Nonlinear viscoelastic properties of MR fluids under large-amplitude-oscillatory-shear

Nonlinear viscoelastic properties of the MR fluid, MRF-132LD, under large-amplitude oscillatory shear were investigated. This was accomplished by carrying out the experiments under the amplitude sweep mode and the frequency sweep mode, using a rheometer with parallel-plate geometry. Investigations under the influence of various magnetic field strength and temperatures were also conducted. MR fluids behave as nonlinear viscoelastic or viscoplastic materials when they are subjected to large-amplitude shear, where the storage modulus decreases rapidly with increasing strain amplitude. Hence, MR fluid behaviour ranges from predominantly elastic at small strain amplitudes to viscous at high strain amplitudes. Large-amplitude oscillatory shear measurements with frequency sweep mode reveal that the storage modulus is independent of oscillation frequency and approaches plateau values at low frequencies. With increasing frequency, the storage modulus shows a decreasing trend before increasing again. This trend may be explained by micro-structural variation. In addition, the storage modulus increases gradually with increasing field strength but it shows a slightly decreasing trend with temperature.     

Thermoreversible gels in oil/EVA systems

In this work we investigate the gel formation of EVA/recycled motor oil systems as a route to obtain synthetic binders which could be used instead of natural bitumen, as well as mixed with natural bitumen to modify adequately its viscoelastic response. The EVA copolymer studied in this work has a vinyl acetate content of 18 wt% and solutions of EVA/motor oil have been prepared up to a concentration of 50 wt%. Dynamic viscoelastic frequency sweeps between 10⁻² Hz and 10² Hz have shown that above 3 wt%, at 25 °C, EVA/motor oil systems form gels. It has been possible to define an elastic equilibrium modulus, G_e, for each gel. The dependence of G_e on concentration has been compared with that of PVC/DOP and SBS/oil gels on the basis of the De Gennes model. Thermal stability of EVA/motor oil gels has also been analyzed, indicating that for the highest polymer concentrations gel point is above 80 °C. Received: 23 December 1999 Accepted: 13 June 2000     

APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR DYNAMIC CALCULATION OF VISCOELASTIC LAYERED PERIODIC PLATE

由于周期性隔振结构动力计算中较少考虑轨道交通载荷及材料黏弹性,因此,本文以黏弹性层状周期板为研究对象,提出了垂向移动简谐载荷下,可以考虑材料黏弹性及板内横向剪切变形的黏弹性层状周期板动力计算近似理论并给出解析解答.设板中性面的横向剪切变形为横截面的整体剪切变形,利用Reissner-Mindlin假设及提出的剪切变形补充计算条件,得到了中性面法线转角与中性面剪应力的关系.基于平衡方程和应力连续条件,建立了黏弹性层状周期板振动控制方程,推导了对边简支对边自由条件下,板垂向位移的简化Fourier级数形式解.与经典层合板模型和有限元计算结果进行了比较,验证了本文解答的有效性.结果表明：（1）黏弹性层状周期板可以显著降低单一材料板在自振频率处的振动响应,但会引起局部低频频段的振动放大;（2）板的垂向位移随着载荷速度的增大而增大,当载荷速度超过300 km/h后,其对板振动响应的影响减弱;（3）黏弹性层剪切模量存在最佳设计值,可使结构的隔振性能最佳;（4）黏弹性层的阻尼特性在低频范围内对结构振动影响较小;（5）可在满足工程实际的情况下适当增加板长,以提高结构的隔振性能.     

Hydroelastic analysis of very large floating structure over viscoelastic bed

Effect of viscoelastic bed on the hydroelastic response analysis of very large floating structures is studied using the linear water wave theory and small amplitude structural response in finite water depth. The floating structure is modeled using Euler–Bernoulli beam equation and the bottom bed is assumed to be viscoelastic in nature and is based on the Voigt’s model. The dispersion relation, phase speed and response amplitude of the floating structure as well as viscoelastic bed surface, pressure distribution along water depth are analyzed to study the effect of viscoelastic bed parameters, flexural rigidity of the floating structure, time period on flexural gravity wave motion. The study reveals that structural response of the floating structure can be mitigated for moderate thickness of the viscoelastic layer. Moreover, both shear modulus and viscosity of the viscoelastic layer play dominant role in reducing the structural response compared to the flexural rigidity of the structure. Further, pressure distribution within the viscoelastic bed decreases at a higher rate compared to the inviscid fluid layer irrespective of shear modulus and viscosity. The present study will be of immense help in the site selection of very large floating structures in the coastal water and installation of various marine facilities over muddy bed.     

