土的本构方程与热力学

介绍一种基于热力学理论建立土力学本构方程的一般性理论框架. 这一方法利用两个势函数即自由能势函数和耗散势函数(或屈服函数)以及固定的过程和框架, 建立土的本构方程. 简要介绍了建立热力学本构方程中所用到的热力学内变量理论, 利用Legendre变换建立了热力学势函数之间以及各耗散函数与屈服函数之间的关系;利用自由能势函数和耗散势函数(或屈服函数)建立土的本构方程及其具体步骤. 最后讨论了土力学本构方程研究的意义以及它和应用之间的关系.      

分数导数型本构关系描述粘弹性梁的振动分析

本文研究粘弹性梁在周期激励作用下的受迫振动问题。梁的材料满足Kelvin-Volgt分数导数型本构关系。基于动力学方程、本构关系和应变－位移关系建立了小变形粘弹性梁的振动方程。采用分离变量法分析粘弹性梁的自由振动,导出模态坐标满足的常微分－积分方程和模态函数满足的常微分方程,对于两端简支的截面梁给出了固有频率和模态函数。对于简谐激励作用下粘弹性梁的受迫振动,利用模态叠加得到了稳态响应。最后给出数值算例说明本文方法的应用。     

粘塑性金属材料蠕变实验及流变模型研究

对固体金属材料Lc4铝合金、TC11钛合金及优质碳素结构钢(20#、35#)在高温下进行了多组蠕变实验,对电沉积镍薄膜在常温下进行了多组加、卸载和蠕变实验,根据实验曲线,采用修正的Burgers流变模型来描述这些材料的蠕变行为,建立了积分型蠕变本构方程和微分型应力应变本构关系,确定了蠕变积分核函数,并对由蠕变方程推导的...     

Oldroyd速率型本构方程显式化的微分算符形式

本文建立了一种条件,在这种条件下,隐式的Oldroyd本构方程是等价于微分型本构方程。并且解释了这些条件的物理意义。最后给出了Maxwell型及Oldroyd型本构方程显式化的微分算符形式。     

基于Kanai-Tajimi谱的非黏滞阻尼结构地震动响应的简明闭式解

针对非黏滞阻尼结构基于Kanai-Tajimi谱的卷积-微分混合动力方程解法较繁琐的问题,提出了 一种新的简明封闭解法.非黏滞阻尼模型能较好地模拟实际工程材料的阻尼特征,常以指数型核函数的卷积形式表示,给出其对应的微分型本构关系.Kanai-Tajimi谱随机地震动模型能较好地描述场地的随机地震动特性,其工程应用时所获...     

非线性正交各向异性弹性材料的本构方程及其势函数

研究了非线性Green弹性材料弹性张量独立分量,归纳推导出各向异性Green弹性材料、具有一个对称面Green弹性材料、 正交各向异性非线性弹性材料独立的弹性常数个数.从张量函数出发,用含有高阶弹性张量的张量多项式,推导出三阶非线性正交各向异性Green弹性材料本构方程及其势函数.并将本构方程及其势函数用张量不变量,标量不变量表示.证明了方程是完备的,不可约的,满足张量函数表示定理.详细研究Green弹性材料势函数存在的充分和必要条件,给出并证明了具有普适性的势函数存在定理.     

大变形中摩擦接触问题的数值模拟及应用

大变形的摩擦接触是复杂的非线性问题 ,本文介绍了一种处理摩擦接触问题的数值方法。采用接触单元技术模拟接触界面 ,基于弹塑性理论形式的非经典Coulomb摩擦定律及罚函数方法建立了摩擦接触的增量本构关系。结合大变形的增量分析格式给出了积分摩擦接触本构方程的回映方法。这种处理摩擦接触问题的方法计算简单、使用方便。给出的计算实例及应用实例说明了方法的精度与稳定性     

THE INVERSE PROPOSITION ABOUT THE SYMMETRY OF LINEAR CONSTITUTIVE LAW

基于线弹性体本构方程系数矩阵的对称性,提出了其对应的逆命题问题,即若材料本构方程是线性且对称的,能否由此确定物体是完全弹性的?论文通过构造势函数的方法对该问题给出了肯定的回答,从而论证了对于符合线性本构关系的材料,其本构方程的对称性与物体的完全弹性相互蕴含,因而是相互等价的.     

