International audienceThis paper studies numerical algorithms for the simulation of mechanical systems including rigid and flexible bodies, kinematic joints and frictionless contact conditions. The condition of impenetrability of the bodies in contact is expressed as a unilateral constraint, with the consequence that impacts and/or instantaneous changes in the velocities may arise in the dynamic response. When dynamic contacts are analyzed between elastic solids and structures, the gap velocity is necessarily discontinuous otherwise a non-physical penetration of the bodies would occur. When contacts between rigid bodies are studied, e.g., in multibody systems, impulsive reaction forces can also occur leading to an instantaneous change in the linear and angular momenta of each body. Standard schemes, such as the Newmark, HHT or generalized-α methods, are not consistent in these cases since the numerical response may artificially generate energy when a contact occurs. In order to analyze impact phenomena, nonsmooth time integration methods have been proposed in the literature and can be classified into two main groups, namely, event-driven schemes and time-stepping schemes. Event-driven schemes are accurate for the free flight smooth motions and are especially suitable for small multi-body systems with a limited number of events, but they become inefficient if frequent transitions occur in a short time. Time-stepping methods, such as Moreau–Jean scheme, have been proven to be convergent and robust even for a large number of events, and are extensively applied as the solution to nonsmooth system models
