丙烯酸弹性体的率相关分数阶黏弹性模型研究

丙烯酸弹性体VHB 4910作为一种重要的介电弹性体,在软体机器人、致动器、俘能器和智能隔振器等领域有很好的应用前景.但材料的非线性黏弹性对其力学行为有显著影响.近来分数阶模型在复杂材料的建模中取得了成功.本文基于分数阶有限变形Kelvin-Voigt流变学模型建立弹性体的三维张量本构,并进一步推导单向拉伸情况下的本构...     

A constitutive model of polyacrylate interpenetrating polymer networks for dielectric elastomers

A physically based method is proposed to represent interpenetrating polymer networks and their electromechanical behavior. The mechanical behavior of the material is nonlinear elastic and the electromechanical coupling arises from electrostatic effects often called the Maxwell stress effect. Ha et al. have synthesized interpenetrating polymer networks (IPNs) that invalidate the need for an external pre-stretch mechanism in dielectric elastomers. IPNs of acrylic elastomer and 1, 6-hexanediol diacrylate were successfully synthesized to create free-standing films with preserved prestretch. This results in a dual polymer network, with one polymer network in tension and the other in compression. The prestretch is preserved chemically in the dominant network. The internal prestretch is accompanied by an overall stiffening of the dual polymer network leading to compromised actuation strains. A mechanistically simple representation of the networks is proposed by means of a model of two springs in parallel, replaced by an equivalent single spring. A material parameter is introduced to account for the effect of the weight percent of the secondary network. The effect of the additive on the preserved prestretch in the primary network and hence the overall stress strain response is determined. Specifically, a modified Ogden strain energy function is proposed that describes the mechanical behavior of the new interpenetrating polymer network. The electromechanical response of the material is described using a previously presented constitutive formulation that works well for single network polymers. The model results indicate that ideally an interpenetrating polymer network DE should not stiffen when the secondary network is formed to avoid reduced actuation strains.     

介电弹性材料的机电耦合性能研究

作为一种新型的电活性聚合物,介电弹性材料可被用作柔性致动器。其中材料的介电性能和机械性能是影响其机电耦合致动性能的关键因素。通过实验方法研究了一种典型的介电弹性材料VHB4910在不同温度和频率下的介电常数和弹性模量,基于实验结果分析了该材料的机电耦合性能。结果表明:依赖于频率和温度的弹性模量是影响该介电弹性材料致动变形的主要因素,对致动性能的影响最大可达4个数量级,材料的介电常数对其致动性能的影响相对较小。     

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.     

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。     

On the Correlation of FEM and Experiments for Hyperelastic Elastomers

Correlation of modern finite element methods (FEM) with advanced experimental techniques for elastomers, biomedical materials, and living organs requires study and modification of the behavior of these materials. In this study, the mechanical behavior of a commonly-used elastomer, silicone rubber, which provides excellent biocompatibility, was examined under different applied loading configurations, and large deformations were investigated through both experiment and simulation. The stress-strain behaviors of silicone rubber were tested, using multiple homogeneous experiments, including uniaxial extension and equibiaxial tension, the load-apex displacement response, and digitized deformed shapes of two of the most-used structures for nonlinear hyperelasticity—the inflation of a clamped circular membrane, and indentation of the membrane by a spherical indenter. Uniaxial and equibiaxial data were evaluated simultaneously, characterized by various constitutive models for implementation in the FE simulation. These constitutive models examined the prediction of the FE simulations for the inflation and indentation tests in comparison to the results of experiments at various load-apex displacement levels. The results showed that the constitutive models calibrated with the uniaxial and equibiaxial tests, predicted nearly the same results as the actual experimental results, particularly for the applied loads that generated moderate strain. However, when the FE simulations based on the constitutive models were adjusted, employing only uniaxial or equibiaxial tests, they predicted different results, where the degree of their correlations with experimental results was incomplete or in some states simply poor. The simulations suggested that the inverse FE procedure should not be restricted to the choice of material models, while more attention should be given to the choice of ranges of deformation.     

Experimental slowing of flexural waves in dielectric elastomer films by voltage

Shape and physical properties of dielectric elastomers are changeable by voltage. Theoretical works show that these changes can be harnessed to tune the propagation of superposed elastic waves. We experimentally demonstrate this concept by manipulating waves in a dielectric elastomer film, focusing on the flexural mode at low frequencies. To this end, we design an experimental apparatus to pre-stretch, actuate, excite waves at low frequencies in a VHB™ 4910 film, and measure the velocity of the fundamental flexural mode. Our results show that the excited wave velocity is slowed down by the applied voltage, and provide experimental proof of concept for the application of deformable dielectrics as tunable waveguides.     

聚氯乙烯弹性体静动态力学性能及本构模型

为揭示聚氯乙烯弹性体在静、动态载荷下的力学性能,采用万能材料试验机和改进的分离式霍普金森压杆实验装置获得了材料在应变率为0.001、0.01、0.1、1 510、2 260和3 000 s?1下的应力应变曲线,并以屈服强度为整形器优选参数,对比了紫铜、铜版纸和铅等3种整形器材料的整形效果。使用修正的ZWT非线性黏弹性本构模型描述聚氯乙烯弹性体在静、动态载荷下的力学性能。结果表明:聚氯乙烯弹性体在静态载荷下具有应变率效应和显著的超弹性特性,动态载荷下表现出较明显的应变率效应和较强的抗变形能力,且静动态载荷下的力学行为受应变历史影响较大。3种整形器材料中铜版纸的整形效果最好。修正后的ZWT非线性黏弹性本构模型能够得到统一参数的本构表达式,且各应变率下的拟合结果与实验结果具有较好的一致性。     

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.     

