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The Double Generator Boundary Augmented bracket structure: a structure-preserving space-time integration framework for coupled thermo-visco-elastodynamics
[La Double Generator Boundary Augmented bracket structure : un cadre d’intégration espace-temps préservant la structure, pour la thermo-visco-élastodynamique couplée]
Benjamin Georgette1 orcid  ; David Dureisseix1 orcid ; Anthony Gravouil1 orcid
1INSA Lyon, CNRS, LaMCoS, UMR5259, 69621 Villeurbanne, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 333-364

The Double Generator Boundary Augmented bracket structure is a double generator bracket formulation, tailored to model continuum thermodynamics. Based on the idea of bracket generated formulations, this framework encompasses balance principles and thermodynamics laws within a unique expression. The present paper develops the methodology to derive this structure from classical equations of continuum thermodynamics for two examples. We consider first a unidimensional small strains generalized standard material, with a general quadratic dissipation potential. Then, we consider the example of large strain thermo-visco-elastodynamics, within the multisymplectic framework. We derive, for the first time, a multisymplectic Poisson bracket for thermo- (visco)-elastodynamics. Eventually, both formulations are shown to recover exactly balance principles and thermodynamics laws.

This paper sets grounds necessary to develop variational integrators from the Double Generator Boundary Augmented bracket structure.

La Double Generator Boundary Augmented bracket structure est une formulation à crochets à deux générateurs pour la thermodynamique des milieux continus. S’appuyant sur l’idée des formulations générées par crochets, elle regroupe les principes de conservation et les lois de la thermodynamique en une unique expression. L’article proposé présente la méthodologie à suivre afin d’obtenir cette structure pour deux exemples, à partir des équations classiques de la thermodynamique des milieux continus. Nous considérons, tout d’abord, un matériau standard généralisé unidimensionnel sous l’hypothèse des petites perturbations, dont le potentiel de dissipation est quadratique. Nous étudions ensuite la thermo-visco-élastodynamique en grandes transformations, dans le cadre multisymplectique. De cet exemple est obtenu, pour la première fois, un crochet de Poisson multisymplectique pour la thermo-(visco)-élastodynamique. Enfin, nous démontrons que les deux formulations contiennent exactement les principes de conservation ainsi que les lois de la thermodynamique.

Cet article pose les fondations nécessaires pour développer des intégrateurs variationnels depuis la DGBA bracket structure.

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DOI : 10.5802/crmeca.357
Keywords: Variational principle, generalized standard materials, thermo-visco-elastodynamics, large strains
Mots-clés : Principe variationnel, matériaux standards généralisés, thermo-visco-élastodynamique, grandes transformations

Benjamin Georgette  1   ; David Dureisseix  1   ; Anthony Gravouil  1

1 INSA Lyon, CNRS, LaMCoS, UMR5259, 69621 Villeurbanne, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Benjamin Georgette; David Dureisseix; Anthony Gravouil. The Double Generator Boundary Augmented bracket structure: a structure-preserving space-time integration framework for coupled thermo-visco-elastodynamics. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 333-364. doi: 10.5802/crmeca.357
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     journal = {Comptes Rendus. M\'ecanique},
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     publisher = {Acad\'emie des sciences, Paris},
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