Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions

The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a "compatibility equation" is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper.     

Poly(phenylene sulfide)/low‐melting‐point metal composites. I. Transient viscoelastic properties and crystallization kinetics

Poly(phenylene sulfide)/low‐melting‐point metal composites (PPSMs) with various loading levels were prepared by melt compounding. The nonisothermal crystallization behavior and transient viscoelastic properties were characterized by the DSC, POM, DMA, and parallel‐plate rheometer. The results reveal that the low‐melting‐point metal (LMPM) particles show nice dispersion at relative low content levels (< 30 wt %). The PPSMs composites present dual characteristics of both the filled polymer composite and polymer blend system in their transient viscoelastic behaviors, which results in occurrence of the stress overshoots with long relaxation time and nonzero residual stress especially at high shear levels. During the crystallization process, the presence of those deformable LMPM droplets facilitates the crystallization kinetics of PPS because of their flow‐promoting action. On the other hand, the LMPM has no heterogeneous nucleating effect and, only plays the role of inert filler, which results in the degradation of the crystal structure of PPS. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 677–690, 2008     

A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics

Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30°C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied “osmotic stress”). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding “elastic swelling” and mechanical bulk moduli. ©1995 John Wiley & Sons, Inc.     

A stability investigation for an incompressible simple fluid with fading memory

The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the finitelinear viscoelasticity theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several results for stability and asymptotic behavior for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamical system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid.E. F. Infante's work was supported in part by the U.S. Office of Naval Research (grant N0014-76-C-0278P002), the U.S. National Science Foundation (grant MCS-76-07247 A03), and the U.S. Army Research Office (grant AROD 31-124-73-G-130); that of J. A. WALKER was supported in part by the U.S. National Science Foundation (grant ENG76-81570) and the U.S. Air Force (grant AFOSR-76-3063A).     

Well‐posedness of the upper convected Maxwell fluid in the limit of infinite Weissenberg number

An iteration scheme is used to show the well‐posedness of the initial‐boundary value problem for incompressible hypoelastic materials, which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume that the stress is a rank‐one matrix T=qq^T, q∈?ⁿ, and develop energy estimates to show that the problem is locally well‐posed. This problem is related to incompressible ideal magnetohydrodynamics (MHD). We show that the general case T=CC^T, C∈?^n×n can be handled by a generalization of the method we developed. Copyright © 2010 John Wiley & Sons, Ltd.     

分数阶粘弹性地基上薄板波动和振动特性分析

本文研究了粘弹性地基上薄板的波动和振动问题．主要讨论了基于分数导数理论的粘弹性地基模型上 薄板弯曲波的传播特性以及固有频率对地基的依赖特性．推导了三种经典粘弹性地基模型的复模量．并利用分 数导数的性质得到分数阶粘弹性地基上 Kirchhoff板中弯曲波的传播速度、衰减系数以及自由振动的复固有频 率．数值算例表明粘弹性地基对弯曲波传播特性存在显著影响,不同粘弹性模型所对应的色散和衰减特性也存 在较大差别．分数阶导数可以实现相邻整数阶导数之间的光滑过渡．利用分数导数的本构关系可以更加真实地 描述粘弹性地基的历史依赖行为,更准确地表现出粘弹性地基板中弯曲波的色散和衰减特性．     

