Exploring inelastic collisions using modified three-dimensional discontinuous deformation analysis incorporating a damped contact model

Most collisions in reality are partially inelastic. The consideration of energy dissipation is important in block collision phenomena. Therefore, damping should be introduced into three-dimensional discontinuous deformation analysis (3D DDA) to address the energy loss in collisions. A damped contact model based on linear spring-dashpot assumption is adopted and incorporated into 3D DDA. The derivation is first presented to obtain the formulae of the damped contact model in normal and shear directions, and then a single-degree-of-freedom example is modelled to validate the modified 3D DDA. Subsequently, inelastic collisions with unconstrained and fixed targets are carefully investigated. A relationship between viscous damping coefficient and coefficient of restitution (COR) is derived. Finally, viscous damping effect in contact is demonstrated by a freefall example of an assembly of blocks. The results suggest that the modified 3D DDA can model the collision behavior under given COR, and the damping effect may be significant and should be properly addressed in simulations.