This work presents an adaptive hierarchical multiscale approach for modeling the trans-scale damage evolution in concrete. The problem domain represented by an adaptive hierarchical multiscale finite element (FE) model is decomposed into two regions, namely the macroscopic elastic region and the multiscale critical region prone to damage. The former is simulated only by macroscopic elements, while the latter is modeled by both macroscopic elements and the coupled-volume mesoscopic FE samples assigned to the integration points belonging to these macroscopic elements. A model update criterion is proposed to adaptively identify the multiscale critical region during the loading process. Innovatively, the coupled-volume meso‑samples are randomly generated on the fly when the macroscopic integration points are first identified to be included in the multiscale critical region. Concrete damage at the macroscale is quantitatively characterized based on its mesoscopic counterpart thanks to the proposed partition-based averaging scheme. The numerical simulations demonstrate that the presented approach can track and quantify concrete trans-scale damage evolution. Importantly, in the simulation of a 480 mm-length dog-bone-shaped specimen, the number of degrees of freedom and computational time are only 8.35 and 17.57% of those of the direct mesoscale simulation, respectively.

这项工作提出了一种自适应分层多尺度方法，用于模拟混凝土中的跨尺度损伤演化。由自适应分层多尺度有限元 (FE) 模型表示的问题域被分解为两个区域，即宏观弹性区域和容易损坏的多尺度临界区域。前者仅由宏观元素模拟，而后者由宏观元素和分配给属于这些宏观元素的积分点的耦合体积细观 FE 样本建模。提出了一种模型更新准则，以在加载过程中自适应地识别多尺度临界区域。创新地，当宏观积分点首次被识别为包含在多尺度临界区域中时，耦合体积细观样本随机生成。由于所提出的基于分区的平均方案，宏观尺度的混凝土损伤基于其细观对应物进行定量表征。数值模拟表明，所提出的方法可以跟踪和量化混凝土跨尺度损伤演化。重要的是，在模拟 480 mm 长的狗骨头形样本时，自由度数和计算时间分别仅为直接中尺度模拟的 8.35% 和 17.57%。由于所提出的基于分区的平均方案，宏观尺度的混凝土损伤基于其细观对应物进行定量表征。数值模拟表明，所提出的方法可以跟踪和量化混凝土跨尺度损伤演化。重要的是，在模拟 480 mm 长的狗骨头形样本时，自由度数和计算时间分别仅为直接中尺度模拟的 8.35% 和 17.57%。由于所提出的基于分区的平均方案，宏观尺度的混凝土损伤基于其细观对应物进行定量表征。数值模拟表明，所提出的方法可以跟踪和量化混凝土跨尺度损伤演化。重要的是，在模拟 480 mm 长的狗骨头形样本时，自由度数和计算时间分别仅为直接中尺度模拟的 8.35% 和 17.57%。