A monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics

A new hybrid multi-time method for multi-time scales structural dynamics simulations is described. A monolithic method in a Schur dual domain decomposition framework is proposed and allows to consider heterogeneous time integrators with their own time discretization and possible large ratio between the time steps for each subdomain. In the proposed method, zero numerical dissipation is ensured at the interface. This implies that the global stability of the coupling method is governed by the stability of each time integrator without influence of the interface. For that purpose, velocity continuity is ensured in a weak sense at the interfaces, and time integrators (Newmark, HHT, Simo, Krenk, Verlet) are introduced in a unified framework (incremental velocity formulation). Furthermore, dynamics governing equations are introduced from a weak formulation in time. In other words, equilibrium equation is no more ensured in a strong sense at a given time step, but rather on average on a time interval. Some numerical examples illustrate the efficiency and the robustness of the proposed method, for ratio of time scales close to 1000 without any numerical dissipation at the interfaces.