Coefficient of restitution and linear-dashpot model revisited

With the assumption of a linear-dashpot interaction force, the coefficient of restitution, epsilon(0)(d)(k, gamma), can be computed as a function of the elastic and dissipative material constants, k and gamma by integrating Newton's equation of motion for an isolated pair of colliding particles. If we require further that the particles interact exclusively repulsive, which is a common assumption in granular systems, we obtain an expression epsilon(d)(k, gamma) which differs even qualitatively from the known result epsilon(0)(d)(k, gamma). The expression epsilon(d)(k, gamma) allows to relate Molecular Dynamics simulations to event-driven Molecular Dynamics for a widely used collision model.