Fractional complex modulus manifested in asphalts

In recent years, a considerable effort has been made to develop a new generation of asphaltic materials based on a combination of polymers and asphalts. Regular and polymer-modified asphalts are studied via fractional relaxation processes, represented here by a fractional rational form of the complex modulus, G ^*. Basic properties of this complex modulus and the forms of generated constitutive equations are studied. Relaxation times of the model are related via a pseudospectrum to the phase angle lag.     

Linear viscoelastic behavior of the Hookean dumbbell with internal viscosity

The linear viscoelastic modulus G(t) predicted by the analytical formulations of Schieber (1993), Wedgewood (1993), Dasbach et al. (1992), and Booij and van Wiechen (1970) for the free-draining Hookean dumbbell with internal viscosity (IV) are compared with exact analytical results and exact numerical results obtained from Brownian dynamics simulations. All of these analytical formulations employ the Booij and van Wiechen expression for the IV force, thereby eliminating errors associated with linearization of the deformational velocity, however the theories differ in the approximations employed to solve configuration moment equations. Comparison with the exact G(t) results provides a means of testing these approximations. The approximate theories all correctly predict the singular part of G(t) at t = 0, providing correct predictions of , however deviations from the exact G(t) are seen in all cases for t > 0.     

A relation between shear flow material functions for a single-integral constitutive equation

This contribution suggests some relations between normal-stress differences and shear stress, both in the steady state and in the transient regimes. It shows that the general form of the BKZ-type equation can be used for the discussion of the relations between several material functions. In addition, a geometric interpretation is offered and some examples are discussed.     

Problems of non-uniqueness when interpreting the effect of fluid inertia on the complex viscosity function

A theoretical investigation is carried out into the interpretation of the effect of fluid inertia on the complex viscosity function as measured on a controlled stress rheometer. The problem of non-unique solutions to the governing equations is considered for the parallel plate geometry. The locations of these solutions are investigated by considering the critical points of the complex mapping associated with the linear viscoelastic equations of motion. It is shown that these critical points play an important role in determining where convergence problems are likely to occur when applying numerical methods of solution to the governing equations. Analytical approximations based on a series expansion about a critical point are developed as an alternative approach to a numerical solution in the neighbourhood of a critical point. In order to verify the theoretical predictions a numerical simulation of the behaviour of a single element Maxwell fluid on a controlled stress rheometer is carried out for a parallel plate geometry. Received: 27 July 1998 Accepted: 9 April 1999     

Nonlinear viscoelastic properties and change in entanglement structure of linear polymer

Simultaneous measurements of stress relaxation and differential dynamic modulus were made at 268 K over a time scale of 10 to 10⁴⁵ s for nearly monodisperse polybutadiene (M _w =2.2x10⁵, 1,2-structure 70%, M _e =3600) and also one having coarse cross-linking (M _c =29000). Static shear strain ranged from 0.1 to 2.0. In a long-time region (t> _k ), the relaxation modulus G (; t) could be expressed by the product G (0; t) h (y). The observed h() agreed well with the Doi-Edwards theory without use of IA approximation. Both the cured and uncured samples showed initial drop of the differential storage modulus G (), ; t) followed by gradual recovery, but did not attain the value before shearing G (, ; t) for the uncured sample showed smaller values than that for the cured one in the whole measured time scale at the higher strain, confirming the two origins of nonlinear viscoelasticity of well entangled polymer; induced chain anisotropy and induced decrement in entanglement density. G (, ; t) curves for the cured sample agreed well with the BKZ predictions. But the curves for the uncured sample agreed well with the BKZ prediction only at the time scale of t< _k . BKZ prediction showed significant upward deviations at t> _k . Such the differences are discussed in terms of the two origins.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

A new boundary integral equation for plane harmonic functions

In this paper, we propose a new boundary integral equation for plane harmonic functions. As a new approach, the equation is derived from the conservation integrals. Every variable in the integral equation has direct engineering interest. When this integral equation is applied to the Dirichlet problem, one will get an integral equation of the second kind, so that the algebraic equation system in the boundary element method has diagonal dominance. Finally, this equation is applied to elastic torsion problems of cylinders of different sections, and satisfactary numerical results are obtained.     

