Energy‐momentum‐entropy consistent numerical methods for large‐strain thermoelasticity relying on the GENERIC formalism. (27th May 2019)

• Record Type: Journal Article
• Authors: Betsch, Peter; Schiebl, Mark
• Is Part Of: International journal for numerical methods in engineering. Volume 119:Number 12(2019)
• Page Start: 1216
• Page End: 1244
• Publication Date: 2019-05-27
• Subjects: structure‐preserving numerical methods -- thermoelasticity -- thermomechanical problems; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6089
• Languages: English
• ISSNs: 0029-5981

Abstract

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.