Adaptive probabilistic modeling of localization, failure and size effect of quasi-brittle materials

在结构材料中，具有随机性质的细尺度特征的存在会极大地影响材料的刚度、极限强度和断裂过程区的大小等性能。不幸的是，如果在数值分析中仔细考虑所有微观尺度的相互作用，甚至是确定性地考虑，通常会出现巨大规模和复杂性的计算模型。为了在微观结构中捕捉损伤过程，同时将问题的复杂性降低到可管理的水平，我们建议在单个模型中结合并利用自适应有限元法和随机场模拟的先进技术。开发的模型将使我们能够逐步放大到材料结构的精细尺度，仅在关键区域局部增加计算需求。在这些地区，随机波动场描述的材料的非均质性对于微裂纹的发展、变形的局部化和随后的宏观裂纹的形成至关重要。这种采用自适应和随机方法的跨学科方法将使我们能够捕获其复杂性的尺寸效应现象，并为具有准脆性材料的大型结构的鲁棒分析和可靠性评估提供计算工具，这是目前可用的方法和工具迄今为止无法实现的……

In structural materials, the presence of fine-scale features with random nature can greatly affect material properties such as stiffness, ultimate strength and the size of the fracture process zone. Unfortunately, if all microscale interactions are minutely taken into account in the numerical analysis, even deterministically, computational models of enormous size and complexity typically emerge. In order to capture the damage process in the microstructure while keeping the complexity of the problem down to manageable levels, we propose to combine and utilize the advanced techniques of the adaptive finite element method and of random field simulations in an single model. The developed model will allow us to gradually zoom into the fine scale of the material structure with locally inctreased computational demand in critical regions only. In these areas, the heterogeneity of the material described by randomly fluctuating fields is essential for the development of microcracks, localization of deformation and the subsequent formation of macrocracks. This interdisciplinary approach employing methods of adaptivity and stochastics will allow us to capture the size effect phenomena in its complexity and to provide a computational tool for robust analysis and reliability assessment of large structures with quasi-brittle materials that is hitherto not possible with the currently available methods and tools...