by a Voronoi cellular structure. The Voronoi construction is a random tessellation of the plane into convex polygons. This is obtained by putting a random set of points onto the plane and then assigning to each point that part of the plane which is nearer to it than to any other point. One advantage of the Voronoi tessellation is that the number of neighbors of each polygon is limited which makes the computer code faster and allows us to simulate larger systems. In our case, the initial configuration of the polygons was constructed using a vectorizable random lattice, which is Voronoi construction with slightly reduced disorder [@rand_lattic]. First, the Voronoi tessellation of a square is performed, and then a circular disc with smooth surface is cut out.

In the model the polygons are rigid bodies. They are neither breakable nor deformable, but they can overlap when pressed against each other. This overlap represents local deformations of the grains. Usually the overlapping polygons have two intersection points which define the contact line. In order to simulate the elastic contact force, we introduce a repulsive force between touching polygons. This force is proportional to the overlapping area $A$ divided by a characteristic 