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

• Applicant: Professor Dr.-Ing. Peter Wriggers
• Subject Area: Mechanics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 117309069

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.

• DFG Programme: Research Grants
• Participating Persons: Professor Dr.-Ing. Stefan Löhnert; Professor Dr.-Ing. Erwin Stein (†)