Discrete element simulation of super-ellipse systems

Abstract

There are two key problems in discrete element simulations of super-ellipse systems. One is the determination of contact point, and the other is the mechanical equilibrium with almost zero kinetic energy. The Newton–Raphson method or its modification used to determine the contact point is only sufficiently numerically stable for suitable deformation parameters, and the state of all particles with almost zero velocity is difficult to reach. In this paper, a novel contact detection method for all deformation parameters is used to determine the contact point, and a rolling resistance model is used to dissipate rotational kinetic energy for mechanical equilibrium. A series of tests are investigated to verify the validity of this method. For random packing under gravity, no residual kinetic energy (or almost 0) is observed, and the force that acts on the bottom is equal to the gravity, meaning that the system reaches mechanical equilibrium. After equilibrium, the process of hopper discharge, in which the kinetic energy remains stable for shape and material parameters, is also modeled. Furthermore, direct shear tests at different shear rates are simulated, and the results meet the rate independence, which is in agreement with experiments. The method is also suitable for investigation of sound propagation properties in the super-ellipse system, and the velocities of compressional and shear waves are calculated in uniaxial compression tests. In addition to super-ellipses, the method can be applied to other particle systems once the shape functions are given. After reaching the equilibrium state, a hole is opened at the bottom, and its width is 15 times the width of the particle. Figure shows the snapshots of particle flow at different times. Then, 0.372 seconds later, after 136 particles drop through the hole, a semi-circular structure of force arch occurs, and the particle flow stops. These findings are different from the results of the previous research and show that the shape has a significant effect on the flow rate.