Comptes Rendus
Article de recherche
Mechanics-guided data-enhanced kinematic models for time-resolved DVC
[Modèles cinématiques améliorés par les données et guidés par la mécanique pour la corrélation d’images volumiques résolue en temps]
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 495-525

X-ray Computed Tomography (XCT) combined with Digital Volume Correlation (DVC) enables for internal displacement and strain measurements in deforming materials. The long acquisition time of tomographic scans restricts analyses to a few static loading steps and prevents from time-dependent or nonlinear mechanism quantification. Projection-based DVC (P-DVC) addresses this limitation by exploiting projections acquired during continuous loading, providing substantially higher temporal sampling.

This study assesses a spacetime framework of projection-enhanced DVC for the in situ investigation of a 3D-printed lattice. Global DVC displacement fields are used to construct reduced spatial bases, namely, (i) a pure data-driven basis, (ii) a mechanics-only basis derived from an elastic compression solution, and (iii) a hybrid mechanics-data basis combining both. P-DVC then exploits the projections to identify the temporal amplitudes associated with these modes, thereby reconstructing the time-resolved kinematics with a resolution of 3.7 s, nearly two orders of magnitude faster than conventional 3D-to-3D DVC.

Nonlinear mechanisms were detected ahead of their clear expression in tomographic reconstructions. The hybrid reduced-order approach provided interpretable kinematic fields while preserving the predictive accuracy of data-driven strategies. The projection-enhanced DVC framework thus enabled for temporally dense and spatially resolved in situ measurements, providing the type of rich datasets required for the identification and learning of complex constitutive models.

La tomographie par rayons X (XCT) combinée à la corrélation d’images volumiques (DVC) permet la mesure de champs de déplacements et des déformations internes dans les matériaux sous chargement. Le temps d’acquisition long des scans tomographiques limite les analyses à quelques pas de chargement statique et empêche la quantification des mécanismes dépendant du temps ou non linéaires. La DVC basée sur les projections (P-DVC) pallie cette limitation en exploitant les projections acquises lors d’un chargement continu, offrant un échantillonnage temporel nettement supérieur.

Cette étude évalue un cadre spatio-temporel de DVC augmentée par les projections pour l’étude in situ d’un métamatériau imprimé en 3D. Les champs de déplacement mesurés par la DVC sont utilisés pour construire des bases spatiales réduites, à savoir : (i) une base purement basée sur les données, (ii) une base purement mécanique dérivée d’une solution de compression élastique, et (iii) une base hybride mécanique-données combinant les deux. La P-DVC exploite ensuite les projections pour mesurer les amplitudes temporelles associées à ces modes, reconstruisant ainsi la cinématique temporelle avec une résolution de 3,7 s, soit près de deux ordres de grandeur plus rapide que la DVC conventionnelle.

Des mécanismes non linéaires ont été détectés avant même leur expression claire dans les reconstructions tomographiques. L’approche hybride d’ordre réduit fournit des champs cinématiques interprétables tout en préservant la cohérence prédictive des stratégies basées sur les données. Le cadre de la DVC augmentée par les projections a ainsi permis des mesures in situ temporellement denses et spatialement résolues, fournissant des données riches nécessaires à l’identification et à l’apprentissage de modèles de comportement complexes.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmeca.370
Keywords: In situ tests, Digital Volume Correlation (DVC), projection-based DVC (P-DVC), spacetime analyses, model reduction
Mots-clés : Tests in situ, corrélation d’images volumiques (DVC), DVC basée sur les projections (P-DVC), analyses spatio-temporelles, réduction de modèles

Pierre Latil  1   ; Malo Valmalle  1   ; Benjamin Smaniotto  1   ; Clément Jailin  1   ; François Hild  1