Viscoelastic response

It is shown that presentation of viscoelastic data in the modulus/frequency form is dominated by the interaction between the infinite frequency compliance and the viscosity. Therefore this form of presentation is insufficient to allow evaluation of the differences in behaviour between viscoelastic materials.     

Isothermal viscoelastic properties of PMMA and LDPE over 11 decades of frequency and time: a test of time–temperature superposition

Many instruments used to measure viscoelastic properties are only capable of subjecting a sample to a limited range of loading frequencies. For thermorheologically simple materials, it is assumed that a change in temperature is equivalent to a shift of the viscoelastic behavior on the log frequency or time axis. For many materials, time–temperature superposition appears to work well for modulus or compliance curves over three decades of time or frequency, but some deviations are known if the window is expanded to five or six decades. To apply a more stringent test of the validity of time–temperature superposition, broadband viscoelastic spectroscopy is used to isothermally study polymethylmethacrylate and low-density polyethylene at several temperatures in the glassy region. Shear modulus and damping (tan δ) are measured isothermally over a wide range (up to 11 decades) of time and frequency. Results indicate that, while modulus curves can be approximately superimposed, the damping (tan δ) curves change in height and shape with temperature.     

Relations Between Relaxation Modulus and Creep Compliance in Anisotropic Linear Viscoelasticity

The results obtained previously for scalar and class P completely monotone relaxation moduli are extended to arbitrary anisotropy. It is shown for general anisotropic viscoelastic media that, if the relaxation modulus is a locally integrable completely monotone function, then the creep compliance is a Bernstein function and conversely. The elastic and equilibrium limits of the two material functions are related to each other. The relaxation modulus or its derivative can be singular at 0. A rigorous general formulation of the relaxation spectrum in an anisotropic viscoelastic medium is given. The effect of Newtonian viscosity on creep compliance is examined. Put some makeup on him and lay him to rest. Anonymous     

Comparison between the dynamic moduli of fully non-linear and quasilinear viscoelastic materials

This paper deals with the non-linear viscoelastic model with multiple hereditary integrals (MHI) in the frequency domain and the conditions that it reduces to single hereditary integral or the quasilinear viscoelastic (QLV) model. It is shown that when the higher order complex moduli are related to the first-order modulus as the MHI model reduces to the QLV model. The coefficients of quasilinearity should be real and independent of amplitude and frequency.     

Dependency of observation parameters on soil dynamic parameters in unconfined impact compression tests

Unconfined impact compression tests were used to measure dynamic parameters of soil samples in the domains of stress wave propagation and dynamic deformation. The high-frequency equivalent Young's modulus, which was determined by the reflection theory of one-dimensional elastic stress waves, increased exponentially with water content. The low-frequency equivalent Young's modulus, which was defined as the initial gradient of a stress-strain curve, decreased exponentially with increasing water content. The high-frequency equivalent Young's modulus was one to two orders of magnitude larger than the low-frequency one. Water content, height of soil samples and drop height affected the dynamic stress-strain relationships of the soil samples. The Maxwell's viscoelastic fluid model described the stress-strain relationships well, and the values of the model parameters varied with water content and frequency.     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

Effects of fluctuations of cross-linking points on viscoelastic properties of associating polymer networks

We study the effects of fluctuations of cross-linking points, or junctions, on the dynamic mechanical and viscoelastic properties of polymer networks formed by multisticker associating polymers on the basis of a single-chain approach. Fluctuations of junctions are implemented by introducing virtual springs. We consider two possible cases for the treatment of virtual springs: the direct contribution from virtual springs is either neglected or included in the stress. We show that, if neglected, the fluctuation of junctions decreases (or softens) the dynamic modulus over a wide range of frequencies. This result agrees qualitatively with the result of several multichain models that predicts the decrease of the static or plateau modulus. We also show that the fluctuation accelerates the associative Rouse mode at low frequencies originating from the association/dissociation process of stickers. These results are apparently reasonable, but it is expected that there are some errors arising from thermodynamical inconsistency due to the neglect of virtual-spring contribution from the total stress against the virtual work principle and the second law of thermodynamics. On the other hand, if the direct contribution from the virtual springs is included in the stress, thermodynamics is satisfied but the plateau modulus does not change, contrary to the multichain prediction. The softening occurs only at the low-frequency regime. Thus, each method has both merits and demerits, and hence the treatment of junction fluctuations in the framework of single-chain approaches requires care and further investigation.     

