Multibody dynamics system with energy dissipation by hardening and softening plasticity

In this work we present a multibody dynamics system composed of geometrically exact nonlinear beams with inelastic behavior, representing flexible system components. The main focus of the work is to introduce advanced energy dissipation models using hardening and softening plasticity into such beam models and to show how they can also recover a vibration amplitude decay typical of viscous damping. The damping model is represented by the constitutive behavior of the flexible beam element chosen as an elasto-viscoplastic response with linear isotropic hardening and subsequent softening plasticity. The formulation is cast within the mixed variational framework, where the strong embedded discontinuity is introduced into displacement/rotation fields in the softening phase leading to localized plastic deformation. We also aim to ensure model capabilities to deliver results for long-term loading simulations, which is of interest for quantifying the risk of fatigue failure for such flexible system component. The corresponding numerical implementation combines the space discretization based on the finite element method with the time discretization based upon energy-conserving or energy-decaying integration schemes. The results of several numerical simulations are presented in the dynamics of flexible-rigid multi-body systems to illustrate a very satisfying performance of the proposed model.