Structure-Preserving Discretization in the Framework of a Discrete Model Problem for Large-Strain Thermo-Viscoelasticity

Valdés, Vanessa K.; Schiebl, Mark; Betsch, Peter

doi:10.23967/wccm-eccomas.2020.136

Cited by 1 publication

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“…[4,5]). Previous work has shown that the midpoint rule as implicit integrator is only partially structure-preserving in dependence of the choice of the thermodynamic variable (compare [6][7][8]). The energy, which has proven to be a suitable numerical stability criterion for isothermal elastic systems is not adequate for the assessment of a dissipative thermomechanic system's stability.…”

Section: Energy-momentum-entropy Consistent Discretizationmentioning

confidence: 99%

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

Valdes y Beck,

Betsch

2023

Proc Appl Math and Mech

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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.

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