Memory decay rates of viscoelastic solids: not too slow, but not too fast either

Fading memory is a distinguishing characteristic of viscoelastic solids. Its assessment is often achieved by measuring the stress due to harmonic strain histories at different frequencies: from the experimental point of view, the storage and loss moduli are, hence, introduced. On the other side, the mathematical modeling of viscoelastic materials is usually based on the consideration of a kernel function whose decay rate is sufficiently fast. For several different solid materials, we have collated experimental evidence showing an high sensitivity to frequency variations of both the storage and loss moduli. By contrast, we prove that the commonly employed viscoelastic kernels (Prony series, continuous kernel, etc.) cannot reproduce this experimental behavior, as the resulting frequency sensitivity of the storage modulus is always zero when assessed at low frequency. This leads to identification problems of the material parameters which are strongly ill conditioned. However, we identify the specific kernel property which is responsible for this misbehavior: the long-term material memory must not decrease too fast. Some viscoelastic kernels, showing the correct memory??s rate of decay, are introduced and their improved ability to match the experimental data analyzed.     

正常及骨关节炎软骨细胞黏弹性研究

采用前交叉韧带切断术造骨关节炎(OA)动物模型，并采用微管吸吮技术和标准线性 黏弹性固体模型研究正常及OA软骨细胞的黏弹性特性. 实验研究表明：OA软骨明显退变， 大体评分及Mankin's评分均明显高于正常软骨. 正常软骨细胞直径与OA软骨细胞直径的差异无显 著意义，而正常软骨细胞与OA软骨细胞的黏弹性特性存在明显差异，正常软骨 细胞的平衡模量E , 瞬间模量E0及表观黏性 明显高于OA软骨细胞. 除正常软骨细胞平衡模量E 仅与细胞直径有微弱 相关性且具有统计学意义外，其余黏弹性参数均与细胞直径以及其 直径和微管直径比率无相关性.     

Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure

A new technique is presented to measure the frequency dependent complex modulus simultaneously at several frequencies instead of consecutively as in a frequency sweep. For this purpose, the strain in a dynamical mechanical experiment is prescribed as a superposition of several different modes (three in our case). The resulting stress is decomposed into sinusoidal components, each of them characterized by their frequency, amplitude, and phase shift with respect to the corresponding strain component. Phase shift and amplitude are expressible in a frequency dependent complex modulus. A single experiment gives, therefore, values for the complex modulus at a set of prescribed frequencies. The method was demonstrated on three stable viscoelastic fluids and was applied to determine the instant of sol-gel transition (gel point) of a crosslinking polymer.     

Viscoelastic measurement of complex fluids using forced oscillating torsion resonator with continuously varying frequency capability

Traditional torsional resonators, often obtaining the viscoelastic moduli of complex fluids only at one or several given discrete frequencies, lack the continuously varying frequency capability. This is an obvious disadvantage of the traditional torsional resonator technique. This paper presents an improved strategy, based on our previous discrete-frequency-measuring method (Wang et al., J Rheol 52:999–1011, 2008), to overcome such restriction and thus accomplish the continuously varying frequency capability of the traditional torsional resonator for measuring the viscoelastic properties of complex fluids. The feasibility of this strategy is demonstrated with the Newtonian fluids (several water–glycerol solutions) of viscosities varying from 10 to 1,400 cp by using our homemade torsion resonator apparatus in the 10 ~ 2,500 rad/s frequency range (continuous frequencies). Some results for typical viscoelastic polymers (two polyethylene oxide (PEO) aqueous solutions) are also given. Additionally, a comparison of the PEO results is made with the common rheometer technique. It is demonstrated that this improved strategy could enable the traditional torsional resonators, with one oscillating resonance mode, to work as the microrheological technique and the common rheometer technique in the continuous frequency range.     

