铁电陶瓷宏细观本构模型

在居里温度以下，铁电陶瓷呈铁电相，具有许多取向不同的铁电畴，取向分布函数描述了铁电畴的取向分布情况文中推广了经典的内变量理论，采用宏细观相结合的方法，建立了铁电陶瓷的宏观行为与细观结构的关系，给出了铁电陶瓷的屈服条件，屈服面的演化规律及取向分布函数的演化规律计算得出了与实验比较符合的电位移－电场关系曲线及应变电场－蝶形关系曲线     

材料三维微结构表征及其晶体塑性有限元模拟

材料的力学性能，尤其是在有限变形下所呈现的宏观各向异性，是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构（晶粒的形貌和取向等）对宏观塑性各向异性的影响，因此，本文建立了能实际反映晶粒形貌的三维Voronoi模型，并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先，建立反映材料微结构的代表性体积单元RVE模型进行计算，并与实验结果进行对比验证。然后，以单向拉伸为例，分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响，并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明，本文模型能够反映微观结构对宏观力学性能的影响，为实际生产制造领域构件的力学性能提供可靠的预测。     

一种基于材料细观特征量的PBX拉伸强度理论模型

为给塑性黏结炸药(PBX)的力学强度设计提供支撑、探索材料细观特征量与材料强度之间的定量规律,应用微裂纹扩展区理论,将PBX炸药的单轴拉伸过程中力学响应特征的变化归结为扩展裂纹取向角度的增加,将扩展裂纹最大取向角与拉伸强度相关联,构建了基于材料细观特征量的拉伸强度理论模型,并采用不同温度的单轴拉伸实验验证了该理论模型的有效性。研究表明:该拉伸强度理论模型可以实现对PBX炸药拉伸强度与炸药微裂纹密度、颗粒/黏结剂界面性能以及颗粒/黏结剂体系的表观杨氏模量、泊松比等细观特征量之间关系的定量描述。     

变幅疲劳载荷下钢纤维混凝土的损伤演化行为研究

本文通过实验分析了变幅疲劳载荷作用下钢纤维混凝土非线性损伤演化行为，指出变载时材料当前的损伤状态和变幅前后应力幅差影响材料的疲劳损伤演化行为。文中给出了损伤演变路径和描述该损伤演化行为的疲劳累积损伤方程。在此基础上，定性定量地分析了Ｍｉｎｅｒ线性累积损伤准则的局限性     

可压超弹性-塑性材料中的空穴生成

本文研究了材料的弹塑性性质对球体中空穴生成问题的影响，材料的弹性用一种可压超弹性材料的本构关系来描述，材料的塑性用满足材料的不可压条件和Tresca屈服条件的理想塑性材料的本构关系来描述。这类超弹性．塑性材料中可以发生空穴的生成现象，得到了在表面拉伸作用下球体中空穴生成时空穴半径与临界拉伸之间的关系式和临界拉伸。球体的变形可分为弹-塑性变形阶段和完全塑性变形阶段，球体中心首先形成塑性变形区域，并有空穴的突然生成；塑性变形区域能够快速增长，并且使球体很快进入完全塑性变形阶段；空穴在弹-塑性变形阶段迅速增长，但进入完全塑性变形阶段后增长较慢。同时给出了不同变形阶段球体中的应力分布。数值结果表明材料的塑性性质对材料中的空穴生成有明显的影响。     

基于微结构损伤的珠光体材料本构行为研究

珠光体材料由许多随机取向的珠光体团组成，每一珠光体团又由铁素体片和渗碳体片交替 叠合而成. 实验表明具有较小片层间距的珠光体材料具有较高的强度和寿命. 通过分析构成 珠光体团的各相及界面的损伤特征，利用损伤耗散功的概念，得到了铁素体、渗碳体与界面 损伤的具有统一形式的演化规律，将其嵌入基于细片层微结构和非经典塑性理论的珠光体团 的弹塑性本构方程，利用Hill自洽方法，得到了珠光体材料的损伤本构描述. 所得到的损 伤本构描述显含表征微结构特征的片层间距，容易证明具有较小片层间距的珠光体材料具有 较好的综合力学性能. 对珠光体材料的拉伸和循环拉压特性进行了分析，得到了与实验一 致的结果.     

