Modeling of materials at a microstructural level is of primary interest in this work. The modeling is approached by the Finite Element Method (FEM), which is commonly used to solve problems in continua.

At this stage a periodic micromechanical model based on the Voronoi algorithm has been developed. The algorithm uses a set of points to generate polygons. By considering the nearest neighbors of every node and dividing the distance between those nodes in half, polygons are formed. If the points are randomly distributed, a set of irregular polygons is created, which in the model represents a microstructure. In Figure 1a, a generated grain structure, containing 50 grains, is shown. Note that the grain structure is periodic and has 3 pairs of equivalent edges, where the small circles indicate the corners between the edges. When the periodic cell is loaded by periodic boundary conditions only a representative part of the material has to be modeled.

The use of FEM requires meshing of the periodic cell, which is done by dividing each grain into triangular elements, in Figure 1b the previous periodic cell has been meshed.

Currently, the micromechanical model is being used to model a two phase ferrite/pearlite steel with different volume fractions of the constituents.

Figure 1: (a) Periodic cell representing a microstructure generated by the Voronoi algorithm, note that the cell has three pairs of equivalent edges, indicated by the circles;  (b) the same periodic cell meshed by triangular elements for enabling use of the finite element method.