An energy-momentum consistent method for transient simulations with mixed finite elements developed in the framework of geometrically exact shells

In this paper, a mixed variational formulation for the development of energy-momentum consistent (EMC) time-stepping schemes is proposed. The approach accommodates mixed finite elements based on a Hu-Washizu-type variational formulation in terms of displacements, Green-Lagrangian strains, and conjugated stresses. The proposed discretization in time of the mixed variational formulation under consideration yields an EMC scheme in a natural way. The newly developed methodology is applied to a high-performance mixed shell finite element. The previously observed robustness of the mixed finite element formulation in equilibrium iterations extends to the transient regime because of the EMC discretization in time. Copyright (C) 2016 John Wiley & Sons, Ltd.