微流道内椭圆粒子黏弹性聚焦数值模拟研究

黏弹性聚焦技术借助微尺度黏弹性流体的惯性和弹性耦合效应,能够实现生物粒子在流道中心的单一位置聚焦排列,被认为是未来生物粒子计数以及检测的理想预处理单元,因而引起了广泛的关注．自然界中的生物粒子往往是非球形的,故而研究不同形状粒子在黏弹性流体中的迁移特性具有十分重要的价值．本文通过格子玻尔兹曼方法耦合浸入边界法,对椭球粒子在直流道内黏弹性流体中的聚焦行为进行了系统的数值模拟研究．结果表明,面积相同但长径比不同的椭圆粒子在黏弹性流体中有不同的旋转周期与迁移速度．长径比更大的粒子旋转周期更长,且长径比大于3.5 的粒子甚至不再有明显的旋转．长径比更大的粒子上下两侧的黏弹性力分布更加平缓,受到指向流道中心的弹性力更小,使得粒子横向迁移速度更慢从而导致了长径比不同的椭圆粒子聚焦至流道中心所需时间的差异．此外,Weissenberg 数Wi 的增加同样能够减弱粒子的旋转,使得长径比稍小的粒子也能和长径比为1.0 的圆形粒子产生明显的分离．上述数值模拟的结论,为不同长径比粒子在黏弹性流体中的聚焦与分选应用提供了重要的理论指导．     

Gel strength and swelling of acrylamide‐protic acid superabsorbent copolymers

The viscoelastic and swelling properties of polyacrylamide‐based superabsorbent copolymers were investigated as a function of the ionic comonomer structure. Superabsorbent copolymers were synthesized by free‐radical crosslinking copolymerization of acrylamide and one of the monoprotic acids (acrylic acid and crotonic acid) or the diprotic acids (maleic acid and itaconic acid) as the investigated ionic comonomer. The reaction composition of all components, i.e. monomer, comonomer, initiator, co‐initiator, and crosslinker, was fixed to be the same for the synthesis of all four superabsorbent copolymer systems. Viscoelastic measurements were performed in all systems where the particles were closely packed. The network structures of all systems were evaluated via viscoelastic and swelling measurements. The results indicated that superabsorbent polymers (SAPs) with high water absorbency were accompanied by low gel strength and the calculated high value of molecular weight between crosslinks ($\bar {M}{}_c$ ) and low value of effective crosslinking density (ν_e). Diprotic acid‐containing SAPs showed higher water absorbency over monoprotic acid‐containing and non‐ionic ones. The differences in $\bar {M}{}_c$ and ν_e values of each system were explained with respect to the differences in the monomer reactivity ratio and hydrophilicity of the comonomers. Copyright © 2010 John Wiley & Sons, Ltd.     

The effect of electron beam irradiation on dynamic shear rheological behavior of a poly (propylene‐co‐ethylene) heterophasic copolymer

In this study the effect of electron beam irradiation on rheological properties of a poly (propylene‐co‐ethylene) heterophasic copolymer is evaluated. Using dynamic viscoelastic measurement in the linear viscoelastic range of deformation, it is observed that the complex viscosity and dynamic modulus of polypropylenes were decreased by increasing the irradiation dose. Polypropylene heterophasic copolymers consist of ethylene propylene rubber phase dispersed in polypropylene homopolymer matrix. The high energy electron beams simultaneously affect both isotactic polypropylene (iPP) matrix and ethylene propylene dispersed phase. The molecular chains of polypropylene homopolymer phase breakdown to smaller species, those are prone to degradation and branching as well. Increase in the melt flow rate behavior and shifting the cross‐over point to higher frequencies and increase in melt strength are due to this phenomenon. At the same time, the ethylene propylene phase of the polypropylene copolymer cross‐links due to irradiation, and a significant effect on the rheological behavior of samples are observed. The mathematical modeling of complex viscosity behavior revealed the conformity of experimental data with modified Carreau equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Deformation and vibration of upright loops on a foundation and of hanging loops

The deformation and vibration of vertical flexible loops are investigated theoretically and experimentally. Both upright and hanging loops are considered. Potential applications include nanorings and carbon nanotubes as force sensors or structural components. The upright tubes rest on a rigid or linearly elastic (Winkler) foundation, and cases with adhesion and nonlocal elasticity are included in the analysis. The hanging loops are suspended by a clamp with zero or finite length. The effects of self-weight, foundation stiffness, work of adhesion, and nonlocal elasticity on the loop height or depth are determined, as well as the effects of self-weight and foundation stiffness on the lowest frequency for in-plane symmetric vibration. Good agreement is attained between theoretical results (based on an inextensible-elastica model) and experimental data.