Multiscale modeling and extended finite element analysis of fracture processes in ceramics

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The reliable prediction of three dimensional microstructural crack initiation and propagation leading to macrocracks and eventually the failure of a structure is yet an unsolved problem. Since microcracks which initiate in highly stressed domains in ceramics usually have a size of the order of the micro constituents 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. In this project we develop an adaptive multiscale method for the accurate prediction of crack initiation and development in ceramics. The adaptive modeling technique used for this project will be a model expansion approach for areas of interest in order to make a numerical treatment feasible. The goal-oriented error estimators for quantities of interest for the combined model and discretization adaptive multiscale numerical method will be developed in the joint project by Prof. Dr.-Ing. Peter Wriggers and Prof. em. Dr.-Ing Dr.-Ing E.h. Dr h.c. mult. Erwin Stein with the key word “multiscale adaptivity”. Since the numerical simulation of highly complex and changing geometries such as advancing cracks using standard finite element techniques is not favorable due to the frequent need of remeshing, we employ the extended finite element method in combination with level set techniques to describe the geometry and to simulate propagating cracks. The computational model developed in this project will be validated by comparison of numerical results to experimental data.