材料三维微结构表征及其晶体塑性有限元模拟

材料的力学性能,尤其是在有限变形下所呈现的宏观各向异性,是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构(晶粒的形貌和取向等)对宏观塑性各向异性的影响,因此,本文建立了能实际反映晶粒形貌的三维Voronoi模型,并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先,建立反映材料微结构的代表性体积单元RVE模型进行计算,并与实验结果进行对比验证。然后,以单向拉伸为例,分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响,并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明,本文模型能够反映微观结构对宏观力学性能的影响,为实际生产制造领域构件的力学性能提供可靠的预测。     

考虑细观变形特征的镁合金宏观本构模型及数值模拟

为了能有效描述镁合金宏观各向异性塑性行为,考虑了滑移、孪生、去孪生三种细观变形模式的特点,给出了相应的硬化函数;根据VonMises屈服准则,发展了一种镁合金宏观本构模型及其迭代算法。模型将变形模式的开启与晶粒取向相关联,同时针对镁合金孪生变形时引起的晶粒重新定向问题,描述了一种晶向偏转的方法。在此基础上编写了ABAQUS/UMAT材料用户子程序;利用开发的本构模型,开展了单轴拉伸、单轴压缩、单轴循环拉压加载条件下镁合金塑性行为的数值模拟,并对随机织构下的镁合金板材轧制过程进行了有限元仿真实验。模拟结果表明:单轴拉伸、单轴压缩和循环加载情形下的镁合金宏观硬化行为与实验结果基本吻合;轧制后镁合金板材表现出了应力-应变不均匀特性,多晶织构演化结果与实验结果基本一致。说明文中所提出的宏观本构模型、晶向偏转模型能够有效描述镁合金的宏观塑性行为和织构演化。     

橡胶弹性材料的一种混合本构模型

该文探讨不可压缩橡胶弹性材料的本构模型.考虑到小变形时分子链的端矢分布符合高斯函数,而大变形时符合非高斯函数,提出一个混合模型,用高斯链网络模型来描述小变形而用8链网络模型来描述大变形.引入权重函数,使小变形和大变形情况下混合模型分别退化或趋于高斯链网络模型和8链网络模型.由Treloar拉伸实验数据拟合得到模型参数,通过这些材料参数混合模型对等双轴拉伸和纯剪切变形模式的预测结果与Tre-loar实验数据基本吻合,说明混合模型具有同时描述不同变形模式的能力.通过比较分析,混合模型的总体预测精度均优于高斯链网络模型和8链网络模型,特别是对剪切变形.     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为，本文建立了基于微结构演化的塑性本构模型。首先，采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验，并对其在不同应变程度下的微结构演化特征进行了分析。研究发现，影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程，并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响，进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后，根据隐式应力更新算法对新模型进行了有限元实现，并与实验结果进行比较，验证了新模型的合理性和预测精度。     

FRP筋粘结式锚具的界面径向弹性模量分析

建立了FRP(Fibre Reinforced Polymer)筋粘结式锚具粘结界面的Rib-scale模型和Bar-scale模型,然后利用Fourier-Bessel级数推导了FRP筋、混凝土以及钢套筒等在径向应力作用下的解析解.解析解与数值解吻合较好,验证了用Fourier-Bessel级数表达的解析解的有效性....     

Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

Modeling Turbulent Droplet Motion in Vaporizing Sprays

The present article is concerned with the influence of turbulent gas-velocity fluctuations on both droplet dispersion and droplet-gas slip velocity in the context of spray simulation. The role of turbulence in generating slip and thus enhancing interphase heat and mass transfer has so far received little attention and is investigated in this work. A model for turbulent gas-velocity fluctuations along droplet trajectories is presented and is first tuned to reproduce elementary dispersion phenomena. It is then shown to give good results for more general dispersion problems as well as for slip velocities. As a fundamental source of information and for the purpose of model validation and comparison, direct numerical simulation (DNS) of droplet motion in homogeneous isotropic steady turbulence (HIST) is used. Dispersion of “injected” droplets (i.e. droplets under the influence of drift due to high injection velocity) as well as slip velocities for linear and nonlinear droplet drag are studied, and reasonable agreement is found with the model. The distributions of the slip velocity are found to be very similar for linear and highly nonlinear drag law. The present model is also used to investigate the influence of turbulence on droplet penetration. Comparison is made with an eddy-interaction model (the KIVA-2 model), which reveals various weaknesses of this model, in particular the underprediction of average slip velocity. The influence of slip due to turbulence on vaporization is shown for a fuel spray injected into a premix gas-turbine combustor. The classical eddy-interaction model is seen to underestimate the rate of vaporization due to the underprediction of slip. This revised version was published online in July 2006 with corrections to the Cover Date.     

截尾Gauss概率密度函数中待定参数的确定

给出一种计算描述标量湍流脉动的截尾Gauss概率密度函数的待定参数的方法. 通过将关于待定参数的代数方程组表示成适于求解的形式，综合应用牛顿法、牛顿下山法和阻尼牛顿法等迭代算法，并恰当地选取待定参数的迭代初值，获得了在标量平均值及其脉动均方值的各种取值条件下待定参数的相应数值.     

十次对称二维准晶中的热应力分析

推导了当考虑热效应时十次对称二维准晶体平面应变问题的通解表示．作为应用，采用所获得的通解首先得到了十次对称二维准晶体中的一个点热源所引起的声子场和相位子场，给出了点热源所引起的声子场和相位子场应力分量的解析表达式；接着获得了在均匀热流作用下十次对称二维准晶体中-绝缘椭圆孔洞所引起的热应力问题的弹性解答，给出了沿椭圆边界环向应力分布的解析表达式；当椭圆的短轴趋于零时，则获得了裂纹问题的解答，给出了应力强度因子、裂纹表面张开位移及能量释放率的解析表达式；推导了在任意热载荷作用下裂尖附近的渐近场．     

A finite element formulation for analysis of functionally graded plates and shells

Summary A finite element formulation is derived for the thermoelastic analysis of functionally graded (FG) plates and shells. The power-law distribution model is assumed for the composition of the constitutent materials in the thickness direction. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. Such formulation accounts for the large gradient of the material properties of FG plates and shells through the thickness without using the Gauss points in the thickness direction. The explicit through-the-thickness integration becomes possible due to the proper decomposition of the material properties into the product of a scalar variable and a constant matrix through the thickness. The nonlinear heat-transfer equation is solved for thermal distribution through the thickness by the Rayleigh-Ritz method. According to the results, the formulation accounts for the nonlinear variation in the stress components through the thickness especially for regions with a variation in martial propperties near the free surfaces.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Integral transform solution for the lid-driven cavity flow problem in streamfunction-only formulation

The basic ideas in the generalized integral transform technique are further advanced to allow for the hybrid numerical-analytical solution of the two-dimensional steady Navier-Stokes equations in streamfunction-only formulation. The classical lid-driven square cavity problem is selected for illustration of the approach. The corresponding biharmonic-type non-linear partial differential equation for the streamfunction is integral transformed in one of the co-ordinates and an infinite system of coupled non-linear ODEs for the transformed potential results in the other independent variable. Upon truncation to an appropriate finite order, the ODE system is numerically solved by well-established algorithms with automatic error control devices. The convergence behaviour of the eigenfunction expansion is demonstrated and reference results are provided for typical values of Reynolds number.     

Singular finite elements for the sudden-expansion and the die-swell problems

The singular finite element method is used to solve the sudden-expansion and the die-swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden-expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die-swell problem is solved using the singular elements constructed for the stick–slip problem. The singular elements accelerate the convergence of the free surface dramatically.     

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.