Review and extension of normal force models for the Discrete Element Method

For the simulation of dense granular systems the Discrete Element Method based on a soft-sphere approach is commonly used. In such simulations collisions between particles take a finite time. The equations of motion are applied for each particle and solved numerically. Therefore models for the forces acting between particles in contact need to be specified. In this paper the focus is set on normal contacts. Based on macroscopic and microscopic accessible parameters like coefficient of restitution, collision time, force, displacement and displacement rate a wide range of commonly used force schemes are reviewed. Results obtained from these commonly used models are compared to experimental data on collisions of different metal alloys, ice and marble as reported in literature. Due to obvious limitations extensions are presented. The new extended models based on linear and non-linear models are compared to experimental data and their accuracy and applicability are discussed.