大变形下初始斜交异性本构方程

采用材料主轴法,建立了初始斜交异性材料在变形构形（Euler描述）下的斜交异性本构方程,以及在初始构形（Lagrange描述）下的形式。具体给出了斜交异性线弹性材料方程的显式,它在Lagrange描述下形式简洁,可方便地用于有限元计算。文中指出,在变形构形下是线弹性的材料,在Lagrange描述下其本构方程一般已成为非线性,我们称之为本构转换非线性。这种非线性在实际的有限元计算中还未引起重视。为理论简明,本构方程是对二维给出的。     

二维Nonlocal线弹性理论的变分原理与对偶方程

基于Eringen提出的Nonlocal线弹性理论的微分形式本构关系,导出了相应的能量密度表达式,进而得到二维Nonlocal线弹性理论的变分原理.利用变分原理导出了对偶平衡方程和相应的边界条件.进而给出了非局部动力问题的Lagrange函数,并引入对偶变量和Hamilton函数,得到了对偶体系下的变分方程.在Hamilton体系下,通过变分得到了二维Nonlocal线弹性理论的对偶平衡方程和相应的边界条件.     

沥青混合料一维非线性粘弹本构方程

本文根据Green-Rivlin提出的Frechet级数,提出了一个兼具长时粘流效应及短时粘弹效应的一维非线性本构方程,并对一种沥青混合料采用蠕变试验方式拟合了本构方程的参数向量。拟合结果表明:这一本构方程形式简洁,物理意义清晰,易于拟合,并对不同应力历史下的应变响应具有广泛的适用性。     

Selection of kernel functions used in a new constitutive equation for viscoelastic fluids

A selection of kernel functions is given to be used in a new integral constitutive equation proposed by Piau whereby the deviatoric stress is calculated from the integral of the history of the past intrinsic rate of rotation and rate of deformation tensors through a representation theorem. Piau has demonstrated the objectivity of a frame moving with a given particle whose axis are directed along the eigenvectors of the rate of deformation tensor. The use of such a framework provides a new approach in the attempt to reduce the computational difficulties associated with conventional constitutive equations written in co-deformational or co-rotational reference frames.The shear and primary normal-stress material functions and the extensional (elongational) stress growth function are defined for the proposed integral constitutive equation. These material functions are used to calculate the kernel functions using steady state, stress relaxation and stress growth data of Attané in simple shear flow for monodisperse polystyrene solutions. The shear and extensional stress growth data of Meissner for a polyethylene melt are also used to show the flexibility of the rheological model.The material functions are first written in terms of five monotonically decreasing functions of the time lag between the past and the present time. Then kernel functions are chosen such that when substituted in the new integral constitutive equation they yield the functions used to describe the data. A further condition imposed on the normalized kernel functions is that they be decreasing functions of time lag.     

Multiple-integral viscoelastic constitutive equations

A class of nonlinear viscoelastic constitutive equations including the K-BKZ constitutive equations, linear viscoelasticity and the Green-Rivlin models is developed. A stored-energy functional is associated with each model in such a way that the energy dissipation rate is non-negative. The theory is developed for 1D viscoelasticity and extended to 3D viscoelastic media.     

Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.     

