How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model

TL;DR

This paper introduces the TC model, a modification of the inelastic hard sphere model that incorporates contact duration to prevent inelastic collapse and allow for multiparticle contacts, enabling simulations of complex granular systems.

Contribution

The paper proposes the TC model, extending the inelastic hard sphere model by including a contact duration parameter to address its main drawbacks.

Findings

Prevents inelastic collapse in simulations.

Allows modeling of multiparticle contacts.

Enables simulations of static and dynamic granular systems.

Abstract

The inelastic hard sphere model of granular material is simple, easily accessible to theory and simulation, and captures much of the physics of granular media. It has three drawbacks, all related to the approximation that collisions are instantaneous: 1) The number of collisions per unit time can diverge, i.e. the ``inelastic collapse'' can occur. 2) All interactions are binary, multiparticle contacts cannot occur and 3) no static limit exists. We extend the inelastic hard sphere model by defining a duration of contact t_c such that dissipation is allowed only if the time between contacts is larger than t_c. We name this generalized model the ``TC model'' and discuss it using examples of dynamic and static systems. The contact duration used here does not change the instantaneous nature of the hard sphere contacts, but accounts for a reduced dissipation during ``multiparticle contacts''. Kinetic and elastic energies are defined as well as forces and stresses in the system. Finally, we present event-driven numerical simulations of situations far beyond the inelastic collapse, possible only with the TC model.