高分子材料的粘弹性摩擦接触力学研究

采用非线性有限元方法研究了高分子材料的粘弹性摩擦接触问题,采用初应变法将粘弹性材料的蠕变应变转化为等价的虚拟节点力,并结合线性粘弹性理论对蠕变应变进行迭代修正,从而获得了粘弹性材料满足摩擦接触条件的解答。文中考虑了接触问题的边界非线性和粘弹性材料的材料非线性。并考虑了接触过程中温度,模量等级时间的增加而改变。     

求解一类非线性粘弹性问题的弹性回复对应原理

本文提出了一个全新的粘弹性理论体系,它把传统的线粘弹性理论作为特殊情况包括在内。其主要结果是两个用于求解一类物理非线性粘弹性问题的弹性回复对应原理。利用它,只要知道相应的非线性弹性问题的解,就可以求出非线性粘弹性问题的解答。对应原理不是基于本构关系的相似性,而是基于从粘弹性现时响应到瞬时弹性响应的可回复性[1]。首先找到非线性粘弹性与非线性弹性本构关系之间的对应,然后导出了两个弹性回复对应原理。通过对改性聚丙烯材料的实验验证了该对应原理的正确性和对此类材料的实用性。     

高分子熔体和浓溶液的流变性能研究Ⅱ．具有高斯链缠结限制作用的物料函数及其粘弹性参数确定的新法

从前一报所提出的具有多重缠结限制作用的高分子非线性粘弹性理论出发，推导出了高分子流体的回忆函数、一般化本构方程和多种流场下多种物料函数：①稳态简单剪切流；②稳态单轴拉伸流；③小振幅的振动剪切流。建议了一种从流动曲线来测定物料函数中的粘弹性参数η０、ｎ＇和α的新方法，用该法测定了多种聚合物熔体的粘弹性参数。最后以大量高分子熔体的流变性能实验数据，对所得到的动、静态剪切物料函数进行了验证，证实了我们所提出高分子熔体的非线性粘弹性分子理论同实验能很好的符合。     

确定Kelvin模型粘弹性材料参数的一种实验方法

从Kelvin模型和Euler-bernoulli梁理论出发，利用弹性-粘弹性相应原理和弹性材料动力学理泠得出粘弹性梁的动力学方程。利用中心差分法分析了粘弹性材料悬臂梁的动态函数。根据振动特性，将材料参数与梁应变响应周期及振幅衰减相联系；利用这种联系，提出了测定Kelvin模型粘弹性材料参数的一种简单实验方法；分别取不同长度的橡胶悬臂梁进行了相应的实验，测出了材料的剪切模量和粘性系数；分析实验结果，得出一些有益的结论。     

高分子熔体和浓溶液流变性能的研究Ⅰ．具有高斯链限制作用的非线性粘弹性分子理论

根据多重缠结模型和多重蠕动机理，用统计力学和动力学相结合的方法，建立了具有缠结限制作用的非线性粘弹性分子理论，计算了处于多重缠结态高分子链的构象统计，得到了高聚物熔体的粘弹性形变自由能，推导出了４种简单形变方式的应力－应变关系。从理论和实验上证实了非线性粘弹理论的时间效应和形变影响是非相关地相互独立的，得到了高聚物熔体和非线性粘弹性模量和柔量的表达式，当其松弛模量和推迟模量中ｎ＇＝１时，相应模量和柔量表达式分别还原为线性粘弹性的表达式。该理论能较好地预测高聚物熔体的非线性和线性粘弹性力学行为，并成功地预测到η０∝Ｍ￣（３．３～３．７）的经验关系式。     

高分子熔体和浓溶液流变性能的研究：Ⅰ.具有高斯链限制作…

根据多重缠结模型和多重蠕动机理，用统计力学和动力学相结合的方法，建立了具有缠结限制作用的非线性粘弹性分子理论，计算处于多重缠结态高分子链手构象统计，得到了高聚物熔体的粘弹性形变自由能，推导出４种简单形变的方式的奕力－应变关系。     

高分子蠕动模型研究进展

介绍了高分子蠕动模型的基本思想及在预测高分子熔体或浓溶液流变学行为时的成功与不足，综述了从不同角度出发对其进行修正及在预测非线性粘弹性行为的研究进展、初步分析了此模型的发展方向。     

