The effects of blood viscoelasticity on the pulse wave in arteries

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Predicting the nonlinear hereditary viscoelasticity of polymers

A mathematical model for the nonlinear hereditary viscoelasticity of polymer materials is proposed to predict deformation processes of various complexity — from simple relaxation and simple creep to complex deformation-relaxation and reverse relaxation processes with alternative loading and unloading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 147–157, November–December, 2007.     

On the analytic expression of the free energy in linear viscoelasticity

Two definitions of free energy for a linear viscoelastic material, due to Graffi and to Coleman and Owen, are considered, and the compatibility of these definitions with some expressions of the free energy proposed in the literature is examined. For the expressions of Staverman and Schwarzl and of Breuer and Onat, the two definitions are proved to be equivalent, and the set of all relaxation functions for which the two expressions are indeed free energies is determined. Two more expressions, proposed by Volterra and Graffi and by Morro and Vianello, are taken into consideration. For them, only the classes of relaxation functions for which they are free energies according to the first definition, is completely characterized. All results are established under regularity assumptions weaker than those usually made in the literature.     

颗粒在黏弹性流体扩张和收缩流中沉降的格子Boltzmann模拟分析

对于Oldroyd-B型黏弹性流体,本文应用格子Boltzmann方法(LBM),实现了流体在二维1:3扩张流道及3:1收缩流道中流动的数值模拟,获得了黏弹性流体在扩张和收缩流道中的流场分布．结合颗粒的受力和运动规则,基于点源颗粒模型,数值分析了颗粒在扩张流和收缩流中的沉降过程和特征,讨论了颗粒相对质量和起始位置以及雷诺数Re和威森伯格数Wi对颗粒沉降特征的影响．结果表明,颗粒相对质量和起始位置以及Re对颗粒沉降轨迹和落点影响较大,而Wi的影响则较小．     

Stability of viscoelastic shear flows in the limit of high Weissenberg and Reynolds numbers

We consider a limit of the upper convected Maxwell model where both the Weissenberg and Reynolds numbers are large. The limiting equations have a status analogous to that of the Euler equations for the high Reynolds number limit. These equations admit parallel shear flows with an arbitrary profile of velocity and normal stress. We consider the stability of these flows. An extension of Howard’s semicircle theorem can be used to show that the flow is stabilized if elastic effects are sufficiently strong. We also show how to analyze the long wave limit in a fashion similar to the inviscid case.     

An alternative approach to the linear theory of viscoelasticity and some characteristic effects being distinctive of the type of material

In the introduction some postulates on which the linear theory of viscoelasticity is based are recalled, and the postulate of passivity is substituted by a stronger postulate called detailed passivity.Next, a symmetric formulation of this theory is presented which is founded in a well-balanced way on the limiting properties of elasticity and viscosity. This leads to the introduction of the basic functions of creep compliance J ⁺(t) and stressing viscosity ⁺(t) associated to one another, whereas the basic functions retardation fluidity ⁺(t) and relaxation modulus G ⁺(t) emerge as their time derivatives. Correspondingly, four complex basic functions are defined as their Carson transforms.In addition to the proper retardation and relaxation terms, these basic functions contain the non-disappearing constants of either instantaneous compliance J ₀ or instantaneous viscosity ₀ and also of either ultimate fluidity or ultimate modulus G . Therefrom ensues a classification of linear viscoelastic materials into four types: instantaneous elasticity or viscosity is allowed to combine with ultimate viscosity or elasticity. The latter alternative, signifying fluidlike or solidlike materials, leads, of course, to a quite different behavior in many situations; however, remarkable distinctive features are associated to the first one as well.A few respective examples are outlined: 1) propagation of shear waves in a half-space with periodic and step-shaped excitation, 2) dissipation of work in a torsional vibration damper, and 3) shear flow between two parallel porous plates with injection and suction.Finally, materials with viscous initial behavior are defended against the notion that they be of no or almost no real significance.Delivered as a Plenary Lecture at the Fourth European Rheology Conference, Seville (Spain), 4–9 September 1994. The herein only outlined topics are taken from a recently pulished monograph (Geisekus, 1994) in which complete derivations of the results and more detailed discussions are given.Dedicated to Professor K. Walters on the occasion of his 60th birthday.     

On the solutions in the linear theory of micropolar viscoelasticity

In the present paper the linear theory of micropolar viscoelasticity is considered. The explicit expression of fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The Green's formulas in the considered theory are obtained. The formulas of integral representations of Somigliana-type of regular vector and regular (classical) solution are presented. The representation formulas of Galerkin-type solution of the system of nonhomogeneous equations and of the general solution of the system of homogeneous equations by means of eight metaharmonic functions are presented. The completeness of these solutions is proved.     

Back to the thermodynamic admissibility of creep-relaxation functions in linear viscoelasticity

The recent discussion on admissibility criteria for the kernels of linear viscoelastic liquids is completed by the results for viscoelastic solids. The necessary and sufficient conditions of thermodynamic admissibility are established. The class of thermodynamically admissible creep-relaxation functions is proved to be wider than it is usually supposed, including as well numerous nonmonotone and even locally negative functions. These nontraditional viscoelasticity kernels find applications in physics of heterogeneous materials, like for instance in mechanics and theology of composites.     

