Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes

Abstract

The distinct element method (DEM) has proven to be reliable and effective in characterizing the behavior of particles in granular flow simulations. However, in the past, the influence of different force–displacement models on the accuracy of the simulated collision process has not been well investigated. In this work, three contact force models are applied to the elementary case of an elastic collision of a sphere with a flat wall. The results are compared, on a macroscopic scale, with the data provided by the experiments of Kharaz et al. (Powder Technol. 120 (2001) 281) and, on a microscopic scale, with the approximated analytical solution derived by Maw et al. (Wear 38 (1976) 101. The force–displacement models considered are: a linear model, based on a Hooke-type relation; a non-linear model, based on the Hertz theory (J. Reine Angew. Math. 92 (1882) 156) for the normal direction and the no-slip solution of the theory developed by Mindlin and Deresiewicz (Trans. ASME. Ser. E, J. Appl. Mech. 20 (1953) 327) for the tangential direction; a non-linear model with hysteresis, based on the complete theory of Hertz and Mindlin and Deresiewicz for elastic frictional collisions. All the models are presented in fully displacement-driven formulation in order to allow a direct inclusion in DEM-based codes. The results show that, regarding the values of the velocities at the end of collision, no significant improvements can be attained using complex models. Instead, the linear model gives even better results than the no-slip model and often it is equivalent to the complete Mindlin and Deresiewicz model. Also in the microscopic scale, the time evolution of the tangential forces, velocities and displacements predicted by the linear model shows better agreement with the theoretical solution than the no-slip solution. However, this only happens if the parameters of the linear model are precisely evaluated. The examination of the evolution of the forces, velocities and displacements during the collision emphasizes the importance of correct accounting for non-linearity in the contact model and micro-slip effects. It also demonstrates how these phenomena need to be considered into the model in order to perform deeper analyses on granular material in motion and, in general, for systems sensitive to the actual force or displacement. For these cases, more accurate models such as the complete Mindlin and Deresiewicz model should be addressed.