基于CT的准脆性材料三维结构重建及应用研究

准脆性材料的结构及其细观组分的力学性质决定了材料的力学性质及破裂机制,在数值模型中尽可能准确的考虑材料的真实结构已成为了数值计算与数值模拟发展的一种趋势。该文以混凝土为研究对象,借助于先进的CT技术获取混凝土内部结构切片图像,利用数字图像处理技术实现了基于CT图像的混凝土材料结构的识别和表征,并针对CT图像具有颜色亮度不均并呈环状分布的特点,提出了环状分区与分割阈值自动识别相结合的CT图像分割算法;在此基础上,建立了基于位图矢量化理论的三维实体材料结构模型的重建方法和三维网格化材料结构模型重建方法,并将三维网格化方法建立的材料结构模型与三维岩石破裂过程分析系统RFPA3D结合进行了初步应用,对混凝土单轴压缩破裂过程进行了数值模拟。通过数值试验与物理实验结果对比发现,考虑混凝土骨料真实分布的数值实验结果与物理实验具有一定可比性,数值试验结果从得到的力学参数和破裂模式方面比较接近于物理实验结果,为深入研究混凝土、岩石、复合材料等力学特征提供了一种可行的研究思路。     

A model material approach to the study of fracture process zone of quasi-brittle materials

A new approach to study the fracture of quasi-brittle materials is introduced: the design and testing of model materials. By model material is understood a material with enlarged microstructure and which material parameters, such as stacking and mechanical properties of particles and cohesion force, can be fully controlled. In this paper a first example to the model materials approach is presented, consisting in 5 mm steel particles bonded in a precise stacking with an epoxy-based glue. It is shown how it is possible to correlate the different fracture mechanisms and ultimate peak load of the model material to the particle pair force and to the fracture process zone size. It is also seen how a quasi-brittle behaviour is produced in the presence of mechanisms that induced the crack to shift fracture planes, that is, in presence of energy dissipative mechanisms.     

Energy-based collapse assessment of concrete structures subjected to random damage evolutions

The assessment of structural capacity against collapse is conducive to the optimal design of new structures as well as checking the safety of existing structures. However, the evaluation cannot be typically carried out by means of destructive tests on prototype or reduced scale structures. In this regard, the numerical models that adequately represent the prototype structures can be alternatively used. Specifically, both the nonlinearities and randomness as well as their coupling effect of materials need to be represented in a unified manner in structural analysis. The present paper aims at providing an effective approach to incorporate the stochastic nature of damage constitutive relationships in collapse analysis and assessment of concrete structures subjected to earthquake ground motions. Within the framework of stochastic damage mechanics, the spatial variability of concrete is represented by a two-scale stationary random fields. The concept of covariance constraint is introduced to bridge the two-scale random fields such that the scale-of-fluctuation of the random material property is satisfied at both scales. Random damage evolution induced structural collapse analysis is achieved via the nonlinear stochastic finite element method. To address the randomness propagation across scales, the probability density evolution method is employed. By exerting the absorbing boundary condition associated with an energy-based collapse criterion on the generalized probability density evolution equation, the anti-collapse reliability of concrete structures can be evaluated with fair accuracy and efficiency. Numerical investigation regarding an actual high-rise reinforced concrete frame-shear wall structure indicates that the random damage evolution of concrete dramatically affects the structural nonlinear behaviors and even leads to entirely different collapse modes. The proposed method provides a systematic treatment of both uncertainties and nonlinearities in collapse assessment of complex concrete structures.     

A nonlocal computational homogenization of softening quasi-brittle materials

In this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi-brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first-order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are introduced for each macroscopic Gauss point, in which the microscopic damage variables and the macroscale consistent tangent modulus and its derivatives are obtained by imposing the macroscopic nonlocal strain on the first RVE, and the macroscopic stress is computed by employing the microscopic damage variables and imposing the macroscopic local strain over the second RVE. Finally, numerical examples are solved to illustrate the performance of the proposed nonlocal computational homogenization technique for softening quasi-brittle materials.     

