In the first approach, only those model grains could be algorithmically generated which have either 100% density or a defined porosity. The pores are spherical and monodisperse. The algorithm was then extended in such a way that now also hard inclusions in the grains can be generated instead of the pores. The inclusions are again spherical and monodisperse. Thus, the influence of such inclusions on the failure behavior of the grains can also be analyzed in the numerical simulations. Instead of (infinitely) hard inclusions, it is also possible to simulate crystalline inclusions in the matrix material. For this purpose, the properties of the model including the bonds are locally varied.

In addition, an approach was developed to allow cracks in the grains to be taken into account in the modeling. For this purpose, a predetermined proportion of the internal connections (bonds), which cause the cohesion of the grain, are dissolved before the actual comminution simulation begins. This corresponds to crack damage within the grain before the comminution process. The figure next to this text shows a schematic comparison of the different models.

The effect that either pores and cracks or hard or crystalline inclusions have on the fracture force of the model grains was systematically evaluated across all simulations. The result is shown in the figure next to this text. The simulations show that the influence of porosity is the greatest. Already at 5% porosity, the fracture force decreases on average to 70% of the initial value. At 10% porosity, the fracture force is only half the reference value for a completely dense grain. Compared to the pores, the effect due to crystalline inclusions is somewhat smaller, followed by the influence due to hard inclusions. 10% of hard inclusions lead to about two thirds of the original breaking strength. The influence of cracks is the smallest. 10% cracks in an otherwise dense grain lead to about 70% of the reference breaking load.

According to a theoretical model by Katchanov, which argues for an increase in stress due to surface porosity, the relative fracture force should be proportional to the volume fraction within the grain, i.e., for example, at 10% porosity it should drop to 90% of the fracture force of a dense grain. However, the simulations show that the effect of porosity is much larger and nonlinear.

Analogous to the evaluation above, the specific comminution energy requirement was also plotted as a function of specific surface area for the vertical roller mill. Here, the torque acting on the roller due to the comminution of the grains was used to calculate the comminution energy. The specific surface area was again determined algorithmically by analyzing the instantaneous total surface area of the grain fragments. The result essentially shows a decreasing specific comminution energy requirement with increasing porosity for a given specific surface area. This is consistent with the result obtained for the cases of simple compression or shear showing decreasing breaking force with increasing porosity.