混凝土三点弯曲梁软化特性的数值计算方法

本文推导了基于虚拟裂纹模型的混凝土梁荷载位移全曲线的计算公式,研究了不同网格剖分、不同的拉伸软化曲线模型和不同的预制裂纹长度等对荷载位移全曲线的影响。计算结果表明,其结果不受网格划分的影响,通过与实验结果对比,证明了其有效性。     

脆性固体损伤和局部软化的有限元分析

本文研究混凝土、岩石一类工程中常用的应变软化材料的有限元分析方法。在作者以往有关粘塑性损伤本构模型的工作基础上，给出了一组便于有限元计算的本构方程表达式。包括损伤弹性矩阵和局部损伤软化矩阵，分别运用于计算硬化和软化阶段的有限元刚度矩阵；对所提出的本构方程的实验验证计算和一些算例的有限元数值分析，表明文中给出的本构方程是可行的，相应的有限元算法能较好地对损伤固体的局部软化效应进行数值分析，并可成功地追踪应力应变响应的软化曲线     

复波数域弥散曲线的求解方法研究

研究了复波数域弥散方程的求解问题,根据相关文献提出了三种求解复波数域弥散曲线的方法,即一种改进的牛顿迭代法——抛物牛顿迭代法、求解方程组的二分法、模值收敛判别法。应用上述三种算法可以求出大部分弥散方程的数值结果。文中引用了参考文献中关于复波数域弥散曲线的算例,应用这三种方法分别对算例中的弥散方程进行求解并绘制相应复波数域弥散曲线。结果表明,这三种方法均可较好地对算例中的弥散方程在复数域中进行求解。通过与参考文献中的算例进行对比,进一步分析了这几种方法的特点和使用范围,介绍了如何应用这几种方法对复波数域弥散方程进行求解。     

桁架结构优化的曲线寻优数值方法

在结构优化设计领域中，首次将曲线寻优理论中的数值解法应用于桁架结构的优化过程，本文针对相应的优化模型，基于对偶规划，推导了曲线寻优算法所依赖的公式，编制了微机上运行的程序，算例表明曲线寻优的数值解法取得了快而稳的满意结果。     

细节疲劳额定值法的拓展应用研究

针对具体工程结构的疲劳特性,结合不同应力疲劳曲线模型(S-N曲线的幂函数模型、Weibull模型、双折线模型)和等寿命曲线模型(Goodman模型和Gerber模型),分别建立细节疲劳强度额定值(DFR)表达式,对传统的基于幂函数型S-N曲线和Goodman型等寿命曲线建立的DFR法进行拓展,并通过算例分析其对结构疲劳寿命评估结果的影响。结果表明:与传统的DFR法相比,拓展后的DFR法提高了对结构不同疲劳安全性设计要求的适用性,实现了其在结构低周和超高周疲劳分析中的应用。     

轻质泡沫混凝土的劈裂破坏力学行为分析

利用平台巴西圆盘加载方式和钢质压条加载方式,对两种厚度为25mm和50mm、不同密度的轻质泡沫混凝土(400～1000kg/m3)进行巴西圆盘劈裂试验,研究密度和厚度对泡沫混凝土裂纹宽度、劈裂强度、断裂韧度、断裂能的影响规律。结果表明,在橡胶垫平台巴西圆盘和钢质压条加载方式下,其劈裂断裂特征大致分为四个阶段:线性弹性段、非线性弹性段、起裂阶段、失稳阶段。同样加载率下最大裂纹宽度随着泡沫混凝土密度增加逐渐减小,劈裂拉伸强度、断裂韧度、断裂能呈幂函数形式增加。借鉴Reinhardt非线性软化曲线,对不同密度泡沫混凝土的应力软化关系进行曲线拟合,建立基于拉伸强度、断裂韧度等控制参数的应力-裂纹宽度关系三段式模型。基于试验结果,对理想多孔材料细观力学预测模型进行修正,获得泡沫混凝土孔隙率与拉伸强度的半经验公式。     

控制混沌振动的局部逆系统算法

研究用局部逆系统方法控制混沌。将逆系统控制律局部线性化建立了局部逆系统控制律关分析了在控制混沌振动中的适用性,通过数值算例与逆系统方法进行了比较并讨论了控制方案的鲁棒性。     

基于uu—a^2uxx=0的脆性材料受拉开裂稳定性分析

本文从混凝土受拉开裂的机理出发，基于虚拟裂缝模型，建立了混凝土开理解的定解方程及其边界、初始条件，通过对波动方程ｕｕ－ａ＾２ｕｘｘ＝０解的稳定性分析，首次从动态角度得到混凝土试件稳定开裂所应满足的条件，最后通过实验和算例证实了本文分析的正确性，为脆性材料拉伸全曲线实验研究奠定了理论基础。     

