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Energy‐momentum‐entropy consistent numerical methods for large‐strain thermoelasticity relying on the GENERIC formalism
Author(s) -
Betsch Peter,
Schiebl Mark
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6089
Subject(s) - discretization , non equilibrium thermodynamics , formalism (music) , entropy (arrow of time) , statistical physics , mathematics , classical mechanics , state variable , numerical analysis , physics , mathematical analysis , quantum mechanics , thermodynamics , art , musical , visual arts
Summary In the present paper, structure‐preserving numerical methods for finite strain thermoelastodynamics are proposed. The underlying variational formulation is based on the general equation for nonequilibrium reversible‐irreversible coupling (GENERIC) formalism and makes possible the free choice of the thermodynamic state variable. The notion “GENERIC consistent space discretization” is introduced, which facilitates the design of Energy‐Momentum‐Entropy (EME) consistent schemes. In particular, three alternative EME schemes result from the present approach. These schemes are directly linked to the respective choice of the thermodynamic variable. Numerical examples confirm the structure‐preserving properties of the newly developed EME schemes, which exhibit superior numerical stability.