A normal force-displacement model for contacting spheres accounting for plastic deformation: Force-driven formulation

In this paper, we present a simple and accurate model for the normal force-displacement (NFD) relation for contacting spherical particles, accounting for the effects of plastic deformation. This NFD model, based on the formalism of the continuum theory of elastoplasticity, is to be used in granular flow simulations involving thousands of particles; the efficiency of the model is thus a crucial property. The accuracy of the model allows for an accurate prediction of the contact force level in the plastic regime. In addition to being more accurate than previously proposed NFD models, the proposed NFD model also leads to more accurate coefficient of restitution that is a function of the approaching velocity of two particles in collision. The novelty of the present NFD model is the additive decomposition of the contact-area radius, and the correction of the curvature of the particles at the contact point due to plastic flow. The accuracy of the proposed model is validated against nonlinear finite element results involving plastic flow in both loading and unloading conditions.