Time integration of nonsmooth mechanical systems using constraints at position, velocity and acceleration levels

The nonsmooth generalized-alpha method aims at the simulation of nonsmooth mechanical systems with elastic bodies. It is based on a separation of smooth and nonsmooth contributions in the equations of motion, so that the nonsmooth contributions are integrated using a consistent backward Euler scheme whereas smooth contributions can be integrated with a higher accuracy. The smooth and nonsmooth motions are nevertheless inherently coupled, so that the numerical solution can be affected by spurious numerical oscillations after the impacts. In this work, we show that these numerical oscillations can be fully eliminated provided that the equations defining the smooth motion involve the constraints at acceleration level with a suitable activation strategy. At every time step, the algorithm thus enforces the bilateral and active unilateral constraints at position, velocity and acceleration levels.