Three-dimensional periodic Voronoi grain models and micromechanical FE-simulations of a two-phase steel

A three-dimensional model is proposed for modeling of microstructures. The model is based on the finite element method with periodic boundary conditions. The Voronoi algorithm is used to generate the geometrical model, which has a periodic grain structure that follows the original boundaries of the Voronoi cells. As an application, the model is used to model a two-phase ferrite/pearlite steel. It is shown that periodic cells with only five grains generate representative stress–strain curves.