基于CorVis ST测量人角膜的弹性模量

根据临床可视化角膜生物力学分析仪(CorVis ST)检测得到近视患者屈光手术前角膜动态变形历程曲线,采用有限元数值模拟逆解方法确定其角膜在体有效弹性模量。采用计算流体动力学(CFD)方法得到CorVis ST喷射气流作用在角膜表面时,瞬态压强值与空间分布的气体载荷函数曲线;建立考虑角膜、巩膜、眼内容物(流体腔)及整眼运动的眼球有限元模型,计算在气流冲击作用时角膜顶点的位移幅值曲线,并与CorVis ST测量结果对比;采用逆解方法计算了4例患者左右眼角膜整体的有效弹性模量,平均值约为0.68MPa,与离体单轴拉伸实验结果接近,表明本文提出的基于CorVis ST临床检测结果逆解在体角膜弹性性能的方法是可行的。     

ECAP对纯铜循环硬化/软化特性的改变

以纯铜棒材试样为研究对象,通过试验研究不同道次等通道转角挤压（ECAP）后材料的单轴拉压循环行为,探讨ECAP后材料循环特性的变化,得到以下结论：（1）具有循环硬化特性的纯铜进行ECAP挤压后,其循环特性可转变为循环软化;（2）第一道次ECAP挤压对材料循环应力应变响应的强化作用最大,后续道次挤压对强化的效用迅速降低,4道次以后挤压的强化作用似可忽略不计;（3）因循环软化,纯铜经ECAP挤压后的循环应力应变曲线大大低于其单调拉伸应力应变曲线,与未经ECAP挤压的结果相反。本文研究表明,评估ECAP对材料的强化效果需同时考察材料单调加载和循环加载的力学性能。     

An isolated cohesive crack in tension

The shape of the back-calculated stress-separation curves obtained from the in-situ fracture of first-year sea ice in the Arctic and Antarctic is convex, and radically different from those for concrete. In these tests, the process zone size changes with crack growth, but the nature of this change differs with the test conditions, load-control or displacement control. These results prompted a closer examination of the cohesive crack model using the simplest cracked configuration, a finite cohesive crack in an infinite elastic medium loaded in tension by a uniform stress at infinity. Different types of strain softening are examined: rectangular softening, linear softening, prescribed cohesive stresses, and prescribed cohesive crack-opening displacements. For each of these cases, crack nucleation is examined; close attention is paid to test control conditions, be they load-control or fixed-grip. The test control conditions alter the fracture, crack nucleation, crack growth, and process zone size behavior significantly. Accurate approximate solutions to linear softening are presented and examined.     

大体积混凝土等效裂纹断裂模型研究

根据大比尺混凝土紧凑拉伸与楔入劈拉试验成果,将裂纹在稳定扩展中断裂有程区应力分布与相应的变形（张开度ω）联系起来,通过“归一化”处理,得到了大体积混凝土断裂过程区长度的解析表达式,建立了大体积混凝土Ⅰ型断裂破坏的等效裂纹断裂模型。     

Cohesive zone model of intermediate crack-induced debonding of FRP-plated concrete beam

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete structures. Debonding along the FPR–concrete interface can lead to premature failure of the structures. In this study, debonding induced by a flexural crack in a FRP-plated concrete beam is analyzed through a nonlinear fracture mechanics method. The concrete beam and FRP plate are modeled as linearly elastic simple beams connected together through a thin layer of FRP–concrete interface. A bi-linear cohesive (bond-slip) law, which has been verified by experiments, is used to model the FRP–concrete interface as a cohesive zone. Thus a cohesive zone model for intermediate crack-induced debonding is established with a unique feature of unifying the debonding initiation and growth into one model. Closed-form solutions of interfacial stress, FRP stress and ultimate load of the plated beam are obtained and then verified with the numerical solutions based on finite element analysis. Parametric studies are carried out to demonstrate the significant effect of FRP thickness on the interface debonding. The bond-slip shape is examined specifically. In spite of its profound effect on softening zone size, the bond-slip shape has been found to have little effect on the ultimate load of the plated beam. By making use of such a unique feature, a simplified explicit expression is obtained to determine the ultimate load of the plated concrete beam with a flexural crack conveniently. The cohesive zone model in this study also provides an efficient and effective way to analyze more general FRP–concrete interface debonding.     