定频变温下粘弹材料动力学特性数据拟合分析

本文研究了粘弹性阻尼材料的耗能机理和动态阻尼特性,采用分数导数模型,并与温频等效原理相结合,得到了粘弹性阻尼材料的复模量、损耗因子与温度关系的参数化数学模型;并结合粘弹性阻尼材料的DMA测试实验数据对模型参量进行了拟合。实验结果和误差分析表明拟合的数学模型能够准确反映粘弹性材料在定频率变温度条件下的动力学特性的变化情况。     

高分子材料中的位错应力场及位错能量

用线粘弹性理论，求出了高分子材料中刃型位错、螺型位错的应力场及位错能量。     

非线性光学聚合物材料

非线性光学聚合物是一类新型的功能高分子材料，在光电子技术和集成光学等领域有广阔的应用前景，文中在介绍非线性光学效应和极化原理的基础上，综述了非线性光学聚合物材料研究现状及进展，着重阐述了掺杂型，功能型及共轭型等非线性光这聚合物的结构与性能，应用优势的存在的问题，并指出了这类材料的研究方向和发展趋势。     

粘弹性复合材料中的渐近均匀化方法

主要研究了由各向同性线弹性加强体和各向同性线粘弹性基体组成的复合材料的问题。在已有的线弹性多层材料的渐近均匀化方法的基础上,应用弹性-粘弹性对应原理,在Carson域中求解粘弹性问题,通过两次运用均匀化方法,得到一类单向强化复合材料的有效模量的表达式。反演可得到单向强化复合材料的有效松弛模量在时间域中的表达式,并且与其它结果进行了比较。     

Creep and recovery of nonlinear viscoelastic materials of the differential type

In this work, the creep and recovery properties of rubberlike viscoelastic materials in simple shear are studied by two special constitutive equations for isotropic, nonlinear incompressible viscoelastic material of the differential type. The creep and recovery processes are of significant importance to both the mechanics analysis and engineering applications. The constitutive equations introduced in this work generalize the Voigt-Kelvin solid and the 3-parameter model of classical linear viscoelasticity. They describe the uncoupled non-Newtonian viscous and nonlinear elastic response of an isotropic, incompressible material. The creep and recovery processes are treated for simple shear deformation superimposed on a longitudinal static stretch. Closed form solutions are provided and both processes are described effectively by the exponential function.     

The use of stress sweep tests for asphalt mixtures nonlinear viscoelastic and fatigue damage responses identification

Asphaltic materials are known to present a behavior that can be approximated by the theory of viscoelasticity. For these materials it is essential to characterize fatigue damage. An important aspect therein is the separation between nonlinear viscoelastic and fatigue damage responses. This is a complex issue, since both nonlinearity and damage have a similar effect on the overall material mechanical behavior, i.e. decrease in the stiffness and increase in the phase angle. This paper presents an experimental and a mathematical procedure to separate the nonlinear viscoelastic from the fatigue damage response for asphaltic materials. Stress sweep tests were used to characterize a hot mixture asphalt at nine conditions (three temperatures and three frequencies). Once all strain values were obtained in a stress controlled sweep test, a statistical analysis was used to find the maximum stress that can be applied to the material without invoking the damage response. The results showed that the transition stress value is directly associated with material properties, the stiffness being an important factor in this result. Consequently, stress, temperature and frequency determine together the mechanical response of the material (linear or nonlinear viscoelastic, fatigue damage and/or plastic deformation). Results from this study can be associated with other fatigue damage approaches in order to better select the stress or strain amplitude that should be used in fatigue tests, and to eliminate the amount of energy that is dissipated in the nonlinear viscoelastic region.     

Bending and creep buckling response of viscoelastic functionally graded beam-columns

The viscoelastic creep response of flexural beams and beam-columns made with functionally graded materials is numerically investigated. The paper highlights the challenges associated with the modeling and analysis of such structures, and presents a nonlinear theoretical model for their bending and creep buckling analysis. The model accounts for the viscoelasticity of the materials using differential-type constitutive relations that are based on the linear Boltzmann’s principle of superposition. The model is general in terms of its ability to deal with any material volume faction distribution through the depth of the beam, and with different linear viscoelastic laws, boundary conditions, and loading schemes. The governing equations are solved through time stepping numerical integration, which yields an exponential algorithm following the expansion of the relaxation function into a Dirichlet series. A numerical study that examines the capabilities of the model and quantifies the creep response of functionally graded beam-columns is presented, with special focus on the stresses and strains redistribution over time and on the creep buckling response. The results show that the creep response of such structures can be strongly nonlinear due to the variation of the viscoelastic properties through the depth, along with unique phenomena that are not observed in homogenous structures.     

