An accurate elasto-plastic frictional tangential force–displacement model for granular-flow simulations: Displacement-driven formulation

We present in this paper the displacement-driven version of a tangential force–displacement (TFD) model that accounts for both elastic and plastic deformations together with interfacial friction occurring in collisions of spherical particles. This elasto-plastic frictional TFD model, with its force-driven version presented in [L. Vu-Quoc, L. Lesburg, X. Zhang. An accurate tangential force–displacement model for granular-flow simulations: contacting spheres with plastic deformation, force-driven formulation, Journal of Computational Physics 196(1) (2004) 298–326], is consistent with the elasto-plastic frictional normal force–displacement (NFD) model presented in [L. Vu-Quoc, X. Zhang. An elasto-plastic contact force–displacement model in the normal direction: displacement-driven version, Proceedings of the Royal Society of London, Series A 455 (1991) 4013–4044]. Both the NFD model and the present TFD model are based on the concept of additive decomposition of the radius of contact area into an elastic part and a plastic part. The effect of permanent indentation after impact is represented by a correction to the radius of curvature. The effect of material softening due to plastic flow is represented by a correction to the elastic moduli. The proposed TFD model is accurate, and is validated against nonlinear finite element analyses involving plastic flows in both the loading and unloading conditions. The proposed consistent displacement-driven, elasto-plastic NFD and TFD models are designed for implementation in computer codes using the discrete-element method (DEM) for granular-flow simulations. The model is shown to be accurate and is validated against nonlinear elasto-plastic finite-element analysis.