Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts

The article is devoted to the study of higher order time integration methods for multibody systems with unilateral constraints. After a brief presentation of the mathematical modeling of nonsmooth multibody systems, several estimates on the local error of consistency of the Moreau time-stepping scheme are given. Based on these estimates, an attempt at an adaptive time-step strategy is presented with academic examples. Finally, higher order event-capturing methods are designed by coupling implicit Runge–Kutta schemes and Moreauʼs time-stepping scheme.