Energy‐Momentum‐Entropy consistent time integration of dissipative thermomechanical systems in an extended framework of GENERIC

Abstract

Energy‐Momentum‐Entropy (EME) time‐stepping schemes are distinguished by their numerical stable and robust behaviour, which stems from their ability to preserve the structure of the underlying system. In the context of closed dissipative thermomechanical systems, they are energy‐ and momentum‐preserving as well as entropy‐producing. In order to illustrate the qualification of the GENERIC framework for the design of EME integrators, a thermoviscoelastic double pendulum is chosen as discrete model problem to which the discrete gradient operator due to Gonzalez [1] is applied. The acronym GENERIC pertains to ‘General Equation for Non‐Equilibrium Reversible Irreversible Coupling’ and provides by design a thermodynamic admissible mathematical framework for the evolution equations of dissipative thermomechanic systems. This contribution enlightens the incorporation of constraints in the GENERIC formalism and the necessity of a Lyapunov function as stability criterion.