Finite element analysis of viscoelastic composite structures based on a micromechanical material model

The stress and creep analysis of structures made of micro-heterogeneous composite materials is treated as a two-scale problem, defined as a mechanical investigation on different length scales. Reinforced composites show by definition a heterogeneous texture on the microlevel, determined by the constitutive behaviour of the matrix material and the embedded fibres as well as the characteristics of the bonding properties in the interphase. All these heterogeneities are neglected by the finite element analysis of structural elements on the macroscale, since a ficticious and homogeneous continuum with averaged properties is assumed. Therefore, the constitutive equations of the substitute material should well reflect the mechanical behaviour of the existing micro-heterogeneous composite in an average sense.The paper at hand starts with the brief outline of a micromechanical model, named generalized method of cells (GMC), which provides the macrostress responses due to macrostrain processes as well as the homogenised constitutive tensor of the substitute material. The macroscopic stresses and strains are obtained as volume averages of the corresponding microfields within a representative volume element. The effective material tensor constitutes the mapping between the macro-strains and the macro-stresses. The cells method is used for the homogenisation of the unidirectionally reinforced single layers of laminates made of viscoelastic resins and flexibly embedded elastic fibres. The algorithm for the homogenisation of the constitutive properties runs simultaneously to the finite element analysis at each point of numerical integration and provides the macro-stresses and the homogenised constitutive properties. The validity of the proposed two-scale simulation is investigated by solving boundary value problems and comparing the numerical results for the structures to the experimental data of creep and relaxation tests or analytical solutions.     

A two-scale method for matrix cracking probability in fibre-reinforced composites based on a statistical representative volume element

This paper presents a two-scale methodology for evaluating the probability of matrix cracking in any point of the transverse section of a fibre-reinforced composite material. At the microscale, the random distribution of fibres has been analyzed by means of optical microscopy and the corresponding images have been used to generate realizations of statistical representative volume elements (SRVE). The size of these SRVEs was chosen in order to guarantee that they are representative of the material in both the mechanical and statistical senses and consequently, allow the statistical simulation of transverse random composites. Finite Element models of these real-microstructure SRVEs were solved with arbitrary values of the boundary conditions. From these results, probability density functions of the stress, strain and dilatational energy density were found. These results can be related to any value of the stress tensor at any point in the macroscale by means of a two-scale methodology. The presented methodology has been applied to three different carbon-fibre reinforced polymers (CFRP), and the results related to experimental data from tensile tests. This approach can be used in the engineering design process as a procedure to define critical strains, stresses or combinations of both to obtain a matrix cracking probability below a desired level.     

Size-scale and slenderness influence on the compressive strain-softening behaviour of concrete

In this article the compressive mechanical behaviour of quasi-brittle materials is analysed by means of experimental tests and by using an ad hoc algorithm for numerical simulations based on the Pseudo-traction and the Boundary-element methods. The experimental analysis is carried out on specimens with three different size-scales, three different values of slenderness and two boundary conditions. The numerical analysis was carried out by taking into account the initial random crack distribution, considering the mutual crack interaction, the crack–boundary interaction and the internal friction between the faces of the cracks. The numerical results, in good agreement with the experimental data, highlight the characteristic strain-softening behaviour of quasi-brittle materials, and the influence of size-scale and slenderness on the structural response. By observing the evolution of the crack patterns, it is possible to emphasize, both experimentally and numerically, the transition from crushing to splitting collapse by increasing the specimen slenderness, as well as the transition from ductile to brittle behaviour by increasing the specimen size-scale.     

Cohesive surface model for fracture based on a two-scale formulation: computational implementation aspects

The paper describes the computational aspects and numerical implementation of a two-scale cohesive surface methodology developed for analyzing fracture in heterogeneous materials with complex micro-structures. This approach can be categorized as a semi-concurrent model using the representative volume element concept. A variational multi-scale formulation of the methodology has been previously presented by the authors. Subsequently, the formulation has been generalized and improved in two aspects: (i) cohesive surfaces have been introduced at both scales of analysis, they are modeled with a strong discontinuity kinematics (new equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure have been considered); (ii) the computational procedure and numerical implementation have been adapted for this formulation. The first point has been presented elsewhere, and it is summarized here. Instead, the main objective of this paper is to address a rather detailed presentation of the second point. Finite element techniques for modeling cohesive surfaces at both scales of analysis (FE\(^2\) approach) are described: (i) finite elements with embedded strong discontinuities are used for the macro-scale simulation, and (ii) continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale. The methodology is validated through numerical simulation of a quasi-brittle concrete fracture problem. The proposed multi-scale model is capable of unveiling the mechanisms that lead from the material degradation phenomenon at the meso-structural level to the activation and propagation of cohesive surfaces at the structural scale.     