基于Cosserat近场动力学的纤维混凝土破坏模拟

本文基于Cosserat近场动力学发展了一种纤维混凝土的近场动力学模型,对纤维混凝土的破坏现象进行研究。该模型考察了物质点独立的转动自由度和物质点间的力偶作用,而且有表征微结构尺寸的内禀长度,相比于传统的近场动力学模型,更适合描述纤维混凝土这类胶结颗粒材料的力学行为。本文采用完全离散的方式对纤维进行建模,引入了纤维拔出实验中拔出位移和切应力的关系,并且采用组构张量描述纤维的局部分布。数值算例部分模拟了单纤维拔出实验、带预制裂纹的平板拉伸实验和三点弯曲梁实验。数值结果和已有的数值模型以及实验进行了对比,验证了所提出模型的正确性。此外,本文还调查了微结构对纤维混凝土破坏的影响,数值结果显示Cosserat剪切模量和内禀长度会影响裂纹的局部分布,但是不会改变裂纹的主方向。     

混凝土黏聚开裂模型若干进展

黏聚模型是用来描述混凝土断裂行为的基本模型, 首先介绍了混凝土的黏聚开裂模型的基本概念,总结了确定黏聚区的本构方程的各种方法,即直接单轴拉伸测试、J积分方法、R曲线法、柔度法和逆推法.然后介绍了黏聚模型在I型和复合型裂纹问题、疲劳断裂问题中的应用以及黏聚模型与混凝土尺寸效应的关系.最后对黏聚开裂模型与桥联模型、带状裂缝模型进行了比较和总结, 指出了该模型存在的问题, 并对其以后的发展方向提出了建议.      

Softening behaviour and correction of the fracture energy

The area under the load–displacement softening curve gives the total external work on the test specimen and not the fracture energy. The fracture energy follows from half this area that is equal to the critical strain energy release rate at the first crack increment. For wood this is correctly applied for mode II. For mode I however, as for other materials, the total area is wrongly regarded, a factor 2 is too high. In some applications, based on crack increment cycles, the error is even a multiple of this factor 2. On the other hand, the measurements at softening may show an apparent decrease of the specific fracture energy that can be explained by a small crack joining mechanism when the ultimate state of the ligament of the test specimen is reached. Post fracture behaviour is thus not comparable with the behaviour of macro crack initiation.It is further shown, by the kinetics of the process, that the irreversible work of an ultimate loading cycle is proportional to the activation energy of the fracture process and not to the driving force of the process. This explains why the crack velocity decreases with the increase of this irreversible work and increases with the stress intensity increase.The fracture energy is a function of the Griffith strength and is thus related to the effective width of the test specimen and not to the ligament length. This also has to be corrected. Based on the derivation of the softening curve, the reported fracture toughness of 720 kN m^−1.5 of double-edge notched tests is corrected to 330 kN m^−1.5 and the value of 467 kN m^−1.5, based on the fracture energy, of the compact tension tests, is also corrected to the right value of 330 kN m^−1.5. A revision of published mode I data, based on the fracture energy obtained by the area of the softening curve, is thus necessary.     

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials

A numerical method is developed to simulate complex two-dimensional crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Potential cracks are represented by pre-inserted cohesive elements with tension and shear softening constitutive laws modelled by spatially-varying Weibull random fields. Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out with extensive investigation of the effects of important numerical algorithms and material properties on numerical efficiency and stability, crack propagation processes and load-carrying capacities. It was found that the homogeneous model led to incorrect crack patterns and load–displacement curves with strong mesh-dependence, whereas the heterogeneous model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing the variance of the tensile strength random fields with increased heterogeneity led to reduction in the mean peak load and increase in the standard deviation. The developed method provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength for structural design.     

基于统一相场理论的早龄期混凝土化-热-力多场耦合裂缝模拟与抗裂性能预测

受水化反应和热量传输等过程影响, 混凝土在养护阶段会发生受约束收缩变形, 并由此在结构内引发较大的拉应力, 而此时混凝土力学性能往往还处于较低水平, 容易导致建造期混凝土结构即出现裂缝等病害. 这种早龄期混凝土裂缝对核安全壳、桥梁隧道、地下结构、水工或海工结构等重大土木工程和基础设施的全生命周期完整性、耐久性和安全性造成严重影响. 为了准确预测早龄期混凝土抗裂性能并量化裂缝演化对混凝土结构行为的不利影响, 亟需开展化-热-力多场耦合环境下的混凝土裂缝建模与抗裂性能分析研究. 针对这一需求, 本工作在前期提出的固体结构损伤破坏统一相场理论基础上, 考虑开裂过程与水化反应、热量传输等之间的相互影响, 建立裂缝相场演化特征(包括基于强度的裂缝起裂准则、基于能量的裂缝扩展准则和基于变分原理的扩展方向判据等)与混凝土水化度和温度之间的定量联系, 提出混凝土化-热-力多场耦合相场内聚裂缝模型, 发展相应的多场有限元数值实现算法并应用于若干验证算例. 数值模拟结果表明, 上述多场耦合相场内聚裂缝模型合理地考虑了水化反应、热量传输、力学行为以及裂缝演化之间的耦合效应, 揭示了早龄期混凝土热膨胀变形和自收缩变形的相互竞争机理, 且分析结果不受裂缝尺度和网格大小等数值参数的影响, 实现了早龄期裂缝演化全过程准确模拟和抗裂性能定量预测, 有望在混凝土结构早龄期裂缝预测和控制方面发挥重要作用.      

A cohesive plastic and damage zone model for dynamic crack growth in rate-dependent materials

Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed.