Contact dynamics as a nonsmooth discrete element method

The contact dynamics (CD) method is presented as a discrete element method for the simulation of nonsmooth granular dynamics at the scale of particle rearrangements where small elastic response times and displacements are neglected. Two central ingredients of the method are detailed: (1) The contact laws expressed as complementarity relations between the contact forces and velocities and (2) The nonsmooth motion involving velocity jumps with impulsive unresolved forces as well as smooth motion with resolved static forces. We show that a consistent description of the dynamics at the velocity level leads to an implicit time-stepping scheme together with an explicit treatment of the evolution of the particle configuration. We also discuss the intuitive features of the CD method with regard to collective phenomena involved in the multicontact dynamics of granular media: the role of the coarse-graining time δtδt, the precision issues and the interpretation of the restitution coefficients.