Material functions for constant-strain-rate elongational flows

The problem of determination of invariant material functions for elongational flows in which two components of the constant strain-rate tensor are equal is briefly discussed, and a method of its solution described. The method is based on simultaneous modeling of the elongational viscosity as measured in uniform uniaxial elongational flow, and the shear viscosity as measured in steady viscometric flow. A single integral model with a strain-rate dependent memory is used to correlate both viscosities over a given experimental range of strain rates. The procedure has been applied to a set of experimental data obtained for a low-density polyethylene melt by Laun and Münstedt.     

自修复体系中微胶囊壁材力学性能的测试与表征

微胶囊自修复技术成为研发自修复聚合物材料的主要途径。由于尺寸效应的影响和制备工艺的差异,有必要表征和测量自修复体系中微胶囊壁材的力学性能。本文从微胶囊中直接剥离出微胶囊壁试样进行纳米压痕测试,通过数据拟合和和量纲分析的方法,建立载荷-位移(P-h)曲线与微胶囊壁材弹塑性力学参数之间的联系,分析得到了微胶囊壁材的弹性模量和特征应力值(σ_0.033),进而得到微胶囊壁材的应力-应变本构关系。     

鲫鱼皮肤和肌肉的力学性能研究

鱼在水中游动时,参与鱼体弯曲变形的组织和器官与水媒介相互作用,形成了不同的游动模式和变形方式。为了更好地理解鱼体变形机制并为今后的流固耦合计算提供基础实验数据,本文采用万能试验机进行单轴拉伸试验,对鲫鱼皮肤和肌肉等生物材料的力学性能进行研究。通过破坏实验的方式确定其杨氏模量,通过松弛实验的方式确定其归一化松弛函数。针对皮肤和肌肉的生物材料粘弹性性质,给出本构方程。通过简化为标准线性固体模型进行讨论,得到的结论是:鲫鱼游动过程中以很小的能量损耗为代价,增加了其有效刚度。     

A proposed method of measuring the complex modulus of a thick viscoelastic layer

A simple, non-destructive method of measuring the complex modulus of a layer of viscoelastic material is proposed. The method relies upon an analysis of the frictionless contact of a rigid smooth indentor and the layer. The contact is maintained by means of a fluctuating normal load. The total load (or the indentation) is required to vary in a simple sinusoidal way. The complex modulus may then be determined from the results of observations made when the contact area is maximum (or minimum).     

On the deformation and fracture of porous materials

The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors. These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison is made between theoretical and experimental results.     

Dual equations and solutions of I-type crack of dynamic problems in piezoelectric materials

This paper firstly works out basic differential equations of piezoelectric materials expressed in terms of potential functions, which are introduced in the very beginning. These equations are primarily solved through Laplace transformation, semi-infinite Fourier sine transformation and cosine transformation. Secondly, dual equations of dynamic cracks problem in 2D piezoelectric materials are established with the help of Fourier reverse transformation and the introduction of boundary conditions. Finally, according to the character of the Bessel function and by making full use of the Abel integral equation and its reverse transform, the dual equations are changed into the second type of Fredholm integral equations. The investigation indicates that the study approach taken is feasible and has potential to be an effective method to do research on issues of this kind.     

关于黏弹性材料的广义Maxwell模型

采用流变力学分析黏弹性材料的流变特性时,常要用到广义Maxwell模型 表达的应力松弛模量. 而从试验中获得的应力松弛模量,其表达式常为 Kohlrausch-William-Watts function(KWW函数)形式. 通过把KWW函数和广义Maxwell模型的拟合问题转化为两 矩阵相等的求解问题后,又把两矩阵的相等等价于两矩阵差值向量的一阶范数为无穷小的问 题,并通过引入广义逆矩阵,求得两矩阵差值向量的一阶范数的最小值,最后以一阶范数的 最小值为目标函数,松弛时间为约束条件,利用单纯形法对两矩阵差值向量的一阶范数的最 小值优化,从而提出了一种针对黏弹材料的KWW函数与广义Maxwell模型转换的计算方法. 借助于MATLAB软件,实现了对黏弹材料的广义Maxwell模型的拟合.     

Two-dimensional time-harmonic dynamic Green’s functions in transversely isotropic piezoelectric solids

The two-dimensional time-harmonic dynamic Green’s functions in an infinite transversely isotropic piezoelectric solid are obtained. After introduction of a new function, the original problem is reduced to the determination of the Green’s function for the two-dimensional Helmholtz equation and that for the two-dimensional Laplace equation. The explicit expressions of all the field components are presented. It is verified that the obtained dynamic Green’s functions can reduce to the corresponding static ones by letting the circular frequency be zero. The asymptotic expansions for Green’s functions at far-field are also given.     

