A finite-element approach based on the first-order FE 2 homogenisation technique is formulated to analyse the alkali-silica reaction-induced damage in concrete structures, by linking the concrete degradation at the macro-scale to the reaction extent at the meso-scale. At the meso-scale level, concrete is considered as a heterogeneous material consisting of aggregates embedded in a mortar matrix. The mechanical effects of the Alkali-Silica Reaction (ASR) are modelled through the application of temperature-dependent eigenstrains in several localised spots inside the aggregates and the mechanical degradation of concrete is modelled using continuous damage model, which is capable of reproducing the complex ASR crack networks. Then, the effective stiffness tensor and the effective stress tensor for each macroscopic finite element are computed by homogenising the mechanical response of the corresponding representative volume element (RVE), thus avoiding the use of phenomenological constitutive laws at the macro-scale. Convergence between macro- and meso-scales is achieved via an iterative procedure. A 2D model of an ASR laboratory specimen is analysed as a proof of concept. The model is able to account for the loading applied at the macro-scale and the ASR-product expansion at the meso-scale. The results demonstrate that the macroscopic stress state influences the orientation of damage inside the underlying RVEs. The effective stiffness becomes anisotropic in cases where damage is aligned inside the RVE.

中文翻译：

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碱硅反应影响混凝土结构的多尺度建模：耦合细观损伤演化和宏观混凝土劣化

通过将宏观尺度的混凝土退化与细观尺度的反应程度联系起来，制定了一种基于一阶 FE 2 均质化技术的有限元方法来分析混凝土结构中碱-二氧化硅反应引起的损伤. 在细观层面，混凝土被认为是由嵌入砂浆基质中的骨料组成的异质材料。碱-二氧化硅反应 (ASR) 的机械效应通过在骨料内部的几个局部点应用温度相关的本征应变来建模，混凝土的机械降解使用连续损伤模型进行建模，该模型能够再现复杂的 ASR破解网络。然后，每个宏观有限元的有效刚度张量和有效应力张量是通过对相应代表性体积元 (RVE) 的机械响应进行均匀化来计算的，从而避免在宏观尺度上使用现象学本构定律。宏观和中观尺度之间的收敛是通过迭代过程实现的。ASR 实验室标本的 2D 模型被分析为概念证明。该模型能够解释在宏观尺度上施加的载荷和在中尺度上的 ASR 产品扩展。结果表明，宏观应力状态会影响底层 RVE 内部的损伤方向。如果损伤在 RVE 内对齐，则有效刚度变为各向异性。