The effects of age on viscoelasticity and deformation recovery of articular chondrocytes

本文旨在表征年龄对软骨细胞在自然生长过程中的黏弹性和恢复变形能力的影响. 结果表明：年龄对软骨细胞黏弹性及其恢复变形能力产生显著影响，老年组软骨细胞各 项黏弹性参数值均明显高于幼年和中年组软骨细胞(p<0.0001), 而后两组无显著差异 (p>0.05); 老年组软骨细胞蠕变达到平衡态所需时间t_E显著小于幼年和中年组 (p<0.05), 而幼年和中年组无显著差异(p>0.05). 老年组软骨细胞最大蠕变位移 L_M显著大于幼年和中年组(p<0.005), 而幼年和中年组无显著差异(p>0.05). 老年组软骨细胞恢复变形时间t_R显著大于幼年和中年组(p<0.005), 而幼年和中年组 无显著差异(p>0.05). 恢复变形前8s的分析发现，幼年组软骨细胞恢复变形率K_y 显著高于中年和老年组(p<0.005), 而中年组(K_a)和老年组(K_o)软骨细胞 的恢复变形率无显著差异(p>0.05); 此外, 实验发现老年组软骨细胞的残余变形L_R 比幼年和中年组显著增大(p<0.005), 而后两组无显著差异(p>0.05). 研究工作对 于软骨组织工程、软骨细胞与支架材料相互作用以及探讨OA发生过程中的力学生物学机制具 有理论意义.     

Tensorial generalized Stokes–Einstein relation for anisotropic probe microrheology

In thermal “passive” microrheology, the random Brownian motion of anisotropically shaped probe particles embedded within an isotropic viscoelastic material can be used to extract the material’s frequency-dependent linear viscoelastic modulus. We unite the existing theoretical frameworks for separately treating translational and rotational probe motion in a viscoelastic material by extending the generalized Stokes–Einstein relation (GSER) into a tensorial form that reflects simultaneous equilibrium translational and rotational fluctuations of one or more anisotropic probe particles experiencing viscoelastic drag. The tensorial GSER provides a formal basis for interpreting the complex Brownian motion of anisotropic probes in a viscoelastic material. Based on known hydrodynamic calculations of the Stokes mobility of highly symmetric shapes in a simple viscous liquid, we show simple examples of the tensorial GSER for spheroids and half-stick, half-slip Janus spheres.     

用振动梁方法测量粘弹性材料的复模量和粘弹性参数

本文利用共振梁方法,通过对一点响应、相位滞后和共振频率的测量,可以获得粘弹性材料的复模量以及标准线性固体模型的三个参数,即松弛模量、松弛系数和蠕变系数.实验结果表明,实验原理正确,测试系统可靠而且简单实用.     

Linear viscoelastic behavior of bidisperse polystyrene blends: experiments and slip-link predictions

The linear viscoelastic behavior of three well-entangled linear monodisperse polystyrene melts and their blends is investigated. The monodisperse melts are blended in a 1:1 weight ratio to obtain three polystyrene bidisperse blends for which the linear viscoelastic behavior is also measured. Special attention is paid to controlling sample size and solvent content, and checking for consistency in the high-frequency regime. We also attempt to estimate uncertainty quantitatively. The experimental results agree well with the discrete slip-link model, a robust mesoscopic theory that has been successful in predicting the rheology of flexible entangled polymer liquids and gels. Using recently developed analytic expressions for the relaxation modulus, predictions of the monodisperse samples are made. The parameters for the model are obtained from the low-frequency crossover of one experiment. Using this parameter set without adjustment, predictions over the fully accessible experimental frequency range are obtained for the monodisperse samples and their blends with very good agreement.     

黏弹性阻尼作用下轴向运动Timoshenko梁振动特性的研究

黏弹性阻尼一直是轴向运动系统的研究热点之一.以往研究轴向运动系统大都没有考虑黏弹性阻尼的影响.但在工程实际中, 存在黏弹性阻尼的轴向运动体系更为普遍.本文研究了黏弹性阻尼作用下轴向运动Timoshenko梁的振动特性.首先, 采用广义Hamilton原理给出了轴向运动黏弹性Timoshenko梁的动力学方程组和相应的简支边界条件.其次, 应用直接多尺度法得到了轴速和相关参数的对应关系, 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似解析解.最后, 采用微分求积法分析了在有无黏弹性作用下前两阶固有频率和衰减系数随轴速的变化; 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似数值解, 验证了近似解析解的有效性.结果表明: 随着轴速的增大, 梁的固有频率逐渐减小.梁的固有频率和衰减系数随着黏弹性系数的增大而逐渐减小, 其中衰减系数与黏弹性系数成正比关系, 黏弹性系数对第一阶衰减系数和固有频率的影响很小, 对第二阶衰减系数和固有频率的影响较大.