尼龙6/蒙脱土复合材料蠕变行为研究

针对经典黏弹性模型不能很好分析黏弹性材料的蠕变行为问题,运用分数阶导数的类标准线性体模型与Prony级数模型研究了黏弹性材料尼龙6/蒙脱土复合材料的蠕变行为.采用原位聚合法制备了尼龙6/蒙脱土复合材料,在室温环境下对其进行蠕变实验.然后运用分数阶导数的类标准线性体模型和Prony级数模型对复合材料的蠕变实验数据进行分析...     

三种分形和分数阶导数阻尼振动模型的比较研究

标准的整数阶导数方程不能准确描述粘弹性材料的记忆性参考文献[1]和阻尼的分数次幂频率依赖[2],因此分形导数、分数阶导数及正定分数阶导数被用于描述粘弹性介质中的阻尼振动.该文通过分析模型和数值模拟,比较了三种模型描述的振动过程.结果显示,当p小于约O.75或大于约1.9时(p为非整数阶导数的阶数),分形导数模型衰减最快;当P大于约0.75且小于约1.9时,正定分数阶导数模型衰减最快,衰减最慢的分别为分数阶导数模型(p<1)和分形导数模型(p>1).且正定分数阶导数模型衰减快于分数阶导数模型,当p接近2时,两种模型较为相近.     

低密度开孔泡沫蠕变松弛特性分析

利用三维Voronoi模型和有限元方法分析了胞壁材料具有粘弹特性的低密度开孔泡沫的蠕变和应力松弛行为.采用了三参量标准线性固体模型来描述胞壁材料的粘弹特性.所得结果表明.低密度开孔泡沫具有与其胞壁材料相同的松弛时间,当相对密度较低时(低于1%)开孔泡沫的松弛模量与胞壁材料的松弛模量和泡沫相对密度平方成正比.此外,计算结果还表明,低密度开孔泡沫在较小的初始应力条件下具有与其胞壁材料相同的延迟时间.其蠕变柔度与胞壁材料的蠕变柔度和泡沫相对密度平方倒数基本成正比.但随着初始应力值的增大,泡沫的延迟时间将会显著增加.     

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.     

粘弹性材料的变形动力学模型

粘弹性材料的变形动力学模型周建平（长沙国防科技大学，４１００７３）关键词粘弹性，本构关系，内变量，老化１引言许多工程材料，特别是聚合物材料的应力应变关系具有粘弹性特征，使得材料或结构在受力过程中发生蠕变或应力松弛现象．从微观上讲，这种粘弹性变形是由于...     

非牛顿流体的广义Maxwell模型及其解

引进带分数阶导数的广义Ｍａｘｗｅｌｌ模型和Ｖｏｉｇｔ模型；用Ｌａｐｌａｃｅ变换正、反演算法，给出了非牛顿流体应力松弛和蠕变近似解析解。分数阶表征了其衰减或增长的变化特性，这是一种研究分数阶导数流变学的分析、计算方法．     

半封闭分数导数粘弹性衬砌隧道的频域响应

混凝土衬砌具有粘弹性性质,以往的经典Kelvin模型、弹性理论和壳体理论都不能刻画其蠕变的全过程。本文基于饱和多孔介质理论,在频率域研究了轴对称荷载和流体压力作用下饱和粘弹性土中半封闭分数导数型衬砌隧洞的稳态动力响应。在引入隧洞部分透水边界条件的基础上,通过分数阶导数粘弹性模型描述衬砌的应力—位移本构关系,并利用衬砌内边界以及接触面的连续性条件,得到了饱和土和衬砌的应力、位移和孔压解答。考察了分数导数阶数、材料参数以及衬砌和土体相对渗透系数的影响。研究表明：分数导数阶数对系统响应影响较大,且依赖于衬砌的材料参数。另外,相对渗透系数对系统响应的影响很大。     

粘弹性流体的分数元模型及圆管起动流

分数元模型所描述的非牛顿流体属于复杂粘弹性流体,其应力与应变的分数阶时间导数成正比.本文提出一种用弹簧和油壶连接组成的分形网络结构来比拟分数元模型的应力-应变特性,利用Heaviside运算微积,证明了该分形网络结构对应的粘弹性流体为1/2阶导数的分数元.并证明了构成其他分数阶导数分数元模型需要引入弹簧和油壶的多重分形网络结构.本文还导出了分数元模型的圆管起动流的解析解,研究了分数元模型起动过程振荡特征与该模型导数阶β之间的关系;发现在β≠1的情况下,随时间的进程,圆管内分数元模型的运动最终均将趋于静止,只有β=1的情况是一个例外.     

