  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.
