length $L_c$ $(\frac{1}{L_c}= \frac{1}{2}[\frac{1}{r_i}+\frac{1}{r_j}]$, where $r_i$, $r_j$ are the radii of circles of the same area as the polygons). The direction of the elastic or normal force is perpendicular to the contact line of the polygons. The complete form of the normal force contains an elastic and damping contribution, whereas the tangential component is responsible for the friction.

Again, to bond the particles together it is necessary to introduce a cohesive force between neighboring polygons. For this purpose we introduce beams. The centers of mass of neighboring polygons are joined together with elastic beams that exert an attractive, restoring force but can break in order to model the fragmentation of the solid. Because of the randomness contained in the Voronoi tessellation, the lattice of beams is also random. The length, the cross-section and the moment of inertia of each beam are determined by the initial configuration of the polygons. The Young’s modulus of the beams and of the particles are considered to be independent of each other. The beams break according to a physical breaking rule, which takes into account the stretching and bending of the connection. The surface of the grains where beams are broken represent cracks. The energy 