粘弹性模型在木材蠕变中的应用

本文是根据短时间的木材弯曲蠕变实验曲线来确定粘弹性模型元件数和元件常数的探讨.通过核桃楸试件三点弯曲蠕变的实验研究表明:实测蠕变曲线与模型的计算曲线有较高的拟合度.因此我们认为在木材物性研究上或在工程应用上可以采用粘弹性模型元件常数.而且在各树种和环境条件下,一旦确定了适合其蠕变的元件数和元件常数,就将和力学性质中的常数一样,来表示蠕变度量,这将给木材的蠕变研究和木材的应用带来很大方便.     

丁基橡胶粘弹性材料的非线性蠕变本构描述

对丁基橡胶ZN-17粘弹性材料进行了不同温度、不同应力水平下的蠕变实验,揭示了该材料的非线性蠕变特性。基于蠕变实验结果,对标准线性固体模型描述该材料蠕变行为的预言能力进行了评估,提出了新的非线性蠕变本构模型。通过与实验结果比较,表明新模型能较好地描述该材料的非线性蠕变特性。     

Characterizing the creep of viscoelastic materials by fractal derivative models

In this paper, we make the first attempt to apply the fractal derivative to modeling viscoelastic behavior. The methodology of scaling transformation is utilized to obtain the creep modulus and relaxation compliance for the proposed fractal Maxwell and Kelvin models. Comparing with the fractional derivatives reported in the literature, the fractal derivative as a local operator has lower calculation costs and memory storage requirements. Moreover, numerical results show that the proposed fractal models require fewer parameters, have simpler mathematical expression and result in higher accuracy than the classical integer-order derivative models. Results further confirm that the proposed fractal models can characterize the creep behavior of viscoelastic materials.     

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     

Boltzmann superposition principle for a time-dependent soft material: assessment under creep flow field

Variety of time-dependent soft materials that undergo evolution of microstructure are known to follow the Boltzmann superposition principle when appropriately transformed from the real to the effective time domain. This behavior is attributed to obliteration of time dependency in the effective time domain by normalizing the real time by the time-dependent relaxation time. This work is aimed at assessing validity of the Boltzmann superposition principle in the effective time domain under application of step changes and ramps in stress for a time-dependent soft glassy material: an aqueous suspension of Laponite, whose rheological properties are known to show strong time and stress dependency. Interestingly, creep experiments started at different aging times and for different constant stresses indeed lead to a comprehensive time–aging time–stress superposition resulting in time and stress dependence of relaxation time and modulus. Subsequently, we analyze compliance response of the material to different kinds of stress step change and ramp combinations. We observe that except few, most of the compliance data plotted in the effective time domain does not overlap on the comprehensive superposition. We analyze this behavior and attribute the observed mismatch to the history dependence of the time evolution of modulus.     

Generalized Cole-Cole behavior and its rheological relevance

Starting from an analysis of the rheological behavior of the complex modulus predicted by the Cole-Cole formalism, a generalized Cole-Cole ansatz is suggested in order to overcome the related difficulties. The corresponding rheological constitutive equation with fractional derivatives belonging to the generalized Cole-Cole respondance is stated and the characteristic material functions of the linear viscoelasticity theory (like the dynamic modulus and compliance, the relaxation and ratardation functions, the spectra, etc.) are derived. Model predictions of these functions will be compared with experimental results from dynamical measurements and creep data on different polymer systems which show cooperative phenomena (polymeric glasses and gelling systems). One can see that the modified ansatz fits the data very well, in spite of its relative simplicity.     

