An Energy-Dissipative Momentum-Conserving Time Integration Algorithm for Viscoplastic Hyperelastic Models Based on the Variational Updates Framework

Traditional time integration algorithms for finite-element discretization are numerically stable only for linear models. To overcome that drawback, a new class of "Energy Momentum Conserving Algorithms" or EMCA and ``Energy-Dissipative Momentum-Conserving'' or EDMC algorithms, verifying the conservation/dissipation laws in the non-linear range, was recently developed. They consist in a mid-point scheme with an adequate evaluation of the internal forces, which strongly assume the existence of an energy potential. Following the variational
visco-plastic constitutive updates formalism, a general energy-dissipative momentum-conserving algorithm for hyperelastic-based formulation is proposed. The main feature of this variational formulation is that the stress tensor always derives from an incremental potential, even if plastic deformations occur, allowing to use it in the above integration algorithms.