1 Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS–Laboratoire de Mécanique Paris-Saclay, 91190 Gif-sur-Yvette, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Pierre Latil; Malo Valmalle; Benjamin Smaniotto; Clément Jailin; François Hild. Mechanics-guided data-enhanced kinematic models for time-resolved DVC. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 495-525. doi: 10.5802/crmeca.370
@article{CRMECA_2026__354_G1_495_0,
     author = {Pierre Latil and Malo Valmalle and Benjamin Smaniotto and Cl\'ement Jailin and Fran\c{c}ois Hild},
     title = {Mechanics-guided data-enhanced kinematic models for time-resolved {DVC}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {495--525},
     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {354},
     doi = {10.5802/crmeca.370},
     language = {en},
}
TY  - JOUR
AU  - Pierre Latil
AU  - Malo Valmalle
AU  - Benjamin Smaniotto
AU  - Clément Jailin
AU  - François Hild
TI  - Mechanics-guided data-enhanced kinematic models for time-resolved DVC
JO  - Comptes Rendus. Mécanique
PY  - 2026
SP  - 495
EP  - 525
VL  - 354
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.370
LA  - en
ID  - CRMECA_2026__354_G1_495_0
ER  - 
%0 Journal Article
%A Pierre Latil
%A Malo Valmalle
%A Benjamin Smaniotto
%A Clément Jailin
%A François Hild
%T Mechanics-guided data-enhanced kinematic models for time-resolved DVC
%J Comptes Rendus. Mécanique
%D 2026
%P 495-525
%V 354
%I Académie des sciences, Paris
%R 10.5802/crmeca.370
%G en
%F CRMECA_2026__354_G1_495_0

[1] Eric Maire; Philip John Withers Quantitative X-ray tomography, Int. Mater. Rev., Volume 59 (2014) no. 1, pp. 1-43 | DOI

[2] Brian K Bay; Tait S Smith; David P Fyhrie; Malik Saad Digital volume correlation: three-dimensional strain mapping using X-ray tomography, Exp. Mech., Volume 39 (1999) no. 3, pp. 217-226

[3] B. K. Bay Methods and applications of digital volume correlation, J. Strain Anal. Eng. Des., Volume 43 (2008), pp. 745-760 | DOI

[4] Ante Buljac; Clément Jailin; Arturo Mendoza; Jan Neggers; Thibault Taillandier-Thomas; Amine Bouterf; Benjamin Smaniotto; François Hild; Stéphane Roux Digital volume correlation: review of progress and challenges, Exp. Mech., Volume 58 (2018) no. 5, pp. 661-708 | DOI

[5] J-Y Buffiere; E Maire; J Adrien; J. P. Masse; E Boller In situ experiments with X ray tomography: an attractive tool for experimental mechanics, Exp. Mech., Volume 50 (2010) no. 3, pp. 289-305 | DOI

[6] Lara Mazy; Greet Kerckhofs A review of in-situ mechanical testing combined with X-ray microfocus computed tomography: application and current challenges for biological tissues, Tomogr. Mater. Struct, Volume 8 (2025), 100062, 12 pages

[7] Avinash C Kak; Malcolm Slaney Principles of computerized tomographic imaging, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, 2001 | Zbl

[8] Eric Maire; Christophe Le Bourlot; Jérôme Adrien; Andreas Mortensen; Rajmund Mokso 20 Hz X-ray tomography during an in situ tensile test, Int. J. Fract., Volume 200 (2016) no. 1, pp. 3-12

[9] Eric Maire; A Owen; J-Y Buffiere; Philip J Withers A synchrotron X-ray study of a Ti/SiCf composite during in situ straining, Acta Mater., Volume 49 (2001) no. 1, pp. 153-163 | DOI

[10] Francisco García-Moreno; Paul Hans Kamm; Tillmann Robert Neu; Felix Bülk; Mike Andreas Noack; Mareike Wegener; Nadine von der Eltz; Christian Matthias Schlepütz; Marco Stampanoni; John Banhart Tomoscopy: Time-resolved tomography for dynamic processes in materials, Adv. Mater., Volume 33 (2021) no. 45, 2104659, 13 pages

[11] EA Zwanenburg; MA Williams; Jason M Warnett Review of high-speed imaging with lab-based x-ray computed tomography, Meas. Sci. Technol., Volume 33 (2021) no. 1, 012003, 18 pages

