A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation

Abstract

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. [S0021-8936(00)03102-0]

Numerical and experimental evaluation of the coefficient of restitution for repeated impacts

“…Further reductions of the computations might be obtained by replacing the nonlinear FE contact model with precalculated contact laws. Such a force-displacement model based on static FE analyses or experiments is proposed by Vu-Quoc and Zhang [22] and Vu-Quoc et al [23]. To check the efficiency of such a model, the computational costs of the precalculations have to be considered in detail but is however beyond the scope of this paper.…”

Implementation of the Jäger contact model for discrete element simulations

“…Investigators have recently modeled the contact problem as an elasto-plastic process [10,21]. VuQuoc and Zhang modeled the normal force-displacement relationship of elasto-plastic spheres [22,23] and, more recently, developed an algorithm for the tangential and normal interactions of elasto-plastic spheres [24,25]. Experimental validation of this advanced normal force model is provided in [26] for polymer spheres.…”

Moderately high speed impact of two identical spheres

“…Goldsimth [6] and Tatara [7] performed experiments and presented various relations between the coefficient of restitution and impact velocity. L. Vu-Quoc et al [8] developed a force-deformation model involving plastic deformation. Johnson [9], Thornton [10] and Stronge [11] proposed theoretical expressions to predict the coefficient of restitution for elastic-plastic impact.…”