Inter-particle contact force calculation between non-spherical particles is a fundamental problem in discrete element method (DEM) with yet no conclusive solutions. This paper presents a general geometric force model (GFM) to calculate contact forces and contact areas between particles with smooth surfaces. Special attention is paid to accurate calculation of the original geometric parameters defined in Hertz theory instead of using the simplified models currently adopted. In particular, a recently proposed mathematical technique is implemented to reliably calculate the principal curvatures and principal directions. The new model is applied to super-quadric particles. In particular, the prediction of the model is compared to those by the simplified models and the accurate contact force database in a comprehensive way based on orientation discretization. The accurate contact force database is obtained by the sub-particle scale finite element method (FEM), and a script is developed to automate the set-up of the FEM model for different contact scenarios. The comparisons show that the new model is obviously more accurate than the simplified models, and the analysis depicts that the errors of the simplified models result from the simplified geometric parameters. Such errors also affect the prediction of the contact area, which is important to the transport properties of particle assemblies. The new force model can be used in DEM to improve the accuracy of the simulation, and can also be useful to the contact mechanics of non-spherical elements.

Keywords: Discrete element method, Contact force, Contact area, Finite element method, Non-spherical particles, Super-quadric particles

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