How to Handle the Inelastic Collapse of a Dissipative Hard-sphere Gas with the Tc Model

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 deening 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 deened 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.