纤维沥青混凝土FRA黏弹性预测模型

纤维沥青混凝土FRA(Fiber reinforced asphalt concrete)的力学行为取决于沥青混合料和纤维的物理属性及几何特征。通过三参数固体模型,考虑纤维的几何特性,构造了一种预测FRA黏弹性行为模型,推导出该模型的本构方程、蠕变柔量和松弛模量表达式。采用该模型研究了纤维体积分、比半径和弹性模量等对FRA松弛模量和蠕变柔量的影响。结果表明,纤维掺入量和比半径对FRA的松弛模量和蠕变柔量影响较大,而弹性模量影响较小。通过试验,验证了FRA预测模型具有较高的精度。在研究试验范围内,SMA-13沥青混凝土的聚丙烯腈纤维(PAN)最佳掺入量和长径比分别为0.3%～0.4%和600～900。     

Application of scaling transformation to characterizing complex rheological behaviors and fractal derivative modeling

It has been long observed that cumbersome parameters are required for the traditional viscoelastic models to describe complex rheological behaviors. Inspired by the relationship between normal and anomalous diffusions, this paper tentatively employs t ^α to replace t, called as the scaling transformation, in the traditional creep compliance and relaxation modulus. With this methodology, the relaxation modulus is found to agree with the well-known Kohlrausch-Williams-Watts (KWW) stretched exponential function. The fitting results confirm that the proposed models accurately characterize rheological behaviors only with one more parameter α. Moreover, it is noted that the present formulations are directly related to the fractal derivative viscoelastic models and the index α is actually the order of the fractal derivative.     

A class of linear viscoelastic models based on Bessel functions

In this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these functions are shown to be expressed by Dirichlet series (that is infinite Prony series). It follows that the corresponding creep compliance and relaxation modulus turn out to be characterized by infinite discrete spectra of retardation and relaxation time respectively. As a matter of fact, we get a class of viscoelastic models depending on a real parameter \(\nu > -1\). Such models exhibit rheological properties akin to those of a fractional Maxwell model (of order 1/2) for short times and of a standard Maxwell model for long times.     

Non-linear viscoelastic behavior of polymer melts interpreted by fractional viscoelastic model

Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melts, using a fractional model. In this paper the authors propose an advanced model for capturing the non-linear trend of the shear viscosity of polymer melts as function of the shear rate. Results obtained with the fractional model are compared with those obtained using a classical model which involves classical Maxwell elements. The comparison between experimental data and the theoretical model shows a good agreement, emphasizing that fractional model is proper for studying viscoelasticity, even if the material exhibits a non-linear behavior.     

From dynamic modulus via different relaxation spectra to relaxation and creep functions

The main goal of the paper is to compare predictive power of relaxation spectra found by different methods of calculations. The experimental data were obtained for a new family of propylene random copolymers with 1-pentene as a comonomer. The results of measurements include flow curves, viscoelastic properties, creep curves and rubbery elasticity of copolymer melts. Different relaxation spectra were calculated using independent methods based on different ideas. It lead to various distributions of relaxation times and their “weights”. However, all of them correctly describe the frequency dependencies of dynamic modulus. Besides, calculated spectra were used for finding integral characteristics of viscoelastic behaviour of a material (Newtonian viscosity, the normal stress coefficient, steady-state compliance). In this sense all approaches are equivalent, though it appears impossible to estimate instantaneous modulus. The most crucial arguments in estimating the results of different approaches is calculating the other viscoelastic function and predicting behaviour of a material in various deformation modes. It is the relaxation and creep functions. The results of relaxation curve calculations show that all methods used give rather similar results in the central part of the curves, but the relaxation curves begin to diverge when approaching the high-time (low-frequency) boundary of the relaxation curves. The distributions of retardation times calculated through different approaches also appear very different. Meanwhile, predictions of the creep curves based on these different retardation spectra are rather close to each other and coincide with the experimental points in the wide time range. Relatively slight divergences are observed close to the upper boundary of the experimental window. All these results support the conclusion about a rather free choice of the relaxation time spectrum in fitting experimental data and predicting viscoelastic behaviour of a material in different deformation modes. Received: 15 March 2000 Accepted: 18 September 2000