损伤粘弹性Timoshenko梁的拟静态力学行为分析

从考虑损伤的粘弹性材料——一种卷积型本构关系出发,应用Timoshenko梁的基本变形假设,建立损伤粘弹性Timoshenko梁的静、动力学行为研究的数学模型.分析了损伤粘弹性Timoshenko梁在阶跃载荷作用下的准静态力学行为,在Laplace域中得到了挠度和损伤的解析表达式．应用数值逆变换技术,考察了材料粘性参数对梁的挠度和损伤的影响,得到不同时刻损伤和挠度随时间的变化曲线．     

小曲率粘弹性索非线性随机稳定性分析

基于Kelvin粘弹性材料本构模型,研究小曲率粘弹性索在窄带随机激励作用下的非线性随机稳定性及均方响应。首先建立小曲率粘弹性索数学模型;然后提出一种确定粘弹性索均方响应及概率渐近稳定性方法;给出了系统均方稳定对激励带宽、幅值、中心频率等要求;给出系统的稳定区域;最后讨论了材料粘性、波速比及介质阻尼对系统不稳定区域的影响。     

损伤对粘弹性矩形板非线性动力特性的影响

研究了考虑损伤效应的粘弹性矩形板在横向周期载荷作用下的非线性动力学问题．基于Von Karman方程、Boltzmann叠加原理和连续损伤力学理论,建立了以中面位移表示的考虑损伤效应的粘弹性薄板的非线性动力学方程,然后,应用有限差分法和Newmark法进行求解,并与相应的文献作出了比较．具体讨论了外载荷参数和板的几何尺寸对含损伤效应的粘弹性板非线性动力响应的影响．数值结果表明,考虑损伤效应时,结构的非线性动力响应会发生显著的变化．     

饱和粘弹性土层中端承桩纵向振动的轴对称解析解

基于弹性和饱和多孔介质理论,将桩和饱和土层分别视为单相弹性介质和饱和粘弹性介质,利用Helmholtz分解和变量分离法,在频率域研究了饱和粘弹性土层中端承桩纵向振动的动力特性,给出了饱和粘弹性土层中桩纵向振动时动力响应的轴对称解析解及桩头复刚度的解析表达式．通过数值计算,给出了桩头动刚度因子和等效阻尼随激励频率的响应,考察了饱和土物性参数、桩土模量比、桩长径比、桩Poisson比等参数对桩头刚度因子和阻尼的影响．研究表明:由于考虑了桩的径向变形效应以及饱和粘弹性土层对桩的径向力作用,轴对称精确解的桩头动刚度因子和阻尼分别与经典Euler-Bernoulli杆模型桩的桩头动刚度因子和阻尼有较大的区别,特别是在若干激励频率处．因此,经典Euler-Bernoulli杆模型桩的适用性具有一定的局限,更加精确的分析应采用三维精确模型．     

具有波阻抗不连续特性的粘弹性介质中的逆散射问题

在时间域内讨论了粘弹性介质的逆散射问题,其中粘弹性介质的波阻抗在远离入射波作用面一侧的交界面上是不连接的。介质的散射算子,传播算子所满足的微分积分方程可以用来反演未知的粘弹性介质的松弛模量,文中给出的反演过程只须利用介质层一侧的反射算子在一个走时来回的时间内的实验测量数据。最后,给出了数值算例,计算结果表明,利用方法可以较准确的反演得到材料松弛模量。     

粘弹性浅拱的非线性动力学行为

研究了外荷载作用下粘弹性浅拱的非线性动力行为.通过d'Alembert原理和Euler-Bernoulli假定建立了浅拱的控制方程,其中非线性粘弹性材料采用Leaderman本构关系.运用Galerkin法和数值积分研究粘弹性浅拱的非线性动力特性.并分析了矢高、材料参数、激励幅值和频率等参数的影响,结果表明一定条件下粘弹性浅拱可出现混沌运动.     

有限变形热粘弹性本构关系的内变量理论 *

基于非平衡态热力学理论 ,提出了一个新的有限变形热粘弹性本构关系 .在定容比热为常数的条件下 ,给出了热学效应和力学效应之间具有解耦形式的自由能表达式 .通过对固体高聚物细观变形机制的分析 ,引进了相应的内变量 ,并在此基础上建立了计及温度效应的有限变形粘弹性本构关系的内变量理论 .此外 ,还推导了参考构形中分子网络具有随机取向分布时本构关系的具体表达式 .讨论了温度变化对松弛时间的影响 .将自由能展开为内变量二次式的粘弹性本构理论仅仅是一种线性化近似 .     

粘性流体两相多孔介质非线性动力问题的罚有限元法

采用基于混合物理论的多孔介质模型,给出粘性流体饱和两相多孔介质非线性动力问题的控制场方程以及相应边值和初值问题的提法,用Galerkin加权残值法导出罚有限元公式,并给出该非线性方程组的迭代求解方法。考虑了体积分数和渗透率与变形相关的情况。用编制的有限元程序计算分析了一维多孔柱体在脉冲载荷作用下的瞬态响应,数值结果表明文中方法正确有效。     

谱变形的非线性双曲型方程

文[1]研究了一个非线性双曲型方程 u_(xt) [(uu_xu_t)/(1-u~2)]-u(1-u~2)=0.方程(*)可以用来描述沿类脂膜扩张波的传播,它所对应的特征值问题的谱是不变的,随着科技的发展,非均匀介质中的传播问题日益受到重视。类问题相应的特征值问题是非保谱的,因此,在[2]中研究了谱变形的特征值问题和发展方程.这本文研究谱变形的非线性双曲型方程     

粘弹性流体在渐缩毛管中渗流规律研究

驱油用聚合物溶液是粘弹性流体,当其在多孔介质中流动时由于拉伸变形会产生额外耗散,因此拉伸压降是不可忽略的.将Binding等人通过机械能平衡原理和最小能量原理建立的非牛顿流体入口收敛流动理论推广应用于渐缩毛管,并以幂指数关系表征剪切粘度与剪切速率关系、第一法向应力差与剪切速率关系、拉伸粘度与拉伸速率关系,从而建立了适用于描述粘弹性流体流动特性的渗流模型,分析了粘弹性流体在渐缩毛管中的渗流规律,利用建立的模型可以准确反映粘弹流体的渗流特性.     