Strain rate effects on dynamic fracture and strength

An experimental procedure and accompanying theoretical analysis is presented to produce a well-characterized technique for quantifying dynamic fracture properties of quasi-brittle materials. An analytical and experimental investigation of mode I fracture of concrete was conducted under the dynamic loading of a split Hopkinson pressure bar. Fracture specimens in the form of notched-cavity splitting tension cylinders were subjected to stress wave loading that produced strain rates nearing 10/s. Fracture parameters were extracted by the application of the two-parameter fracture model, a nonlinear fracture model for quasi-brittle materials. Finite element analysis verified the experimental configuration and addressed inertial contributions within the dynamic environment. Ultra-high-speed digital photography was synchronized with the fracture process to provide additional validation and insight to the experimental technique. Results show that the effective fracture toughness and specimen strength both increase significantly with loading rate. The numeric and photographic results validate the experimental technique as a new tool in determining rate dependent material properties.     

Study on crack curving and branching mechanism in quasi-brittle materials under dynamic biaxial loading

Attempts are made to analyze the temporal and spatial effect and the complex mechanical behaviors of microcracks and the macro crack at mesoscopic scale based on the damage evolution principle. The mechanism of crack curving and branching in quasi-brittle materials under dynamic biaxial loading is investigated. The effects of different ratios between the load in the horizontal and vertical directions (for convenience, the loading ratio is denoted by B in this paper), crack dip angles and material homogeneity on crack curving and branching are considered. The results indicate that: Crack curving is mainly controlled by the loading ratio, while initiation and propagation of branch microcracks are related to the stress level. The initial dip angle of crack can vary the stress configuration at the crack tip zone. If the loading ratio remains constant, the crack tends to propagate toward the vertical direction with increasing crack dip angle. It is also found that heterogeneity due to defects in the material play an important role in the distribution of tiny voids and cracks in the material and the crack propagation mode. The results in this study are not only in good agreement with the physical test results, but also can provide some valuable reference for studies on the tensile properties and failure modes of heterogeneous quasi-brittle materials with internal defects.     

基于定长裂缝试件的脆性材料尺寸效应实验方法

由于脆性或准脆性材料内各类微缺陷的影响,材料的力学性能,如名义破坏应力,　刚度以及断裂韧性等随试件的大小而改变,具有明显的尺寸效应。通常情况下,描述材料尺寸效应的Ｂａｚａｎｔ尺寸效应律是建立在一系列相似试件的基础上通过实验方法确定的。　本文提出了一种新的用含固定长度裂缝试件测定断裂韧性和有效断裂过程区大小的实验方法和计算公式。与相似试件测定方法相比,实验结果吻合很好。根据本文提出的定长裂缝试件实验方法,在保证与相似试件相同脆性指数范围的前提下,可以用小试件进行测量。     

多孔材料辐射-传热耦合性能的统计二阶双尺度计算

对多孔材料辐射-传热耦合计算的数学模型, 即Rosseland方程, 给出了一种统计的二阶双尺度分析方法, 并针对典型问题进行了数值模拟。建立了考虑辐射项的统计二阶双尺度计算公式, 给出了统计意义下热流密度极值的预测算法, 并通过与理论解的比较对算法进行了验证, 利用本文中方法研究了孔洞体分比和空间分布状态对陶瓷多孔材料热传导系数、 辐射传导系数和热流密度极值的影响。结果表明: 孔洞体积分数的增加将导致有效热传导系数下降; 热流密度极值随孔洞体积分数的增加而变大, 并且在高温时辐射的作用明显增大; 数值试验表明, 使用统计二阶双尺度方法及其有限元算法预测孔洞随机分布复合材料结构的热性能是有效的。     

A composite approach for modeling deformation behaviors of thermoplastic polyurethane considering soft-hard domains transformation

Thermoplastic polyurethane elastomers (TPUs) are the most used engineering thermoplastics combining the properties for both elastomers and glassy materials. TPUs have good physical and mechanical properties, excellent chemical and abrasion resistances. Compared with typical thermoset rubbers, TPUs are easier to be processed and recycled. However, the deformation behaviors of TPUs are very complex due to their nonlinear, hysteresis, rate and temperature dependences, and softening properties. Therefore, development of a constitutive model with microstructure considerations is important for predicting the deformation behavior of TPUs under mechanical loading as well as during forming processes such as rolling and stretching. In this work, TPUs were taken as a two-phase material consisting of both hard and soft phases corresponding to their hard and soft domains. A new composite constitutive model for stress-strain response of TPUs was proposed taking into account the microstructure of TPUs as well as its evolution (hard to soft phase transformation) induced by deformation. Excellent agreement between model predictions and experimental results for the loading-unloading behaviors of two TPUs with different hard and soft segment contents confirmed the efficacy of our proposed composite constitutive model.     

