基于细观力学方法的混凝土热膨胀系数预测

建立混凝土材料的有效性质与微结构参数之间的关系,是混凝土材料优化设计的基础。本文用细观力学方法对复合材料宏观有效热膨胀系数进行研究,得到了含有一球形夹杂物的无限大介质在均匀变温作用下的应力场。假定混凝土为由骨料和砂浆基质组成的二相复合材料,根据混凝土宏观体积热膨胀量与组成混凝土的各相介质细观体积热膨胀量相等的原则,采用基于Mori-Tanaka方法的混凝土宏观有效剪切模量,推导出混凝土有效热膨胀系数的解答。对稀疏解法、自洽方法和有限单元数值试验结果的比较说明,本文提出的基于自洽方法的混凝土宏观有效热膨胀系数的理论公式能够较好的描述混凝土的热学特性,该方法可以推广到多相复合材料宏观有效热膨胀系数的预测中。     

复合材料的宏观性能与参数设计

本文综述了预测复合材料宏观性能──有效刚度的几类方法：自洽模型、单胞模型以及它们的结合──自洽有限元法．阐述了复合材料发生弹塑性变形时的有关力学问题．基于细观力学的定量分析结果，探讨了面向材料宏观刚度的细观结构参数设计的基本原则，以期对建立复合材料细观结构设计的力学和数学模型有所启发．     

混凝土材料宏观力学特性分析的细观单元等效化模型

提出了一种混凝土材料宏观力学特性分析的新方法—细观单元等效化模型。该方法从描述混凝土材料的细观尺度入手,采用Monte Carlo法生成由骨料颗粒及砂浆基质组成的混凝土试件的随机骨料模型;然后,依据混凝土材料特征单元尺度来剖分有限元网格并投影到建立的随机骨料模型上,各细观单元的有效力学特性则采用复合材料等效化方法来确定。本文方法体现了材料非线性宏观力学特性源于其内在的不均匀性这一认识,而对不均匀性的描述则是以网格剖分是否影响其宏观力学特性为准则。因此,本文方法较其他细观力学方法最大的优点在于极大地减小了体系自由度数目（特别是对于三维问题）,从而提高了计算效率。算例分析初步验证了本文方法的高效性。     

水饱和花岗岩本构模型及地下爆炸波的数值研究

采用广义自洽方法描述介质的细观几何结构,基于混合物理论建立了水饱和岩石含损伤弹塑性本构模型,提出了一个适用于爆炸波数值计算的饱和水体积分数演化方程,也即给出了本构关系中的闭合方程.使用Biot有效应力描述水压对岩石强度的影响,在有效应力空间里建立了水饱和岩石剪切屈服和破坏的强度准则,并引入了剪胀效应对强度的影响因子.对地下封闭核爆炸的力学效应开展了数值模拟,系统地研究了含水花岗岩中地下爆炸波的传播特征以及含水量对爆炸应力波传播规律的影响.     

混凝土断裂过程的力学模型与数值模拟

混凝土是一种典型的非均匀准脆性材料，其断裂过程是非常复杂的. 评述了混凝土断裂以及断裂过程研究的进展状况，主要总结了一些研究混凝 土断裂的宏观力学方法和模型，介绍了从混凝土的细观层次出发模拟其断裂 过程的数值模型.最后，简单介绍了作者用细观数值方法模拟混凝土宏观断 裂过程的研究成果.     

基于降阶均匀化理论的混凝土双尺度力学性能分析

混凝土材料细观特性对宏观力学性能有着重要影响。为进一步分析混凝土细观特性对宏观力学行为的影响规律,将混凝土材料简化为由骨料、砂浆和界面三相组成,编制了随机凸多面体骨料生成、投放和网格剖分算法,建立可用于有限元计算的满足级配要求的随机细观模型。针对直接使用细观力学模型计算量较大的问题,采用降阶均匀化理论,对混凝土细观胞元模型进行预处理并编制了相应的双尺度计算程序。对不同强度混凝土进行了单轴静态压缩双尺度计算,与实验数据和细观力学模拟结果符合较好。研究表明,降阶均匀化理论在加快求解速度的同时具有较高的精度,可以用于混凝土的多尺度力学性能分析。     

近片层γ-TiAl基合金宏观屈服的微观表征

将近片层-γTiAl基合金视为以等轴γ颗粒为基体,PST颗粒为夹杂的两相复合材料,基于细观力学自洽理论,对合金的有效弹性模量及基体和夹杂中的应力和应变场进行了解析分析计算,并结合细观力学的宏细观关联方法,确定了近片层-γTiAl基合金的宏观屈服的微观表征.结果表明:夹杂颗粒中的应力和应变场与外载及夹杂的体积分数f和椭球长细比ρ有关,软取向PST夹杂颗粒的微变形屈服导致近片层-γTiAl基合金材料的整体宏观屈服.     