On Temperature-Related Shift Factors and Master Curves in Viscoelastic Constitutive Models for Thermoset Polymers

Mechanics of Composite Materials - Reliable accelerated testing routines involving tests at enhanced temperatures are of paramount importance in developing viscoelastic models for polymers. The...     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

A mathematical boundary integral equation analysis of standard viscoelastic solid polymers

Structural analysis of viscoelastic solid polymers is one of the most important subjects in engineering structures. Several attempts have been so far made for the integral equation approach to viscoelastic problems. From the basic assumptions of viscoelastic constitutive equations and weighted residual techniques, a simple but effective boundary element formulation (BEF) is implemented for the standard linear solid (SLS) viscoelastic models. The SLS model provides an approximate representation of the observed behavior of a real polymer in its viscoelastic range. This formulation needs only Kelvin’s fundamental solution of isotropic elastostatics with material constants prescribed as explicit functions of time. This approach avoids the use of relaxation functions and mathematical transformations, and it is able to solve the quasistatic viscoelastic problems with any load time-dependence and boundary conditions. As an application, a numerical example is provided to validate the proposed formulation. The problem of the pressurization of thick-walled cylindrical viscoelastic tanks made of PMMA polymer is completely analyzed by this approach.     

Modelling an anomalous stress relaxation in glassy polymers (the Kitagawa effect)

Constitutive relations are derived for the nonlinear viscoelastic response of glassy polymers. The model is based on the concept of adaptive links (a version of the theory of transient networks), where the rates of annihilation of active links are determined by the Eyring formula. Adjustable parameters in the constitutive equations are found by using experimental data for a polyester resin in standard relaxation tests. The stress-strain relations are applied to describe an anomalous stress relaxation in solid polymers observed in tensile test after strain reversal (the Kitagawa effect). Qualitative agreement is demonstrated between results of numerical simulation and observations.     

Degree of cure-dependent modelling for polymer curing processes at small strains

In this paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach, cf. Hossain et al., 2010. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure and rheological properties of polymers

The viscoelastic properties of linear flexible-chain polymers with a narrow distribution, for which M > 5M_c (M_c corresponds to the formation of a three-dimensional entanglement network), their mixtures, and concentrated solutions are examined. It is established that under the influence of deformation the polymer may undergo a transition to the rubbery state, which thus defines the limit of its flow state; this transition is also observed in mixtures and concentrated solutions of high-molecular-weight polymers with a narrow distribution. The relative simplicity of the rheological properties of linear high-molecular-weight polymers and their mixtures is determined by the sharpness of the transition to the rubbery state. It has been found that in mixtures of high-molecular-weight polymers the apparent viscosity mechanism associated with a decrease in dissipative losses on transition of the high-molecular-weight components to the rubbery state is dominant; on a broad range of molecular weights (M > M_c), and moreover for polymer solutions, the decrease in entanglement network density under the influence of deformation acquires considerable importance. It is established that the separate effect of the high-molecular-weight components on the viscoelastic properties of their mixtures contradicts the idea of a random network of macromolecular chains. Attention is drawn to the temperature dependence of the viscosity of polymers with a narrow distribution and the dynamic properties of their mixtures. Problems of theoretical and practical interest associated with the particular rheological properties of polymer systems at high deformation rates are defined.     

Modelling structural recovery in amorphous polymers

Constitutive equations are derived for linear viscoelastic response and enthalpy relaxation in amorphous polymers in the vicinity of the glass transition temperature. According to the concept of cooperative relaxation, a glassy polymer is treated as an ensemble of weakly-connected relaxing regions. Mechanical relaxation in a region occurs when the thermally activated flow unit reaches some liquid-like state. Structural recovery is modeled as a sequence of hops in which rearranging regions change their traps. A constitutive model for the linear viscoelastic behavior and enthalpy relaxation in a glassy polymer is validated using experimental data in mechanical and calorimetric tests on polycarbonate and poly (methyl methacrylate). Fair agreement is demonstrated between observations and results of numerical simulation.     

Local discontinuous Galerkin approximation of non-Fickian diffusion model in viscoelastic polymers

In this paper, we investigate a fully discrete local discontinuous Galerkin approximation of a non-linear non-Fickian diffusion model in viscoelastic polymers. For the spatial discretization, we adopt local discontinuous Galerkin finite element method and for the time discretization we use backward Euler method. We derive the stability estimate and a priori error estimate for the discrete scheme. Numerical examples are given to verify the theoretical findings.     

Variant of statistical interpretation of the formation of viscoelastic deformations of polymers

A variant of a statistical probability interpretation of elementary micromechanisms of formation of viscoelastic deformations of polymers is examined with the aid of the concept of dissymmetric media and the dissymmetry coefficient. A new rheological relationship is obtained, a particular case of which is the known equation of a typical linear viscoelastic body. A method is given for determining the relaxation spectrum for different intensity functions figuring in the rheological relationships. The results of the calculation are compared with the experimental data, exemplified by the creep of polyamide P-68.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 392–396, May–June, 1973.