An implicit–implicit multirate time integrator for multibody systems with unilateral constraints

Using a monolithic synchronous time-integration method to solve large multibody systems with unilateral constraints due to contact and impact is inefficient because nonsmooth behaviors limit the time steps to be very small. Considering the multiscale dynamics responses of the subdomains with and without nonsmooth behaviors, an implicit–implicit multirate time-integration method is proposed for multibody systems with unilateral constraints. A Newmark algorithm with large time steps is used in the subdomain without contact, while the Moreau-θ algorithm with small time steps is employed in the subdomain with contact. Different subdomains are coupled by enforcing the velocity and position continuity simultaneously at the interface at the macrotime step. A hybrid MPI–OpenMP parallel solution procedure is designed to improve the simulation efficiency. The accuracy and efficiency of the proposed method is validated by five numerical examples. Compared to the synchronous method, the parallel HMTI method can achieve up to a 56% reduction of computation time for a complex multibody system.