基于均匀化理论的混凝土宏细观力学特性研究

在细观层次上将混凝土视为由砂浆基质、骨料及其界面组成的三相复合材料,在此基础上,采用有限元方法,对混凝土弹性本构关系进行数值模拟,利用位移渐近展开技术和均匀化理论建立了多尺度力学框架下的有限元平衡方程,重点考察了单胞尺寸对宏观力学性能的影响,得到了相对最大骨料粒径的最小单胞尺寸,即5～10倍最大骨料粒径.作为例证,对混凝土三点弯梁进行了宏细观尺度数值仿真研究,结果表明:基于本文方法可以较好地反映混凝土的宏观力学行为.此外,由于骨料、砂浆的相互作用,应力分布呈现出宏观渐变平滑与细观局部突变的特征.     

钢筋锈胀引发混凝土保护层开裂破坏的细观数值研究

钢筋锈蚀膨胀引起保护层混凝土开裂是影响钢筋混凝土结构耐久性和服役寿命的重要因素。考虑到混凝土细观结构组成对保护层破坏模式的影响,从细观角度出发,将混凝土看作由骨料、砂浆基质及两者间界面过渡区组成的三相复合材料,建立了描述钢筋锈胀力学行为的混凝土随机骨料模型。采用塑性损伤本构关系模型来表征砂浆基质和过渡区界面的力学行为,假定钢筋均匀锈蚀,对钢筋锈胀引起的混凝土保护层开裂破坏过程进行了细观数值研究。对比了宏观均匀模型与细观非均质模型下获得的保护层破坏模式,探讨了径厚比(c/d)、钢筋位置(中部和角区)及混凝土拉伸强度对保护层破坏模式及保护层胀裂时钢筋锈蚀水平的影响,得到了一些有益结论。     

混凝土受拉性能多尺度均匀化数值模拟研究

为研究混凝土的细观结构对其受拉性能的影响,本文首先采用蒙特卡罗方法生成了多组混凝土随机骨料模型;然后划分有限元网格并映射到所建立的混凝土随机骨料数值模型上,采用复合材料均匀化方法建立了混凝土多尺度均匀化数值模型。考虑骨料随机分布和骨料形状,通过数值分析得到了在单轴拉伸情况下混凝土损伤分布特性及宏观应力-应变关系,在考虑随机性与非均质性的同时得到了较为理想的结果。运用多尺度均匀化的建模方法不仅能反应混凝土细观结构的影响,而且等效化模型的模拟计算时间大大减少,节约计算资源,提高了计算效率,具有优越性。     

A multi-phase micromechanical model for unsaturated concrete repaired using the electrochemical deposition method

Most concrete structures repaired using the electrochemical deposition method (EDM) are not fully saturated in reality. To theoretically illustrate the deposition healing process by micromechanics and quantitatively describe the effective properties of unsaturated concrete during the EDM healing process, a multi-phase multi-level micromechanical framework is proposed based on the microstructure of unsaturated concrete and the EDM’s healing mechanism. In the proposed model, the volume fractions of water and deposition products, the water effect (including further hydration and viscosity in pores) and the shapes of pores in the concrete are comprehensively considered. Moreover, multi-level homogenization procedures are employed to predict the effective properties of unsaturated concrete repaired using the EDM. For the first-level homogenization of this model, a modified function is presented to correct the Mori–Tanaka (M–T) method, which is used to predict the effective properties of equivalent inclusions composed of deposition products and water. To demonstrate the feasibility of the proposed micromechanical model, predictions obtained via the proposed multi-phase micromechanical model are compared with the experimental data, including results from extreme states during the EDM healing process. Finally, the influences of equivalent aspect ratios and deposition product properties on the healing effectiveness of EDM are discussed based on the proposed micromechanical model.     

Multi-level modeling of woven glass/epoxy composite for multilayer printed circuit board applications

The objective of this paper is to develop a hybrid homogenization method to predict the elastic properties of a common woven glass/epoxy composite substrate for multilayer circuit board applications. Comprehensive high resolution 3D finite element (FE) models of a quarter of the repeated unit cell (RUC) for the woven glass/epoxy composite were developed based on different micromechanical schemes. . Specifically, four different micromechanics schemes were investigated: self-consistent, Mori–Tanaka, three-phase approach and composite cylinder assemblage (CCA). The element based strain concentration matrices were determined and used to obtain the homogenized woven glass/epoxy composite properties via a specially developed MATLAB code. Attention was further devoted to the predictions of the homogenized elastic moduli of the multilayer printed circuit board (PCB). The results from our simulations, based on Mori–Tanaka and CCA, are in good agreement with existing experimental results, indicating that the newly proposed homogenization scheme can be used as a design tool to predict the overall properties of woven composite materials typically used in multilayer PCB applications.     

基于细观力学分析的砂土弹塑性本构模型

利用细观力学分析中的自洽理论建立了在固结排水条件下的砂土弹塑性本构模型,在该模型中考虑了部分砂土颗粒因剪切作用在颗粒接触面滑移而引起的整体剪切模量的降低,给出了求解整体剪切模量的解析方法,并将模型预测与不同应力路径的试验结果作了比较,证明该模型是合理的.     