On the basic laws of anisotropic viscoelasticity

The main aim of this work is to develop a consistent formulation of the rheological behavior for different anisotropic polymer systems. The unified theory of anisotropic viscoelasticity is developed based on the symmetry principles. The Maxwell rheological equation is extended to nonsymmetric anisotropic liquids. Transitions from the most general anisotropy to particular cases of anisotropy are established. It appears that the coupled relaxation of symmetric and antisymmetric stresses is a natural phenomenon in nonsymmetric viscoelasticity. Within the concept of an internal state variable, a stress–order relation is derived for a fully nonlinear case. The order tensor dynamics is also considered. A simple method of deriving the equation of the internal rotational motion is developed for the general macroscopic anisotropy. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece     

The mirror relations and nonlinear viscoelasticity of polymer melts

An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS ₁₂ () = – a ( – 1) (a = 0 for 1,a = 1 for 1) for the mirroring of the viscosities,S ₁₂ () = – a (–k ²/) (a = 0 for k, a = 1 for k) for the mirroring of the first normal-stress coefficients, and for the third relation. Here denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.     

Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

Due to the increasing use of passive absorbers to control unwanted vibrations,many studies have been done on energy absorbers ideally, but the lack of studies of real environmental conditions on these absorbers is felt. The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink(NES). In this paper, the Burgers model is assumed for the viscoelasticity in an NES, and a linear oscillator system is considered for inve...     

A physically-based,quasilinear viscoelasticity model for the dynamic response of polyurea

Polyurea, a promising material for damage mitigation in impact scenarios, has been investigated through plane-wave, pressure-shear plate impact (PSPI) experiments to obtain its mechanical response at high pressures and high strain rates. Based on these experimental results, a physically-based, quasi-linear, viscoelasticity model is introduced to capture the observed nonlinear pressure-volume behavior, the strong dependence of shearing resistance on pressure, and the strong relaxation of deviatoric stresses. This model has been implemented in finite element software ABAQUS to simulate the response of polyurea P1000 under the impact conditions of a variety of PSPI experiments. Simulation results agree reasonably well with those of the experiments.     

On the simulation of the transient temperature field or some viscoelasticity problems by structural analysis program

An idea is presented to solve the parabolic differential equation by the hyperbolic differential equation. We can simulate and compute the transient temperature field problems by a structural analysis program. Using only a single structural analysis program, the users can compute both temperature and thermal stress distributions on the same finite element mesh. The method thus extends the application of the structural analysis programs which have been implemented widely. As an example, the transient temperature field problem of a square plate is computed. The result is consistent with the theoretical result. A similar method for simulating some viscoelasticity problems of Kelvin model is also presented.     

黏弹性流体扩展及收缩流动的格子Boltzmann模拟分析

本文应用格子Boltzmann 方法(LBM)并结合Oldroyd-B 模型,讨论了不可压缩的 Navier-Stokes 方程和平流扩散本构方程的解耦及各自求解方法,以及两类问题的边界处理格式,实现了黏弹性流体在二维1:3 扩展流道以及3:1 收缩流道中的流动的数值模拟．获得了不同雷诺数Re 和维森伯格数Wi 以及黏度vs 下流动的流线分布,计算给出了漩涡的涡心位置和大小,并分析了参数Re、Wi 和vs 对流动特点的影响．模拟结果表明本文所采用模型和边界处理方法具有良好的精度和稳定性．     

A fundamental relationship between the relaxation spectra and the tangent distribution function in the theory of linear viscoelasticity

The tangent distribution function (TDF) is analyzed within the theory of linear viscoelasticity on mechanical properties. A proof is given that both the relaxation and retardation spectra can be derived from the TDF, through a Fredholm integral equation. Furthermore, the relaxation strength can be calculated as a consequence of this relationship. Finally, as an example, the relationship is applied to discrete spectra.     

Inertia effects of the fluid and cylinder in coaxial cylindrical rheometer

The inertias of the fluid and the inner cylinder in coaxial cylinder rheometer (CACR) have great influence on the unsteady flow of non-Newtonian fluid. Even for the Newtonian fluid there exist the so called “stress overshoot” phenomenon. In the present article this phenomenon was studied in detail and a method correcting the measured results for an unsteady flow in the rheometer was proposed. It is found that the inertia effect of the fluid can be ignored when the gap between cylinders is small. The project was supported by the Youth Foundation of the Fourth Military Medical University     

Linear viscoelasticity,simple and planar melt extension of linear polybutadienes with bimodal molar mass distributions

Shear oscillations, simple and planar elongations have been performed with anionically polymerized polybutadienes (PB) and their blends at room temperature. The PB components were of different molar mass averages and of narrow molar mass distributions; the blends had bimodal molar mass distributions and are represented by the weight ratio w of the high molecular component. The crossover G() = G() obtained from oscillatory measurements shows correlations with molecular parameters. For the zero shear viscosity the well-known relation ₀ M _w ^3.4 is found. The recoverable equilibrium shear compliance J _e ⁰ is nearly the same for the components; for the blends it strongly depends on w with a pronounced maximum at small w. In elongation outside the linear region strain hardening is found; its magnitude depends on M _w of the components, the composition w of the blend, the mode of elongation (simple or planar), and the elongational strain rate. The hardening revealed in the increase of the elongational viscosity above the linear viscoelastic limit increases as a function of w up to a maximum similar to J _e ⁰ such that, for both properties, the molecular processes may be the same. The elongational viscosity µ₂ (from the lateral stress in planar elongation) is above the linear viscoelastic limit for bimodal and below this limit for conventional broad molar mass distributions. In general, it can be stated that with a more narrow molar mass distribution of linear polymers the elongational behavior of the melts comes closer to the linear viscoelastic limit.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.Extended version of a paper presented at the Annual Conf. German Soc. of Rheology, Berlin, May 13–15, 1991.     

Finite viscoelasticity of filled rubbers: the effects of pre-loading and thermal recovery

Received October 17, 2001 / Published online February 28, 2002