Inverse problem for the viscoelastic medium with discontinuous wave impedance

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Excess pressure losses in the capillary flow of molten polymers

The excess pressure losses due to end effects in the capillary flow of a linear low-density polyethylene resin (LLDPE) were studied both experimentally and numerically. First, they were determined experimentally by using two methods: i) by extrapolating experimental data of pressure drop versus length-to-radius ratios (L/R) to zero capillary length and ii) by means of using orifice dies (L/R 0). Both methods resulted in about the same end corrections. Numerical simulation was also used to model this important aspect of experimental rheology. The constitutive equation used in the simulations is a multimode K-BKZ equation proposed by Papanastasiou et al. (1983, J. Rheol. 27:387) and further modified by Luo and Tanner (1988, Int. J. Num. Meth. Eng., 25:9). It was found that the numerical predictions agreed qualitatively, but underestimated the experimental data for the various geometries used to determine the end effects.Dedicated to the memory of Professor Tasos C. Papanastasiou     

半解析有限元法分析非线性粘弹体在板材模具中的流动

聚合物熔体在模具中的均匀性决定板材成型的质量。熔体具有非线性记忆性的粘弹效应,同时流道十分复杂。为准确、简便地分析熔体流动情况,针对板材机头流道的特点,提出了流动计算新的方法——有限柱半解析法,即在流道的厚度方向采用富氏级数描述流动分布,把三维有限元方程简化成为二维,得到以流量和压力为未知量的有限元方程。同时采用K-BKZ积分型本构模型描述熔体的非线性记忆性,给出求解非线性方程组的迭代方法,取得较好的收敛性。对两种典型的板材模具进行了分析计算,得出模具出口处的流量分布,通过把结果与三维有限元分析的结果相比较,表明该方法可以准确地分析板材模具中熔体的流动。     

Solutions of some simple boundary value problems within the context of a new class of elastic materials

Some simple boundary value problems are studied, for a new class of elastic materials, wherein deformations are expressed as non-linear functions of the stresses. Problems involving ‘homogeneous’ stress distributions and one-dimensional stress distributions are considered. For such problems, deformations are calculated corresponding to the assumed stress distributions. In some of the situations, it is found that non-unique solutions are possible. Interestingly, non-monotonic response of the deformation is possible corresponding to monotonic increase in loading. For a subclass of models, the strain-stress relationship leads to a pronounced strain-gradient concentration domain in the body in that the strains increase tremendously with the stress for small range of the stress (or put differently, the gradient of the strain with respect to the stress is very large in a narrow domain), and they remain practically constant as the stress increases further. Most importantly, we find that for a large subclass of the models considered, the strain remains bounded as the stresses become arbitrarily large, an impossibility in the case of the classical linearized elastic model. This last result has relevance to important problems in which singularities in stresses develop, such as fracture mechanics and other problems involving the application of concentrated loads.     

Numerical modeling of the thermomechanical behavior of steels with allowance for the propagation of Luders bands

A thermomechanical model based on physical representations of the motion of dislocation continuum and a model for the initiation and propagation of plastic shear are proposed to describe slow flows of the type of Luders bands. Two-dimensional calculations of Luders band propagation are performed for HSLA-65 steel samples under compression at various strain rates and temperatures. The calculation results are in good agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 146–155, September–October, 2007.     

Al基含能结构材料的Johnson-Cook本构模型及失效参数研究

利用万能实验机和Hopkinson杆装置测试了Al基含能结构材料在不同温度下的静动态力学性能,分析实验结果得到了温度效应和应变率效应对材料力学性能的影响及该合金的Johnson-Cook本构模型参数.结合二维数字图像相关(DIC)方法,研究了Al基含能结构材料的失效应变与应力三轴度及温度之间的关系,得到了该合金的Johnson-Cook失效模型参数.通过平面撞击实验获得了Al基含能结构材料粒子速度和应力波波速之间的经验线性关系和该合金的Grüneisen系数.基于实验获得的材料本构关系和状态方程参数,完成了Al基含能结构材料超高速撞击多层间隔薄钢板的数值模拟,结果表明,数值模拟中靶板的毁伤模式、破孔直径及弹坑主要散布区和实验结果吻合.