Abstract We present a modeling framework for propagating the uncertainty, stemming from random heterogeneity of concrete microstructure, to its mesoscale elastic properties at the level of statistical volume element. The microstructure of concrete is modeled as a three-phase composite, consisting of aggregates (inclusions) in mortar (matrix), and interfacial transition zone (ITZ), a thin high porosity zone surrounding aggregates. There is inherent randomness in the composition and mechanical properties of these constituents, which in turn causes spatial heterogeneity in the local material behavior. We present a statistical characterization process to quantify the uncertainty associated with local aggregate volume fraction and aggregate size distribution. We then adopt and test a probabilistic model based on the random matrix theory and maximum entropy principle to construct a stochastic description for bounded apparent elasticity tensors at the mesoscale level, in which the bounds are obtained through a computational calibration process based on the theory of micromechanics and numerical homogenization. The framework provides an efficient way to model and simulate the local statistical fluctuations of material properties that are linked to phenomena occurring at the subscale level of heterogeneity.

中文翻译：

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在模拟混凝土的中尺度弹性特性中微观结构随机性的概率放大

摘要 我们提出了一种建模框架，用于在统计体积元素水平上将不确定性传播到其中尺度弹性特性，这种不确定性源于混凝土微观结构的随机异质性。混凝土的微观结构被建模为三相复合材料，由砂浆（基质）中的骨料（夹杂物）和界面过渡区 (ITZ) 组成，界面过渡区 (ITZ) 是围绕骨料的薄高孔隙率区域。这些成分的组成和机械性能具有内在的随机性，这反过来又会导致局部材料行为的空间异质性。我们提出了一个统计表征过程来量化与局部聚集体体积分数和聚集体尺寸分布相关的不确定性。然后，我们采用并测试基于随机矩阵理论和最大熵原理的概率模型，构建中尺度水平的有界表观弹性张量的随机描述，其中边界是通过基于微观力学理论的计算校准过程获得的。和数值同质化。该框架提供了一种有效的方法来建模和模拟材料特性的局部统计波动，这些特性与发生在异质性子尺度水平的现象有关。