The objective of this paper is to find the optimum number of hierarchy levels and their cell sizes for contact detection algorithms based on a versatile hierarchical grid data structure, for polydisperse particle systems with arbitrary distribution of particle radii. These algorithms perform as fast as O(N) for N particles, but the prefactor can be as large as N for a given system, depending on the algorithm parameters chosen, making a recipe for choosing these parameters necessary. We estimate theoretically the calculation time of two distinct algorithms for particle systems with various packing fractions, where the sizes of the particles are modelled by an arbitrary probability density function. We suggest several methods for choosing the number of hierarchy levels and the respective cell sizes, based on truncated power-law radii distributions with different exponents and widths. The theoretical estimations are then compared with simulation results for particle systems with up to one million particles. The proposed recipe for selecting the optimal hierarchical grid parameters allows to find contacts in arbitrarily polydisperse particle systems as fast as the commonly-used linked-cell method in purely monodisperse particle systems, i.e., extra work is avoided in presence of polydispersity. Furthermore, the contact detection time per particle even decreases slightly with increasing polydispersity or decreasing particle packing fraction. Dinant Krijgsman and Vitaliy Ogarko have contributed equally to this study.

We perform experiments and discrete element simulations on the dosing of cohesive granular materials in a simplified geometry. The setup is a simplified canister box where the powder is dosed out of the box through the action of a constant-pitch screw feeder connected to a motor. A dose consists of a rotation step followed by a period of rest before the next dosage. From the experiments, we report on the operational performance of the dosing process through a variation of dosage time, coil pitch and initial powder mass. We find that the dosed mass shows an increasing linear dependence on the dosage time and rotation speed. In contrast, the mass output from the canister is not directly proportional to an increase/decrease in the number coils. By calibrating the interparticle friction and cohesion, we show that DEM simulation can quantitatively reproduce the experimental findings for smaller masses but also overestimate arching and blockage. With appropriate homogenization tools, further insights into microstructure and macroscopic fields can be obtained. This work shows that particle scaling and the adaptation of particle properties is a viable approach to overcome the untreatable number of particles inherent in experiments with fine, cohesive powders and opens the gateway to simulating their flow in more complex geometries

Discrete element methods are extremely helpful in understanding the complex behaviors of granular media, as they give valuable insight into all internal variables of the system. In this paper, a novel discrete element method for performing simulations of granular media is presented, based on the minimization of the potential energy in the system. Contrary to most discrete element methods (i.e., soft-particle method, event-driven method, and non-smooth contact dynamics), the system does not evolve by (approximately) integrating Newtons equations of motion in time, but rather by searching for mechanical equilibrium solutions for the positions of all particles in the system, which is mathematically equivalent to locally minimizing the potential energy. The new method allows for the rapid creation of jammed initial conditions (to be used for further studies) and for the simulation of quasi-static deformation problems. The major advantage of the new method is that it allows for truly static deformations. The system does not evolve with time, but rather with the externally applied strain or load, so that there is no kinetic energy in the system, in contrast to other quasistatic methods. The performance of the algorithm for both types of applications of the method is tested. Therefore we look at the required number of iterations, for the system to converge to a stable solution. For each single iteration, the required computational effort scales linearly with the number of particles. During the process of creating initial conditions, the required number of iterations for two-dimensional systems scales with the square root of the number of particles in the system. The required number of iterations increases for systems closer to the jamming packing fraction. For a quasistatic pure shear deformation simulation, the results of the new method are validated by regular soft-particle dynamics simulations. The energy minimization algorithm is able to capture the evolution of the isotropic and deviatoric stress and fabric of the system. Both methods converge in the limit of quasi-static deformations, but show interestingly different results otherwise. For a shear amplitude of 4 %, as little as 100 sampling points seems to be a good compromise between accuracy and computational time needed.

Abstract. Discrete particle simulations of granular materials under 2D, isochoric, cyclic pure shear have been performed and are compared to a recently developed constitutive model involving a deviatoric yield stress, dilatant stresses and structural anisotropy. The original model shows the cyclic response qualitatively, but suffers from an arti¿cial drift in pressure. With a small modi¿cation in the de¿nition of the stress anisotropy and an additional limit-pressure term in the evolution equation for the pressure, it is able to show the transient as well as the limit cycles. The overall goal -beyond the scope of the present study -is to develop a local constitutive model that is able to predict real life, large scale granular systems.

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