Stochastic nature of granular particle interaction and its influence on the system dynamics

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The adequate description of particle interaction is a necessary prerequisite for the understanding of the dynamics of granular systems and, thus, for quantitatively correct (predictive) simulations. Particle systems of industrial scale consist in most cases of a very large number of particles which in turn interact in a complicated way, mainly because of their complex shape and their surface properties. Therefore, for the simulation of particle systems we have to compromize between an adequate number of particles and an adequate description of the grains' interaction: While the frequently applied model of spherical particles allows for the simulation of many thousand grains, this model certainly oversimplifies the interaction of realistic sharply edged particles. On the other hand, while possible in principle, highly sophisticated modeling of single grains and their complex interaction can be simulated only for small systems over short real times, even on very powerful computers. The present research project seeks a solution of the problem in stochastic modeling of the particle interaction which reflects the complex geometry of the particles (leading to complex interaction) in a statistical sense. If successful, this type of modeling will combine the computational efficiency of the simulation of spherical particles with the realistic description of particle interaction provided by more complex particle and particle interaction models.In the first funding period the research was focused on the particle interaction in normal direction. As main results we a) derived a mapping of particle geometry and surface texture to the stochastic properties of a fluctuating coefficient of normal restitution which may be used for highly efficient event-driven particle simulations. Moreover, b) we derived a fluctuating interaction force scheme for particle interaction in normal direction which can be used in time-stepping algorithms (DEM).The complete description of granular system dynamics requires also the knowledge of the quantities determining the tangential interaction of particles, that is, the coefficient of tangential restitution (for event-driven simulations) and the tangential component of the interaction force (for DEM simulations). The derivation of these quantities from the geometric shape properties of the particles and their surface properties will be subject of the present proposal. Moreover, we aim also to compute both components (normal and tangential) for particles whose shape is strongly non-spherical. Thus, we aim to a complete description of the interaction of granular particles by means of stochastic coefficients of restitution (normal and tangential) or stochastic forces, respectively. These characteristics shall be used to test the method of stochastic description by means of simple, however, technical relevant systems.