预应力对LY12铝层裂强度的影响

通过过盈配合的热装配方法和机械夹紧方法对LY12铝合金平面样品施加了径向预应变,采用平面飞片撞击方法获得了预应力对层裂特性的影响。结果表明:当飞片以500 m/s的速度撞击样品,预应变为0（无预应变）、25110-6、1 10810-6、1 88610-6时,层裂强度分别为1.130、0.935、0.755、0.643 GPa,初始预应力（变）明显降低了LY12铝层裂强度,证实了材料的层裂强度与初始应力状态密切相关,可为以后的非一维平面应变下的层裂研究提供参考。     

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.     

预应变对中子辐照高纯铝拉伸性能的影响

金属材料的中子辐照硬化和脆化一直都是核能安全领域十分关注的重要问题之一. 为了进一步认识预应变对中子辐照金属材料塑性形变和最终断裂特性的影响规律, 及其微观机理, 本文研究了10%拉伸预应变高纯铝的拉伸应力-应变曲线、失稳应力和失稳应变等随辐照剂量的变化规律. 结果表明, 辐照剂量越高, 预应变高纯铝内部孔洞的尺寸和数密度越高, 导致屈服强度和极限拉伸强度越高, 均匀延伸率和失稳应变越小, 表现出典型的辐照硬化和脆化效应, 但失稳应力与辐照剂量几乎无关. 相同辐照剂量条件下, 预应变引入的高密度位错能够显著降低辐照孔洞的尺寸和数密度, 加之辐照退火效应的综合影响, 导致预应变能够降低高纯铝屈服强度的增长率和失稳应变的下降率, 从而表现出一定的抑制辐照硬化和脆化的能力, 预应变还能够提高高纯铝的失稳应力, 但整体而言预应变并不能提高高纯铝的延性. 最后, 基于J-C本构模型的中子辐照退火态金属材料的脆化模型能够直接应用于预应变金属材料, 且模型预测结果与实验结果吻合较好.      

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

Fatigue Life Estimation for an NBR Rubber and an Expanded Polyurethane

In this paper, we deal with the mechanical behavior of elastomeric materials subjected to high cyclic loading in cases of high strain. First, a methodology for material parameter identification is used for a constitutive visco-hyperelastic law with discontinuous damage, modeling the Mullins effect. Then a fatigue model characterized by a strain energy density-based criterion is proposed and implemented in the finite element code, Code-Aster [1]. Two kinds of elastomer are considered, an incompressible rubber and an expanded compressible polyurethane. Cyclic tensile tests were performed to identify material fatigue parameters. Finally, a numerical application using a finite element model is presented. This model is a plate perforated by a ?6 mm hole for the first sample and a ?10 mm hole for the second one. The results obtained from the finite element model are compared to experimental results.     

预应变对中碳钢扭转疲劳特性的影响

应用扭转疲劳试验机对退火后的非预应变45#钢及其3种预应变材料进行 实验. 实验结果表明：预应变量小于5%时,与非预应变材料相比疲劳极限降低10\%; 预应变量大于5{%}时,随着预应变量的增加,其疲劳极限有恢复的趋势,当预应变量达到 8%时,预应变材料与非预应变材料的疲劳极限几乎相等;当循环应力达到1*10^7$时,各种试件表面都有明显的停留裂纹存在.     

Constitutive relation of viscoelastic dielectric elastomer

In this paper, we present a modified model describing the constitutive relation of viscoelastic 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.     

Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials

Elastomeric materials experience stretch-induced softening as evidenced by a pre-stretched material exhibiting a significantly more compliant response than that of the virgin material. In this paper, we propose a fully three-dimensional constitutive model for the observed softening of the stress-strain behavior. The model adopts the Mullins and Tobin concept of an evolution in the underlying hard and soft domain microstructure whereby the effective volume fraction of the soft domain increases with stretch. The concept of amplified strain is then utilized in a mapping of the macroscopic deformation to the deformation experienced by the soft domain. The strain energy density function of the material is then determined from the strain energy of the soft domain and thus evolves as the volume fraction of soft domain evolves with deformation. Comparisons of model results for cyclic simple extension with the experimental data of Mullins and Tobin show the efficacy of the model and suggest that an evolution in the underlying soft/hard domain microstructure of the elastomer captures the fundamental features of stretch-induced softening. Model simulations of the cyclic stress-strain behavior and corresponding evolution in structure with strain for uniaxial tension, biaxial tension and plane strain tension are also presented and demonstrate three-dimensional features of the constitutive model.     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

Contribution of Kinematical and Thermal Full-field Measurements for Mechanical Properties Identification: Application to High Cycle Fatigue of Steels

The purpose of this work is to extend the use of unconventional tests and full field measurements (kinematical and thermal) to the identification of the effect of a wide plastic pre-strain range on the high cycle fatigue properties of a dual-phase steel. An unconventional specimen is designed. The geometry of this specimen permits a constant gradient of pre-strain to be obtained after a monotonic tensile test. Then, a self-heating test under cyclic loading is carried out on the pre-strained specimen. During this cyclic test, the thermal field is measured using an infrared camera. Finally, a suitable numerical strategy is proposed to identify a given thermal source model taking into account the influence of plastic pre-strain. The results show that, with the unconventional test and the procedure developed in this work, the influence of a plastic pre-strain range on fatigue properties can be identified by using only one specimen when, for a classical fatigue campaign, a great number of specimens is required.