[12] Clément Jailin; Ante Buljac; Amine Bouterf; François Hild; Stephane Roux Fast 4D tensile test monitored via X-CT: Single projection based Digital Volume Correlation dedicated to slender samples, J. Strain Anal. Eng. Des., Volume 53 (2018) no. 7, pp. 473-484

[13] Viktor Kosin; Amélie Fau; Clément Jailin; Benjamin Smaniotto; Thomas Wick; François Hild A projection-based approach to extend digital volume correlation for 4D spacetime measurements, Comptes Rendus. Mécanique, Volume 351 (2023) no. G2, pp. 265-280 | DOI

[14] Ana Mandić; Viktor Kosin; Clément Jailin; Zvonimir Tomičević; Benjamin Smaniotto; François Hild Damage detection in a polymer matrix composite from 4D displacement field measurements, Materials, Volume 16 (2023) no. 18, 6300, 28 pages

[15] Ana Vrgoč; Viktor Kosin; Benjamin Smaniotto; Clément Jailin; Zvonimir Tomičević; François Hild 4D full-field measurements over the entire loading history: Evaluation of different temporal interpolations, Coupled Syst. Mech., Volume 12 (2023) no. 6, pp. 503-517

[16] V Kosin; B Smaniotto; M Tarantino; A Fau; T Wick; F. Hild Quantifying damage in an AlSi10Mg porous metamaterial through projection-enhanced DVC, Meas. Sci. Technol., Volume 36 (2025) no. 7, 075002, 23 pages

[17] A. Mandic; V. Kosin; B. Smaniotto; L. Salvi; M. G. Tarantino; F. Hild Damage quantification in an AlSi10Mg cellular metamaterial using 4D measurements, Meas. Sci. Technol., Volume 36 (2025) no. 8, 085017, 16 pages

[18] Katia Bertoldi; Vincenzo Vitelli; Johan Christensen; Martin Van Hecke Flexible mechanical metamaterials, Nat. Rev. Mater., Volume 2 (2017) no. 11, pp. 1-11

[19] Xiaoyu Zheng; William Smith; Julie Jackson; Bryan Moran; Huachen Cui; Da Chen; Jianchao Ye; Nicholas Fang; Nicholas Rodriguez; Todd Weisgraber et al. Multiscale metallic metamaterials, Nat. Mater., Volume 15 (2016) no. 10, pp. 1100-1106 | DOI

[20] Tarasankar DebRoy; Huiliang L Wei; James S Zuback; Tuhin Mukherjee; John W Elmer; John O Milewski; Allison Michelle Beese; A de Wilson-Heid; Amitava De; Wei Zhang Additive manufacturing of metallic components — Process, structure and properties, Prog. Mater. Sci., Volume 92 (2018), pp. 112-224 | DOI

[21] J. Y. Buffière; E. Maire; J. Adrien; J. P. Masse; E. Boller In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics, Exp. Mech., Volume 50 (2010) no. 3, pp. 289-305 | DOI

[22] Wim Van Aarle; Willem Jan Palenstijn; Jeroen Cant; Eline Janssens; Folkert Bleichrodt; Andrei Dabravolski; Jan De Beenhouwer; K Joost Batenburg; Jan Sijbers Fast and flexible X-ray tomography using the ASTRA toolbox, Opt. Express, Volume 24 (2016) no. 22, pp. 25129-25147 | DOI

[23] Joseph Lifton; Tong Liu Ring artefact reduction via multi-point piecewise linear flat field correction for X-ray computed tomography, Opt. Express, Volume 27 (2019) no. 3, pp. 3217-3228 | DOI

[24] Thibault Taillandier-Thomas; Stéphane Roux; Thilo F Morgeneyer; François Hild Localized strain field measurement on laminography data with mechanical regularization, Nucl. Instrum. Methods Phys. Res., Sect. B, Volume 324 (2014), pp. 70-79 | DOI

[25] François Hild; Amine Bouterf; Ludovic Chamoin; Hugo Leclerc; Florent Mathieu; Jan Neggers; Florent Pled; Zvonimir Tomičević; Stéphane Roux Toward 4D mechanical correlation, Adv. Model. Simul. Eng. Sci., Volume 3 (2016) no. 1, 17, 26 pages

