温度对介电弹性体材料力电耦合变形的影响（固体力学大会文章）

介电弹性体（Dielectric elastomer,简称DE）材料是一类在电场激励下可以产生大幅度尺寸或形状变化的新型柔性功能材料。DE材料具有非常宽的温度应用范围,这种宽的温度工作范围和快速大变形性能为各种柔性致动器结构提供了良好的基础,但作为一种粘弹性高分子材料,温度对其性能的影响也是非常明显的。然而到目前为止,所有关于DE材料驱动性能的研究仅局限于室温条件下,温度变化对DE材料力电耦合稳定性的影响几乎没有相关报道。基于此,通过实验研究了温度对最常用的DE材料（VHB 4910,3M）力电耦合变形的影响,结果表明：升高温度可以提高DE材料的力电耦合变形;温度越高,DE材料越容易发生力电耦合失效。然后,从热力学和粘弹性力学出发,建立了考虑温度影响后的DE材料的粘弹性力电耦合模型,数值模拟理论结果和实验结果非常吻合。     

Flutter analysis of a viscoelastic tapered wing under bending–torsion loading

The dynamic stability of a tapered viscoelastic wing subjected to unsteady aerodynamic forces is investigated. The wing is considered as a cantilever tapered Euler–Bernoulli beam. The beam is made of a linear viscoelastic material where Kelvin–Voigt model is assumed to represent the viscoelastic behavior of the material. The governing equations of motion are derived through the extended Hamilton’s principle. The resulting partial differential equations are solved via Galerkin’s method along with the classical flutter investigation approach. The developed model is validated against the well-known Goland wing and HALE wing and good agreement is obtained. Different solution methods, namely; the k method, the p-k method, and the flutter determinant method are compared for the case of elastic wing. However, when the viscoelastic damping is introduced, the k and p-k methods become less effective. The flutter determinant method is modified and employed to carry out non-dimensional parametric study on the Goland wing. The study includes the effects of parameters such as the taper ratio, the density ratio, the viscoelastic damping of wing structure and many other parameters on the flutter speed and flutter frequency. The study reveals that a tapered wing would be more dynamically stable than a uniform wing. It is also observed that the viscoelastic damping provides wider stability region for the wing. The investigation shows that the density ratio, bending-to-torsion frequency ratio, and the radius of gyration have significant effects on the dynamic stability of the wing. Based on the obtained results, a wing with an elastic center and inertial center that are located closer to the mid-chord would be more dynamically stable.     

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.     

Application of scaling transformation to characterizing complex rheological behaviors and fractal derivative modeling

It has been long observed that cumbersome parameters are required for the traditional viscoelastic models to describe complex rheological behaviors. Inspired by the relationship between normal and anomalous diffusions, this paper tentatively employs t ^α to replace t, called as the scaling transformation, in the traditional creep compliance and relaxation modulus. With this methodology, the relaxation modulus is found to agree with the well-known Kohlrausch-Williams-Watts (KWW) stretched exponential function. The fitting results confirm that the proposed models accurately characterize rheological behaviors only with one more parameter α. Moreover, it is noted that the present formulations are directly related to the fractal derivative viscoelastic models and the index α is actually the order of the fractal derivative.     

Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the generalized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.     

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.     

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.     

Experimental study and electromechanical model analysis of the nonlinear deformation behavior of IPMC actuators

This paper develops analytical electromechanical formulas to predict the mechanical deformation of ionic polymer–metal composite(IPMC) cantilever actuators under DC excitation voltages. In this research, IPMC samples with Pt and Ag electrodes were manufactured, and the large nonlinear deformation and the effect of curvature on surface electrode resistance of the IPMC samples were investigated experimentally and theoretically. A distributed electrical model was modified for calculating the distribution of voltage along the bending actuator. Then an irreversible thermodynamic model that could predict the curvature of a unit part of an IPMC actuator is combined with the electrical model so that an analytical electromechanical model is developed. The electromechanical model is then validated against the experimental results obtained from Pt-and Ag-IPMC actuators under various excitation voltages. The good agreement between the electromechanical model and the actuators shows that the analytical electromechanical model can accurately describe the large nonlinear quasi-static deflection behavior of IPMC actuators.     

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%.     

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.     

Bifurcation of response of a nonlinear viscoelastic spherical membrane

The quasistatic inflation of a nonlinear viscoelastic spherical membrane by monotonically increasing pressure is considered. The deformation is assumed to be spherically symmetric. For the constitutive equation assumed, circumstances are shown to exist when the radius history must either have a jump discontinuity or bifurcate. A necessary condition for bifurcation and its dependence on material properties and radius history is analysed. Examples of bifurcation for various pressure histories are presented. Post-bifurcation branches are constructed and the possibility of secondary bifurcation is discussed.     

