The dynamics of granular materials is examined by a Discrete Element Method. Other numerical methods available in the literature to address this problem include Non-Smooth Contact Dynamics and Event-Driven Methods, that both represent non-smooth methods. In DEM, the contact is regularized by allowing the solid bodies to slightly overlap. The geometric overlap measure is used to compute the contact forces and the whole contact is integrated in time, which assumes that time steps smaller than the contact time are employed. As for classical DEM, our variant relies on an explicit time integration of the Newton's equations and standard contact laws usually involving elastic rebound and viscous dissipation in the normal direction, plus Coulomb friction in the tangential direction. We believe that the two nice assets of our DEM variant implemented in our code Grains3D are the following:
- slightly shrink the two objects,
- use the GJK algorithm,
- reconstruct the geometric contact features.
Fig 1. Allowed overlapping between two particles in the DEM spirit to compute the contact forces
Fig 2. 4 iterations of the GJK algorithm to compute the minimal distance between a point and a convex object (which is a generalization of the problem of the minimal distance between 2 convex shapes)
Fig 3. The contact detection strategy in Grains3D: a combination of geometric transformations and the GJK algorithm