A micromechanical study of drying and carbonation effects in cement-based materials

This paper is devoted to a micromechanical study of mechanical properties of cement-based materials by taking into account effects of water saturation degree and carbonation process. To this end, the cement-based materials are considered as a composite material constituted with a cement matrix and aggregates (inclusions). Further, the cement matrix is seen as a porous medium with a solid phase (CSH) and pores. Using a two-step homogenization procedure, a closed-form micromechanical model is first formulated to describe the basic mechanical behavior of materials. This model is then extended to partially saturated materials in order to account for the effects of water saturation degree on the mechanical properties. Finally, considering the solid phase change and porosity variation related to the carbonation process, the micromechanical model is coupled with the chemical reaction and is able to describe the consequences of carbonation on the macroscopic mechanical properties of material. Some comparisons between numerical results and experimental data are presented.     

A stochastic homogenization approach to estimate bone elastic properties

The mechanical properties of bone tissue depend on its hierarchical structure spanning many length scales, from the organ down to the nanoscale. Multiscale models allow estimating bone mechanical properties at the macroscale based on information on bone organization and composition at the lower scales. However, the reliability of these estimates can be questioned in view of the many uncertainties affecting the information which they are based on. In this paper, a new methodology is proposed, coupling probabilistic modeling and micromechanical homogenization to estimate the material properties of bone while taking into account the uncertainties on the bone micro- and nanostructure. Elastic coefficients of bone solid matrix are computed using a three-scale micromechanical homogenization method. A probabilistic model of the uncertain parameters allows propagating the uncertainties affecting their actual values into the estimated material properties of bone. The probability density functions of the random variables are constructed using the Maximum Entropy principle. Numerical simulations are used to show the relevance of this approach.     

A unified energy approach to a class of micromechanics models for composite materials

Several micromechanics models for the determination of composite moduli are investigated in this paper, including the dilute solution, self-consistent method, generalized self-consistent method, and Mori-Tanaka's method. These micromechanical models have been developed by following quite different approaches and physical interpretations. It is shown that all the micromechanics models share a common ground, the generalized Budiansky's energy-equivalence framework. The difference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated. As a bonus of this theoretical development, the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applicability of the generalized self-consistent method can be extended to materials containing microcracks, multiphase inclusions, non-spherical inclusions, or non-cylindrical inclusions. The relevance to the differential method, double-inclusion model, and Hashin-Shtrikman bounds is also discussed. The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

Micromechanical modelling of dry and saturated cement paste: Porosity assessment using ultrasonic waves

This article assesses the relationship between porosity and ultrasonic parameters of cement paste. It includes theoretical assessment of ultrasonic wave velocities of cement paste materials. Theoretical micromechanical models describing cement paste as a two-phase composite were detailed. Mechanical (bulk and shear moduli) and ultrasonic (longitudinal and transverse velocities) properties were evaluated. They were then, compared to the experimental ultrasonic properties measured on dry and fully water saturated samples with varying porosity First, the obtained micromechanical results showed that the correlation between acoustic velocity and porosity yielded the expected values: longitudinal and transverse velocities decrease with porosity. Secondly, the dilute inclusion model was able to represent the acoustic parameter of the cement paste only at low porosity, up to 20%. The self-consistent model under-estimated the measured ultrasonic properties for almost all porosity ranges. The Mori–Tanaka and the Kuster–Toksöz models succeeded in describing the acoustic parameters in dry and saturated states when assuming spherical shaped pores.     

功能梯度材料结构热力耦合概率分析方法

基于自洽平均微观力学W-T(Wakashima-Tsukamoto)模型和拉丁超立方抽样,建立一种功能梯度平板热力耦合概率分析方法.以材料物理属性和空间分布的不确定性随机参数作为概率分析的输入,以热应力作为输出,基于本征正交分解POD(Proper Orthogonal Decomposition)对热应力的随机时间历...     

An explicit expression of the effective moduli for composite materials filled with coated inclusions

The obvious shortcoming of the generalized self-consistent method (GSCM) is that the effective shear modulus of composite materials estimated by the method can not be expressed in an explicit form. This is inconvenient in engineering applications. In order to overcome that shortcoming of GSCM, a reformation of GSCM is made and a new micromechanical scheme is suggested in this paper. By means of this new scheme, both the effective bulk and shear moduli of an inclusion-matrix composite material can be obtained and be expressed in simple explicit forms. A comparison with the existing models and the rigorous Hashin-Shtrikman bounds demonstrates that the present scheme is accurate. By a two-step homogenization technique from the present new scheme, the effective moduli of the composite materials with coated spherical inclusions are obtained and can also be expressed in an explicit form. The comparison with the existing theoretical and experimental results shows that the present solutions are satisfactory. Moreover, a quantitative comparison of GSCM and the Mori-Tanaka method (MTM) is made based on a unified scheme. The project supported by the National Natural Science Foundation of China under the Contract NO. 19632030 and 19572008, and China Postdoctoral Science Foundation