and silicone) were fabricated and an experimental setup was developed to investigate the dynamic response by measuring capacitance and radial deformation. In the sensing experiments, a sweep of dynamic pressure profiles (0–5 Hz) are applied. It is observed that silicone transducers have a larger dynamic sensing range. In the actuation experiments, the deformation of the silicone actuator is monitored while a voltage signal (4.5 kV) is applied from 0 to 30 Hz. The silicone actuator shows a good actuation response. The comparison between numerical and experimental results for the DE transducers shows an overall error of 3%.     

Propagation of instability in dielectric elastomers

When an electric voltage is applied across the thickness of a thin layer of an dielectric elastomer, the layer reduces its thickness and expands its area. This electrically induced deformation can be rapid and large, and is potentially useful as soft actuators in diverse technologies. Recent experimental and theoretical studies have shown that, when the voltage exceeds some critical value, the homogenous deformation of the layer becomes unstable, and the layer deforms into a mixture of thin and thick regions. Subsequently, as more electric charge is applied, the thin regions enlarge at the expense of the thick regions. On the basis of a recently formulated nonlinear field theory, this paper develops a meshfree method to simulate numerically this instability.     

Temperature effects on the dynamic response of viscoelastic dielectric elastomer

Viscoelasticity and temperature can significantly affect the performance of a dielectric elastomer. In the current study, we use a thermodynamic model to describe the effect of temperature and viscoelasticity on the electromechanical response undergoing a cyclic electric load by taking into account of the temperature dependent dielectric constant. Because of the significant viscoelasticity in the dielectric elastomer, the deformation and the nominal electric displacement can not keep in phase with the electric field at low frequencies. The results show that the magnitude of the cyclic electromechanical actuation strain increases with the decrease of the temperature and decreases with the increasing frequency, and viscoelasticity can result in significant hysteresis for dielectric elastomers under a relative low temperature and a low frequency.     

Electro-elastomers: Large deformation analysis of silicone membranes

Electro-elastomers are large strain smart materials capable of both sensing and actuation. Typical electro-elastomer setups consist of either a silicone or acrylic membrane sandwiched between two compliant grease electrodes. Silicone electro-elastomers have maximum elastic strains between 200% and 350%. Acrylic electro-elastomers are more widely employed due to larger actuation strains but are softer than silicone and have a lower force output [Goulbourne, N.C., Frecker, M., Mockensturm, E.M., Snyder, A.J., 2003. Modeling of a dielectric elastomer diaphragm for a prosthetic blood pump. In: Proceedings of SPIE, Smart Structures and Materials: EAPAD, San Diego; Goulbourne, N.C., Mockensturm, E.M., Frecker, M., 2005b. Quasi-static and dynamic inflation of a dielectric elastomer membrane. In: Proceedings of SPIE, Smart Structures and Materials: EAPAD, San Diego]. A numerical formulation for the large deformation response of electro-elastomer membranes subject to electromechanical loading is derived in this paper. The approach is based on modifying the elastic membrane theory of Green, Adkins, and Rivlin [Adkins, J.E., Rivlin, R.S., 1952. Large elastic deformations of isotropic materials IX. The deformation of thin shells. Philosophical Transactions of the Royal Society of London. Series A Mathematical and Physical Sciences 244, 505–531; Green, A.E., Adkins, J.E., 1970. Large Elastic Deformations. Oxford University Press, London]. The electro-elastic stress state is defined as the combination of the electrical Maxwell stress and the mechanical stress for hyperelastic materials [Goulbourne, N.C., Mockensturm, E.M., Frecker, M., 2005a. A nonlinear model for dielectric elastomer membranes. ASME Journal of Applied Mechanics 72, (6) 899–906]. This paper augments our previous work by presenting a mathematical solution procedure for simulating the field responsive behavior of silicone electro-elastomers configured for both in-plane and out-of-plane deformation. Thin axisymmetric membranes subject to electromechanical loads are the focus of this investigation. The numerical analysis shows that there is a delicate balance between the electrical and the mechanical portions of the stress, which must be maintained for the overall stress to remain tensile and by extension the electro-elastomer to remain stable. It is shown that at very high voltages the stress can become negative ultimately leading to transducer failure. For sensing applications, the varying capacitive behavior of electro-elastomers is used to extract information about the membrane’s deformed state.     

Shape measurement and control of deployable membrane structures

The shape inaccuracies of inflatable antennas and the potential shape control of the surface of those structures are investigated. Surface shape inaccuracies are due to geometric nonlinear deformation. Correcting the shape of these inflatables focused on the integration of piezopolymer actuators on the membranes. The out-of-plane displacements of a membrane structure were assessed with the shadow moiré method. The experimentally measured shape of the structure confirmed the extent of deviation from the ideal optical surface, a paraboloid of revolution. Active control of the shape of the membrane was tested using a piezoelectric material, polyvinylidene fluoride (PVDF). The deformation caused by actuation of the membrane structure was evaluated using electronic speckle pattern interferometry. An analytical solution was developed to verify the extent of shape correction that can be achieved by embedded PVDF actuators. It was confirmed that micron-level shape corrections are possible for future space-based sensors that use inflatable antennae technology.     

The Mechanical Response of Shape Memory Alloys Under a Rapid Heating Pulse

Shape memory alloy (SMA) actuators are very promising due to their large strain and work-output, but are considered to be very slow due to their cooling rate. In this article, we explore the capabilities of a fast one-directional actuation mode based on one-occasional rapid Joule heating of SMA elements. For this purpose, a unique experimental system has been developed that applies a high-voltage electric pulse to a detwined NiTi wire and measures the resulting displacement due to the martensite to austenite phase transformation. The electric pulse is tuned to produce variable temperature jump of up to 160°C within a risetime of few microseconds. One end of the wire is clamped while the displacement of the other end is monitored both by a laser doppler vibrometer and by an optical encoder that measures the displacement of a grating device. Analysis of experimental results reveals a dead time delay between the electric pulse and the wire’s response, which is attributed to the austenite nucleation time and which determines the limit on the fastest possible shape memory actuation. Further analysis reveals relations between the dead weight used and the average acceleration and maximal velocity obtained. In particular, the maximal velocity correlates to a constant kinetic energy delivered by the wire, which suggests a constant integrand over the stress-strain curve regardless of the dead-weight used. A comparison of actuation performances demonstrates that our actuation experiments are significantly advantageous over other fast actuation methods in almost every actuation aspect reviewed. This demonstrates the great potential of SMA for applications that require high speeds and large displacements one-occasional actuation.     

A mathematical model for cylindrical,fiber reinforced electro-pneumatic actuators

In recent years, dielectric elastomers have received increasing attention due to their unparalleled large strain actuation response (>100%). The force output, however, has remained a major limiting factor for many applications. To address this limitation, a model for a fiber reinforced dielectric elastomer actuator based on the deformation mechanism of McKibben actuators is presented. In this novel configuration, the outer cylindrical surface of a dielectric elastomer is enclosed by a network of helical fibers that are thin, flexible and inextensible. This configuration yields an axially contractile actuator, in contrast to unreinforced actuators which extend. The role of the fiber network is twofold: (i) to serve as reinforcement to improve the load-bearing capability of dielectric elastomers, and (ii) to render the actuator inextensible in the axial direction such that the only free deformation path is simultaneous radial expansion and axial contraction. In this paper, a mathematical model of the electromechanical response of fiber reinforced dielectric elastomers is derived. The model is developed within a continuum mechanics framework for large deformations. The cylindrical electro-pneumatic actuator is modeled by adapting Green and Adkins’ theory of reinforced cylinders to account for the applied electric field. Using this approach, numerical solutions are obtained assuming a Mooney–Rivlin material model. The results indicate that the relationship between the contractile force and axial shortening is bilinear within the voltage range considered. The characteristic response as a function of various system parameters such as the fiber angle, inflation pressure, and the applied voltage are reported. In this paper, the elastic portion of the modeling approach is validated using experimental data for McKibben actuators.     

基于周期拼装的平面压电作动器结构拓扑优化

具有狭长形状的压电作动器有利于输出较大的位移,而采用周期拼装方式实现这类结构则具有制造成本相对较低的优点.本文提出了基于周期拼装的平面压电作动器结构拓扑优化设计的数学模型.其中,以位移输出点作功最大化为设计目标,考虑了材料体积和控制能耗约束,对结构基体材料和压电材料的分布以及控制电压的分布进行优化设计.本文给出了结构响...     

带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正，逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比，外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力，从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究，应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层板采用高阶和一阶剪切变形理论进行计算，结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言，由于激励器是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。因此，对于厚度剪切型激励器，剪切变形理论的选取对于板变形结果的好坏有重要的作用。     

An interface crack with partially electrically conductive crack faces under antiplane mechanical and in-plane electric loadings

An interface crack in a bimaterial piezoelectric space under the action of antiplane mechanical and in-plane electric loadings is analyzed. One zone of the crack faces is electrically conductive while the other part is electrically permeable. All electro-mechanical values are presented using sectionally-analytic vector-functions and a combined Dirichlet-Riemann boundary value problem is formulated. An exact analytical solution of this problem is obtained. Simple analytical expressions for the shear stress, electric field and also for mechanical displacement jump of the crack faces are derived. These values are also presented graphically along the corresponding parts of the material interface. Singular points of the shear stress, electric field and electric displacement jump are found. Their intensity factors are determined as well. Intensity factors variations with respect to the external electric field and different ratios between the electrically conductive and electrically permeable crack face zones are also demonstrated.     

Coupled solution for anisotropic piezoelectric materials with cracks

The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity and electric displacement inside electrically permeable cracks are all constants.     

Puncture characterization of rubber membranes

Puncture resistance is among the major mechanical properties of rubber membranes, yet the intrinsic material parameters controlling the puncture of these materials are still unknown. To evaluate puncture resistance, the ASTM F1342 standard test is currently the most commonly used method. Using a conical puncture probe, this test is designed for any type of protective clothing, including coated fabrics, laminates, textiles, plastics, elastomeric films or flexible materials. This work aims to investigate the quantitative material parameters that control the puncture resistance of thin rubber membranes. Three commercial rubbers commonly used in protective gloves are investigated. The results demonstrate that the probe-tip geometry strongly affects the results in puncture characterization. The maximum puncture force depends on the contact surface between the elastomer membrane and the probe tip. The indentation force has been calculated for elastomer membranes with large deformations in the absence of friction, using the Mooney strain-energy function. The puncture strengths of elastomer membranes are much lower than their tensile and biaxial strengths. The puncture of rubber membranes is controlled by a maximum local deformation that is independent of the indentor geometry.