[26] P. Auger; T. Lavigne; B. Smaniotto; M. Spagnuolo; F. Dell’Isola; F. Hild Poynting Effects in Pantographic Metamaterial Captured via Multiscale DVC, J. Strain Anal. Eng. Des., Volume 56 (2021) no. 7, pp. 462-477 | DOI

[27] H. Leclerc; J. Neggers; F. Mathieu; F. Hild; S. Roux Correli 3.0, Agence pour la Protection des Programmes, Paris (France), IDDN.FR.001.520008.000.S.P.2015.000.31500, 2015

[28] F. dell’Isola; P. Seppecher; M. Spagnuolo; E. Barchiesi; F. Hild; T. Lekszycki; I. Giorgio; L. Placidi; U. Andreaus; M. Cuomo; S. R. Eugster; A. Pfaff; K. Hoschke; R. Langkemper; E. Turco; R. Sarikaya; A. Misra; M. De Angelo; F. D’Annibale; A. Bouterf; X. Pinelli; A. Misra; B. Desmorat; M. Pawlikowski; C. Dupuy; D. Scerrato; P. Peyre; M. Laudato; L. Manzari; P. Göransson; C. Hesch; S. Hesch; P. Franciosi; J. Dirrenberger; F. Maurin; Z. Vangelatos; C. Grigoropoulos; V. Melissinaki; M. Farsari; W. Muller; E. Abali; C. Liebold; G. Ganzosch; P. Harrison; R. Drobnicki; L. A. Igumnov; F. Alzahrani; T. Hayat Advances in Pantographic Structures: Design, Manufacturing, Models, Experiments and Image Analyses, Contin. Mech. Thermodyn., Volume 31 (2019) no. 4, pp. 1231-1282 | DOI

[29] Hugo Leclerc; Jean-Noël Périé; François Hild; Stéphane Roux Digital volume correlation: what are the limits to the spatial resolution?, Mech. Ind., Volume 13 (2012) no. 6, pp. 361-371 | DOI

[30] Rafael Vargas; Viktor Kosin; Joël Lachambre; Jérôme Adrien; Clément Jailin; Stéphane Roux; Eric Maire Image-based geometry calibration for a double-tomograph, Meas. Sci. Technol., Volume 37 (2026) no. 1, 015404, 18 pages

[31] P. C. Hansen The L-Curve and its use in the numerical treatment of inverse problems, Computational inverse problems in electrocardiography (P. Johnston, ed.) (Advances in Computational Bioengineering), Volume 5, WIT Press (2000), pp. 119-142

[32] Clément Jailin; Ante Buljac; Amine Bouterf; Martin Poncelet; François Hild; Stéphane Roux Self-calibration for lab-μCT using space-time regularized projection-based DVC and model reduction, Meas. Sci. Technol., Volume 29 (2018) no. 2, 024003, 13 pages

[33] Cédric Fragnaud; Clément Remacha; Julián Betancur; Stéphane Roux CAD-based X-ray CT calibration and error compensation, Meas. Sci. Technol., Volume 33 (2022) no. 6, 065024, 14 pages

[34] Thibault Taillandier-Thomas; Stéphane Roux; François Hild Soft route to 4D tomography, Phys. Rev. Lett., Volume 117 (2016) no. 2, 025501, 5 pages | MR

[35] Clément Jailin; A Bouterf; Martin Poncelet; Stéphane Roux In situ μ CT-scan mechanical tests: fast 4D mechanical identification, Exp. Mech., Volume 57 (2017) no. 8, pp. 1327-1340 | DOI

[36] Robert J. Guyan Reduction of stiffness and mass matrices, AIAA J., Volume 3 (1965) no. 2, p. 380 | DOI

[37] Eric Maire; Gabriel Bonnard; Jérôme Adrien; Xavier Boulnat; Jean Michel Létang; Joël Lachambre Dual beam microfocus high-energy tomography: Towards multimodal and faster laboratory experiments, Tomogr. Mater. Struct, Volume 5 (2024), 100030, 10 pages

Cité par Sources :

Commentaires - Politique