Large amplitude oscillatory shear rheology of three different shear-thickening particle dispersions

We present a large amplitude oscillatory shear rheology (LAOS) investigation of three different shear-thickening particle dispersions - fumed silica in polyethylene oxide (FLOC), fumed silica in polypropylene glycol (HydroC), and cornstarch in water (JAM). These systems shear-thicken by three different mechanisms - shear-induced formation of particle clusters flocculated by polymer bridging, hydrocluster formation, and jamming. The viscoelastic non-linearities of the three fluids were studied as a function of strain and strain-rate space through the use of Lissajous-Bowditch curves and local nonlinear viscoelastic moduli of an oscillatory shear cycle. The nonlinear behaviors of the three fluids were compared and contrasted to understand the nonlinear shear-thickening mechanism of each. Both HydroC and JAM dispersions were found to exhibit strong strain stiffening of the elastic moduli and strain thickening of the loss moduli behavior associated with possible hydrocluster formation and particle jamming. However, the FLOC dispersion, in contrast, showed strong strain softening and strain thinning behavior at large strain amplitudes associated with yielding of the microstructure. The expected thickening of the loss modulus of FLOC in LAOS with increasing strain was not observed even though viscosity of FLOC was found to shear-thicken in steady-shear measurements. This disagreement is likely due to very large strain amplitudes required for shear-thickening to occur by shear-induced polymer bridging mechanism. The hypothesis was confirmed through stress growth experiments. Conversely, the HydroC and JAM dispersions required relatively small applied strains for shear-thickening to occur by hydrocluster and jamming mechanism. The comparison of local intra-cycle nonlinearity through Lissajous-Bowditch plots and nonlinear viscoelastic parameters indicated that the elastic nonlinearities of all three systems are primarily driven by a strong dependence on the magnitude of the applied strain-rates within an oscillatory cycle rather than the amplitude of the applied strain. A close inspection of the LAOS data reveals strong differences in the viscoelastic nonlinearities of these three different shear-thickening dispersions which can be used to create a nonlinear rheological fingerprint for each and offers valuable new insights into the nonlinear dynamics associated with each of the shear-thickening mechanisms.     

“Equivalent” Electromechanical Coefficient for IPMC Actuator Design Based on Equivalent Bimorph Beam Theory

This paper addresses an “equivalent” electromechanical coupling coefficient that may be used in designing Ionic Polymer Metal Composite (IPMC) actuators. The coefficient is not a material constant and derived from equivalent bimorph beam model. The collective effect of the membrane thickness and operating voltage on the coefficient is demonstrated by using a design of experiment (DOE) of three and five levels of the two factors, respectively. Experiments and linear finite element analyses with MD.NASTRAN at DOE points are performed. The tip displacement and the coupling coefficient are reported and their response surface (RS) approximations as function of the thickness and voltage are constructed. Experiments and RS predictions indicate that actuator thickness and applied voltage are two interacting major factors for maximum tip displacement. The equivalent coupling coefficient is primarily driven by the thickness of actuator moreover voltage appears to contribute as the thickness increases. The initial curvature of the strips before electrical excitation is also shown to be a factor for “equivalent” coupling coefficient, it is not, however sufficient to explain the variation in the experimental data. A correction factor approach is proposed and applied to the straight beam tip displacement RS that filters out experimental variation. A corrected RS enables including the pre-imposed initial curvature as design parameter along with the actuator thickness and the operating peak voltage when predicting the tip displacement and the equivalent coupling coefficient.     

The effects of composition,temperature, and annealing on the rheological properties of InZn in situ composites

High viscoelastic damping is observed in InZn materials over ranges of composition, frequency, temperature, and annealing time. Microscopy reveals InZn when cast segregates into a heterogeneous micro-structure resembling an in situ composite consisting of a zinc matrix with soft indium platelet inclusions. This morphology is predicted to be advantageous for maximizing the damping figure of merit Etanδ by viscoelastic composite theory. InZn is found to be linearly viscoelastic, unlike other high damping metals. The damping of InZn varies little over a substantial range of temperature, in contrast with polymers. For 5 % In material, the optimal composition, Etanδ is 2.8 GPa at 10 Hz, compared to a peak of 0.6 GPa for high damping rubbers. After annealing for 13 years, Etanδ was still high at 1.9 GPa. InZn demonstrates high damping under a wide range of conditions.     

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.     

