An elastoplastic contact force–displacement model in the normal direction: displacement–driven version

We present an elastoplastic normal force–displacement (NFD) model for spheres in collision. Among several possible applications of this model are the granular–flow simulations using a discrete–element method. The proposed NFD model is consistent with the formalism of the continuum theory of elastoplasticity, and is validated with nonlinear finite–element analyses. A key feature of this NFD model is the additive decomposition of the radius of the contact area into an elastic part and a plastic part. Further, the contact curvature is corrected, and the Hertzian contact mechanics generalized, to account for plastic deformation. The present displacement–driven version of the elastoplastic NFD model—whose force–driven version was presented by Vu–Quoc, Zhang and Lesburg in 1988—is developed particularly for granular flow simulations. Results of sphere–on–sphere collisions are discussed. In particular, the resulting coefficient of restitution varies with the incoming velocity. A comparison of the results obtained from the present NFD models with those from other models is given.