Verification and validation of multiscale fracture in ceramics by discretization and model adaptivity

误差控制的二维可靠预测——更重要的是——三维微观结构裂纹的起裂和扩展，导致宏观裂纹，它们的发展路径，最终由脆性材料（如陶瓷）制成的结构部件的失效，仍然是一个广泛未解决的问题。由于脆性材料在高应力域中产生的微裂纹通常在形成后不久就具有晶粒数量级的大小，因此对大尺度结构中微裂纹向宏观裂纹发展的研究显然是一个多尺度现象，不能用单一尺度的数值分析来处理。它也不能用代表性体积元（RVEs）来解决。在这个项目中，我们将开发目标导向的误差估计量，用于组合模型和离散自适应多尺度数值方法，以便在规定的误差容限下预测陶瓷裂纹的起裂和发展。与模型简化方法相反，本项目使用的自适应建模技术将是一种从宏观到中观（和微观）尺度的模型扩展方法，以允许有效的数值处理。由于高度复杂和变化的几何形状（如推进裂缝）的数值模拟由于频繁的重新网格划分而不利于标准有限元技术，因此dr . ing将在耦合项目中开发一种与水平集技术相结合的适当扩展有限元方法。Stefan Löhnert用关键词“多尺度XFEM”。本文和耦合项目中建立的计算模型将通过自适应数值结果与实验数据的比较来验证，并将在耦合项目中进行测量。

The error-controlled reliable prediction of 2D - and more important - for 3D microstructural crack initiation and propagation leading to macrocracks, their progression paths and eventually the failure of a structural component made of a brittle material (such as ceramics) is yet a widely unsolved problem. Since microcracks initiated in highly stressed domains of brittle materials usually have a size of the order of crystal grains shortly after their formation, the investigation of microcracks developing to macrocracks in a large scale structure clearly is a multiscale phenomenon and cannot be treated in a single scale numerical analysis. It also cannot be solved by using representative volume elements (RVEs). In this project we are going to develop goal-oriented error estimators for quantities of interest for combined model-and-discretization-adaptive multiscale numerical methods in order to predict crack initiation and progression in ceramics with prescribed error tolerances. In contrast to model reduction approaches, the adaptive modeling technique used for this project will be a model expansion approach from macro to meso (and micro) scale to allow for an efficient numerical treatment. Since numerical simulations of highly complex and changing geometries, such as advancing cracks, with standard finite element techniques are not favorable due to frequent remeshing, an adequate extended finite element method in combination with level set techniques will be developed in the coupled project by Dr.-Ing. Stefan Löhnert with the key word „multiscale XFEM . The computational model developed in this and in the coupled project will be validated by comparison of adaptive numerical results with experimental data, which will also be measured in the coupled project.