Viscoelastic behavior of PMMA/grafted PBA nanoparticle systems in the molten state

The viscoelastic properties of poly(methyl methacrylate) (PMMA)/grafted poly(butyl acrylate) (PBA) nanoparticle systems were investigated. The rubber particles consist of PBA core (60 nm in diameter) and grafted PMMA shell. The grafting degree, defined as the weight ratio of grafted PMMA to PBA particles, ranges from 0.8 to 1.5. Two series of samples, A series with 7.5 wt.% of PBA content and B series with 12 wt.% of PBA content, were used. The systems exhibited fast and slow relaxation process, the former reflecting the relaxation of the matrix PMMA chains and the latter being attributed to grafted PBA particles. For A series samples, time-temperature superposition (TTS) was held well over the frequency (ω) and temperature (T) ranges measured. However, for B series samples, TTS was not satisfied at low ω due to the particle-particle interaction of grafted PBA particles, although the samples obeyed TTS at high ω associated with the relaxation with entanglement of matrix PMMA. At high T and low ω region, the B series samples showed a sol-gel transition at elevating T and the critical gel behavior characterized with a power-law relationship, G′ = G″/tan(nπ/2) ∝ ωⁿ, was observed. This behavior suggested formation of a self-similar, fractal structure of grafted PBA particles. The critical gel temperature (T _gel) and the critical exponent (n) were determined for the B series samples. TEM observations revealed that as-prepared A and B samples had well-dispersed particles but the B samples after viscoelastic measurements had fragmented networks of the PBA particles, confirming that the sol-gel transition occurred for the PMMA/grafted PBA systems at elevating T.     

Monoharmonic vibrations and vibrational heating of an electromechanically loaded circular plate with piezoelectric actuators subject to shear strain

The paper addresses the forced flexural vibrations and dissipative heating of a circular viscoelastic plate with piezoactive actuators under axisymmetric loading. A refined formulation of this coupled problem is considered. The viscoelastic behavior of materials is described using the concept of complex moduli dependent on the temperature of dissipative heating. The electromechanical behavior of the plate is modeled based on the Timoshenko hypotheses for the mechanical variables and analogous hypotheses for the electric-field variables in the piezoactive layers of the actuator. The temperature is assumed constant throughout the thickness. The nonlinear problem is solved by a time stepping method using, at each step, the discrete-orthogonalization and finite-difference methods to solve the elastic and heat-conduction equations, respectively. A numerical study is made of the effect of the shear strain, the temperature dependence of the material properties, fixation conditions, and geometrical parameters of the plate on the vibrational characteristics and the electric potential applied to the actuator electrodes to balance the mechanical load Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 104–114, September 2008.     

Bending of a radially prestressed annular plate by tilting a central rigid inclusion

A thin annular plate contains a rigid, circular, central inclusion. The plate is subjected to a large axisymmetric radial load at its outer edge, where it is also restrained against transverse displacement and rotation. A couple applied to the rigid inclusion causes it to rotate about its diameter out of the plane of the plate. We use the method of matched asymptotic expansions to find an approximate expression for the applied couple as a function of the angle of rotation of the rigid inclusion. If the outer radius of the annulus is very large compared to the inner radius, then the couple required to rotate a truly rigid inclusion is 25% higher than the couple required to rotate an inclusion whose membrane strain stiffness is the same as that of the plate (cf. ref. [3]) through the same small angle.     

Modeling of dielectric viscoelastomers with application to electromechanical instabilities

Soft dielectrics are electrically-insulating elastomeric materials, which are capable of large deformation and electrical polarization, and are used as smart transducers for converting between mechanical and electrical energy. While much theoretical and computational modeling effort has gone into describing the ideal, time-independent behavior of these materials, viscoelasticity is a crucial component of the observed mechanical response and hence has a significant effect on electromechanical actuation. In this paper, we report on a constitutive theory and numerical modeling capability for dielectric viscoelastomers, able to describe electromechanical coupling, large-deformations, large-stretch chain-locking, and a time-dependent mechanical response. Our approach is calibrated to the widely-used soft dielectric VHB 4910, and the finite-element implementation of the model is used to study the role of viscoelasticity in instabilities in soft dielectrics, namely (1) the pull-in instability, (2) electrocreasing, (3) electrocavitation, and (4) wrinkling of a pretensioned three-dimensional diaphragm actuator. Our results show that viscoelastic effects delay the onset of instability under monotonic electrical loading and can even suppress instabilities under cyclic loading. Furthermore, quantitative agreement is obtained between experimentally measured and numerically simulated instability thresholds. Our finite-element implementation will be useful as a modeling platform for further study of electromechanical instabilities and for harnessing them in design and is provided as online supplemental material to aid other researchers in the field.     

人工肌肉作动器的参数优化设计

由于电活性聚合物材料在电场作用下所表现出的许多优异的力学性能,如大应变、响应快、能量转换率高等特点,使得这种高分子智能材料引起了广泛关注,有望被加工成作动器、传感器及俘能器等能量转换器,在工程应用中发挥巨大作用。 但是,由于描述电活性聚合物材料变形的状态方程的非线性性,及其在力电载荷作用下多种失效模式的存在,使得设计电活性聚合物能量转换器面临诸多的困难。本文针对美国人工肌肉公司(Artificial Muscle Inc.)开发的一款电活性聚合物薄膜作动器的优化设计开展研究,主要研究了不同初始预拉伸对薄膜厚度、拉伸变形、应力及电场强度等的影响效应,结果表明,在某一预拉伸下,薄膜中的电场分布将趋于均匀。本文所提供的研究方法,可为此类作动器的优化设计提供基本的分析模式。