On Energy-Entropy-Momentum integration methods for discrete thermo-visco-elastodynamics

This paper presents a novel Energy-Entropy-Momentum integration method (EEM) for the solution of thermo-visco-elastic discrete elements. These elements dissipate energy through heat that may flow toward the environment and may change their mechanical properties. EEM methods are second order accurate and thermodynamically consistent, namely, they discretely fulfill the laws of thermodynamics and can be interpreted as a natural generalization of Energy-Momentum methods. Their formulation depends strongly upon the choice of the thermodynamical variable: temperature, entropy or others. Unlike previous works, which propose EEM formulations based on entropy, this work focuses mainly on a novel EEM method that uses temperature. The method's performance is analyzed in terms of numerical accuracy and consistency related with thermodynamics and symmetries. The temperature-based formulation has more theoretical and numerical complexity, but presents important practical advantages respect to its entropy-based counterpart. Moreover, the numerical experiments suggest that it renders higher accuracy in both temperature and internal variables.