A constitutive equation for the Mullins effect in stress controlled uniaxial extension experiments

A one-dimensional constitutive equation for the Mullins effect in rubberlike materials, which is motivated by the two phase microstructural material model proposed by Mullins and Tobin [I], is developed in [2]. The constitutive equation is used in [2] to predict the effect of stress softening on the small transverse vibration of a rubber string loaded in uniaxial extension. The two functions which comprise the constitutive equation were assumed to be monotone, but no further analysis of the actual nature of these functions was necessary.In this paper, we examine more closely how the results of a stress controlled uniaxial extension experiment can be used to gain insight into the specific nature of the microstructural strain and the strain amplification functions which comprise the constitutive equation. We examine experimental representations of the two functions which are independent of any special microstructural interpretations. Stress controlled uniaxial extension experiments with buna-n, neoprene, and silicone rubber cords are examined. We demonstrate how the experimental data can be applied to yield representations of the functions of interest to within a multiplicative constant; but no attempt is made to find specific analytical representations of these functions. For buna-n and neoprene samples, we observe behavior consistent with our monotone assumptions, while anomalous behavior is observed with silicone rubber.     

超弹性材料本构关系的最新研究进展

超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.      

STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS 1)

超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.     

耦合蠕变损伤的Chaboche粘塑性模型的研究

Chaboche粘塑性统一本构模型由于没有包含损伤变量,在应力恒定时只能得到不变的塑性应变速率,因此不能描述蠕变第三阶段的加速过程.该文按照Lemaitre有效应力的概念,采用Kachanov损伤演化方程,推导了耦合损伤的Chaboche粘塑性流动方程和硬化方程,并链接到有限元软件ANSYS中,将之用于高温合金钢P91的蠕变寿命计算,结果表明耦合损伤模型的模拟值与实验数据基本吻合;为该模型描述蠕变损伤和疲劳交互作用奠定了基础.     

Extended irreversible thermodynamics,generalized hydrodynamics,kinetic theory,and rheology

The gist of extended irreversible thermodynamics and generalized hydrodynamics is presented within the context of rheology of complex molecules (e.g., polymers) in this paper. Then, the constitutive equation for stress developed for polyatomic fluids in a previous paper is applied to rheology of polymeric fluids. This constitutive equation is fully consistent with the thermodynamic laws. It is shown that the collision bracket integrals appearing in the constitutive equation can be recast in terms of friction tensors of beads and equilibrium force-force correlation functions if the momentum relaxation is much faster than the configuration relaxation and there exist such relaxation times. The force-force correlation functions reduce to those related to the mean square radius of gyration of the polymer if the Hookean model is taken for forces. By treating the recast collision bracket integrals in the constitutive equation as empirical parameters, we analyze some experimental data on shear rate and elongation rate dependence of polymeric melts and obtain excellent agreement with experiment. We show that the empirical parameters can be related to the zero shear rate viscosity and the ratio of the secondary to the primary normal stress coefficient. Therefore, for the plane Couette flow geometry considered in the paper, the constitutive equation is completely specified by the limiting material functions at zero shear rate and relaxation times.Work supported in part by the Natural Sciences and Engineering Research Council of Canada and Fonds FCAR, Quebec. This paper was presented at the Symposium on Recent Developments in Structured Continua II held at Magog, Quebec, Canada, May 23–25, 1990.     

Closed form solution for a nonlocal elastic bar in tension

A simple mechanical one-dimensional problem in the context of nonlocal (integral) elasticity is solved analytically. The nonlocal elastic material behaviour is described by the “Eringen model” whose nonlocality features all reside in the constitutive relation. This relation, of integral type, contains an attenuation function (usually assumed symmetric) aimed to capture the diffusion process of the nonlocality effects; it also exhibits a convolution format. The governing equation is a Fredholm integral equation of second kind whose analytical treatment, even for the usual choice of a symmetric kernel, is not easy to develop. In the present paper, assuming a specific shape for the attenuation function, a closed form solution in terms of strains is alternatively obtained by solving a Volterra integral equation of second kind. The latter can be easily solved with standard techniques, at least for the adopted kernel, taking also advantage from the symmetry of the solution. Such a closed form solution is an essential result to validate the effectiveness of numerical procedures aimed to solve more complex mechanical problems in the context of nonlocal elasticity.