Statistical analysis of stress and deformation state in polycrystalline aggregates with a large number of grains

The present thesis is focused on the numerical modeling and simulation of polycrystalline structures with the macroscopic dimensions and realistic boundary conditions. The microstructure of polycrystals is represented by the randomized three-dimensional Voronoi diagram assuming the convexity of grains and faces. In order to achieve the macroscopic dimensions of structures, a large number of grains must be calculated and generated within the geometrical model. On the other hand, several assumptions such as the simple grain material model, grains interaction approach, etc. should be introduced to reduce the computational costs. The developed software framework generates the geometrical and finite element models of a polycrystal considering arbitrary shape of sample, thickness of the grain boundary layer, number of grains, and other geometrical properties.