Energy-momentum-consistent simulation of planar geometrically exact beams in a port-Hamiltonian framework

We propose a new, port-Hamiltonian formulation for the highly nonlinear dynamics of planar geometrically exact beams, which are amenable to arbitrary large deformations and rotations. A structure-preserving spatial and temporal discretization procedure - using mixed finite elements and second-order time-stepping methods - is proposed. It is observed that the present approach is objective, locking-free and provides an exact discrete representation of the energy and angular momentum balance. By comparing the approach to a classical displacement-based scheme from the literature it is shown that the port-Hamiltonian formulation paves new ways for the design of energy-momentum schemes in computational mechanics. Numerical examples underline the applicability to flexible multibody systems and beneficial numerical performance. AMS (2020) classification: 65M60, 65P10, 70E55, 70K99, 74K10, 93C20.