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

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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...