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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 …