The statistical second-order two-scale method for thermomechanical properties of statistically inhomogeneous materials

A statistical second-order two-scale (SSOTS) method is established in a constructive way for predicting the thermomechanical properties of statistically inhomogeneous materials. For this kind of composite materials, the complicated micro-characteristics of inclusions, including their shape, size, orientation, spatial distribution, volume fraction and/or material properties and so on, lead to changes of the macroscopic thermomechanical properties, such as stiffness, coefficient of thermal expansion and strength of material. In this paper, a statistical model at an arbitrary position of the composite material is defined to represent the microstructure of the statistically inhomogeneous media at first. And then, the statistical second-order two-scale analysis formulation is derived. Finally, the numerical results for some statistically inhomogeneous composites are calculated by SSOTS algorithm, and compared with the data by experimental and theoretical methods.     

用能量方法研究混凝土断裂过程区的力学性能

准脆性混凝土自由裂缝前缘断裂过程区的发展与其非线性断裂特征及尺寸效应现象密切相关。它的物理力学行为的量化分析对理解混凝土断裂破坏机理和建立适用于混凝土结构裂缝稳定分析和安全评估断裂准则尤为重要,一直是混凝土断裂力学研究的核心问题。该文依据Hillerborg给出的断裂能定义,给出了计算单位长度断裂过程区发展能量耗散的通用表达式。以三点弯曲梁为例,采用非线性软化本构关系,进一步给出了计算此平均能量耗散的具体步骤及对应的公式。在根据实测的三点弯曲梁的断裂能回归拟合了特征裂缝张开位移w0后,计算了每个试件整个断裂全过程中不同荷载时刻断裂过程区耗能的平均值。结果表明:随着裂缝扩展,断裂过程区能量耗散的变化和试件尺寸无关,可描述断裂过程区混凝土材料的力学性能。     

The statistical second‐order two‐scale method for mechanical properties of statistically inhomogeneous materials

A class of random composite materials with statistically inhomogeneous microstructure, for example, functionally graded materials is considered in this paper. The microstructures inside a component are gradually varying in the statistical sense. In view of this particularity, a novel statistical second‐order two‐scale (SSOTS) method is presented to predict the mechanical properties, including stiffness, and elastic limit. To develop this method, the microstructures of statistically homogeneous, and inhomogeneous materials are represented. In addition the SSOTS formulas are derived based on normalized cell depending on the position variables by a constructing way, and the algorithm procedure is described. The mechanical properties of the different inhomogeneous materials are evaluated. The numerical results are compared with the experimental findings. It shows that the SSTOS method is effective. Copyright © 2010 John Wiley & Sons, Ltd.     

考虑骨料尺寸的混凝土岩石边界效应断裂模型

该文比较了边界效应模型（BEM）和尺寸效应模型（SEM）在研究材料断裂性能方面的不同。提出了由处于准脆性断裂状态的三点弯曲试件的峰值荷载P_max,同时确定材料参数--断裂韧度K_IC与拉伸强度f_t的理论与方法。由于实验室条件下混凝土试件高度W与骨料最大粒径d_max的比例W/d_max约为5~20,试件的非均质性明显,破坏为准脆性断裂控制。因此,区别于以连续介质力学为基础的应用于准脆性断裂研究的力学模型,该文研究将骨料最大粒径d_max引入相应的断裂模型解析表达式中,由参数组合β d_max来计算结构峰值状态对应的裂缝扩展量,通过离散参数β的不同取值,实现了对材料参数--断裂韧度与拉伸强度的准确预测。基于不同学者的相同尺寸W而不同初始裂缝长度a₀,以及相同初始缝高比a₀/W而不同尺寸W的几何相似的砂浆、混凝土及岩石类材料试件的试验成果（骨料最大粒径d_max从1.2 mm~40 mm变化）,验证了所提理论与方法的合理性。     

Damage process in heterogeneous materials analyzed by a lattice model simulation

Several materials of technological interest could be considered as heterogeneous and their random nature can be accounted to be the cause of the nonlinear behavior. The quantitative evaluation of damage in materials subjected to stress or strain states has great importance due to the critical character of these phenomena, which, at a certain point, may suddenly give rise to catastrophic failure. In previous studies, Carpinteri and his coworkers have presented different aspects of the damage process characterization in heterogeneous materials. Three of these aspects demand our attention: (i) the brittleness number to measure the brittleness level of the structure under investigation; (ii) the fractal dimension in which the damage process develops; and (iii) the global indexes obtained for the Acoustic Emission (AE) analysis. In the present work, a version of the discrete element method formed by bars is used to explore these concepts. A set of quasi-brittle material specimens is simulated and, when it is possible, the numerical results are compared with experimental data. Moreover, a discussion of the obtained results aids to better understand the behavior of this kind of materials, describing the numerical method as a viable tool to extract information from experimental tests on the damage process.