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Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking
[Formulation en transformation finie du principe d’écart d’équilibre discret  : application à la régularisation mécanique pour le suivi de mouvement]
Comptes Rendus. Mécanique, Volume 351 (2023), pp. 429-458.

Le principe de l’écart d’équilibre offre un bon compromis entre la robustesse et la précision pour la régularisation du suivi du mouvement, car il impose simplement que le mouvement suivi corresponde à celui d’un corps se déformant sous l’effet de charges arbitraires. Cet article présente une extension du principe de l’écart d’équilibre dans le cadre des grandes déformations, un nouveau terme de régularisation pour contrôler les tractions de surface, les deux dans le contexte du suivi de mouvement par éléments finis, et une reformulation «  problème inverse  » cohérente du problème de suivi de mouvement avec régularisation mécanique. Les performances de suivi de la méthode proposée, avec une résolution de déplacement allant jusqu’à la taille du pixel de l’image, sont démontrées sur des images synthétiques représentant divers mouvements avec différents rapports signal-sur-bruit.

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The equilibrium gap principle offers a good trade-off between robustness and accuracy for regularizing motion tracking, as it simply enforces that the tracked motion corresponds to a body deforming under arbitrary loadings. This paper introduces an extension of the equilibrium gap principle in the large deformation setting, a novel regularization term to control surface tractions, both in the context of finite element motion tracking, and an inverse problem consistent reformulation of the tracking problem. Tracking performance of the proposed method, with displacement resolution down to the pixel size, is demonstrated on synthetic images representing various motions with various signal-to-noise ratios.

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DOI : 10.5802/crmeca.228
Keywords: Motion tracking, Mechanical regularization, Equilibrium gap principle, Finite element method, Inverse problems
Mot clés : Suivi de mouvement, Régularisation mécanique, Principe de l’écart d’équilibre, Méthode des éléments finis, Problèmes inverses

Martin Genet 1, 2

1 Laboratoire de Mécanique des Solides, École Polytechnique/IPP/CNRS, Palaiseau, France
2 Équipe MΞDISIM, INRIA, Palaiseau, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Martin Genet. Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 429-458. doi : 10.5802/crmeca.228. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.228/

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