Response of gradient-viscoelastic bar to static and dynamic axial load

Summary. The response of a bar to static or dynamic axial load is studied analytically on the basis of a simple linear theory of gradient viscoelasticity. The governing equations of axial equilibrium and motion are first obtained by combining the basic equations. They are also obtained by a variational statement, which provides in addition all possible boundary conditions. A correspondence principle between the gradient elastic and gradient viscoelastic formulation and solution is established. Thus, the Laplace transformed with respect to time viscoelastic solution is obtained from the corresponding elastic one by simply replacing the elastic modulus by its Laplace transform times the Laplace transform parameter. The time domain response is finally obtained by a numerical inversion of the transformed solution. Two boundary value problems, one quasi-static and one dynamic, are studied and the gradient viscoelasticity effect on the solutions is assessed.     

Torsion of functionally graded nonlocal viscoelastic circular nanobeams

The elastostatic problem of functionally graded circular nanobeams under torsion, with nonlocal elastic behavior proposed by Eringen, is preliminarily formulated. Exact solutions are detected for nanobeams with arbitrary axial gradations of elastic properties and radially quadratic distributions of shear moduli. Extension of the treatment to nonlocal viscoelastic composite circular nanobeams is then performed. An effective solution procedure based on Laplace transform is developed, providing a new correspondence principle in nonlocal viscoelasticity for functionally graded materials. Displacements, shear strains and stresses are established for nonlocal viscoelastic nanobeams made of periodic fiber-reinforced materials, with polymeric matrix described by a Maxwell model connected in series with a Voigt model.     

Viscoelastic contact problems with friction

A mechanically rough rigid indentor of abitrary asymmetric curved profile is pressed against the surface of a linear viscoelastic half-space whose behaviour in shear and dilatation is similar. In the first place complete adhesion is assumed and the viscoelastic solution is found to be expressible in terms of corresponding elastic solutions. The shape of the contact area and the tangential component of displacement of a point of the surface of the viscoelastic body inside the contact area are unaffected by the viscoelasticity of the body. Fully adhesive contact between two viscoelastic bodies may be treated similarly. Also, certain frictional elastic contact problem solutions, where the contact area contains regions of slip as well as regions of adhesion, are extended to viscoelasticity.     

A quasi-correspondence principle for Quasi-Linear viscoelastic solids

In this paper we show that the correspondence principle that allows one to obtain solutions to boundary-initial value problems for Linear viscoelastic solids from solutions to that for a linearized elastic solid can be extended, in many circumstances, to the case of the Quasi-Linear viscoelastic solids introduced by Fung. We illustrate the ability to generalize the correspondence principle by considering a variety of problems including torsion, transverse loading of beams and several problems that involve a single non-zero stress component. This extension is however not possible for certain classes of problems and we present a specific example where the correspondence principle breaks down. The correspondence principle between Linear elasticity and Linear viscoelasticity also breaks down under certain conditions, however the correspondence between the solutions for Linear viscoelasticity and Quasi-Linear viscoelasticity is even more fragile in that it breaks down while the classical correspondence works, and hence we refer to the correspondence as a quasi-correspondence principle.     

Time integration in linear viscoelasticity—a comparative study

One of the key tasks in computational viscoelasticity is the time integration of the constitutive equation. It is important that the behaviour of the integrators is well understood since they are used in a variety of applications. In the present paper, the performance of conventional semi-analytical methods and implicit Runge-Kutta methods for the integral model of linear viscoelasticity with Prony series is evaluated analytically and numerically. Although a linear viscoelastic constitutive equation is considered, the analyzed integrators can be extended to handle also Schapery-type nonlinear constitutive equations. Numerical examples involving a simple uniaxial problem and multiaxial simulations are presented in order to analyze and compare the time integrators.