Experimental Mechanics

, Volume 57, Issue 3, pp 443–456 | Cite as

Finite Element Stereo Digital Image Correlation: Framework and Mechanical Regularization

  • J.-E. Pierré
  • J.-C. PassieuxEmail author
  • J.-N. Périé


The use of Finite Element meshes in Digital Image Correlation (FE-DIC) is now widespread in experimental mechanics but, so far, FE have been much less used in Stereo-DIC. The first goal of this paper is to explain in detail how to use FE in Stereo-DIC by means of a formulation in the world coordinate system. More precisely, the paper describes how to calibrate possibly non-linear model of cameras and to measure shapes and displacements with an FE mesh. It also shows that, with such a framework, it is possible to regularize the measurement with an FE model based on the same mesh. For instance, using this technique, it is possible to measure the rotation field of a bending plate in addition to its displacement.


Digital image correlation Stereovision Finite element Mechanical regularization Plate kinematics 



This work was funded by the French “Agence Nationale de la Recherche” under the grant ANR-12-RMNP-0001 (VERTEX project).


  1. 1.
    Beaubier B, Dufour JE, Hild F, Roux S, Lavernhe S, Lavernhe-Taillard K (2014) CAD-based calibration and shape measurement with stereoDIC: Principle and application on test and industrial parts. Exp Mech 54(3):329–341. doi: 10.1007/s11340-013-9794-6
  2. 2.
    Besnard G, Hild F, Roux S (2006) ”Finite-Element” Displacement Fields Analysis from Digital Images: Application to Portevin–Le Châtelier Bands. Exp Mech 46(6):789–803. doi: 10.1007/s11340-006-9824-8 CrossRefGoogle Scholar
  3. 3.
    Dufour JE, Beaubier B, Hild F, Roux S (2015) CAD-based Displacement Measurements with Stereo-DIC: Principle and First Validations. Exp Mech. doi: 10.1007/s11340-015-0065-6 Google Scholar
  4. 4.
    Dufour JE, Hild F, Roux S (2015) Shape, displacement and mechanical properties from isogeometric multiview stereocorrelation. The Journal of Strain Analysis for Engineering Design. doi: 10.1177/0309324715592530 Google Scholar
  5. 5.
    Garcia D, Orteu JJ (2001) 3d deformation measurement using stereo-correlation applied to experimental mechanics. In: Proceedings of the 10th FIG International Symposium Deformation measurements, pp 19–22Google Scholar
  6. 6.
    Horn BKP, Schunck BG (1981) Determining optical flow. Artif Intell 17 (1–3):185–203. doi: 10.1016/0004-3702(81)90024-2 CrossRefGoogle Scholar
  7. 7.
    Lawson C, Hanson R (1995) Solving Least Squares Problems. Soc Ind Appl Math. doi: 10.1137/1.9781611971217
  8. 8.
    Leclerc H, Périé JN, Hild F, Roux S (2012) Digital volume correlation: what are the limits to the spatial resolution? Mechanics & Industry 13(06):361–371CrossRefGoogle Scholar
  9. 9.
    Leclerc H, Périé JN, Roux S, Hild F (2009) Integrated Digital Image Correlation for the Identification of Mechanical Properties. In: gagalowicz A, Philips W (eds) Computer Vision/Computer Graphics CollaborationTechniques, no. 5496 in Lecture Notes in Computer Science. Springer, Berlin Heidelberg, pp 161– 171Google Scholar
  10. 10.
    Leclerc H, Périé JN, Roux S, Hild F (2011) Voxel-Scale Digital Volume Correlation. Exp Mech 51(4):479–490. doi: 10.1007/s11340-010-9407-6
  11. 11.
    Lucas BD, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: Proceedings of Imaging Understanding workshop, pp 121–130Google Scholar
  12. 12.
    Miller K (1970) Least squares methods for ill-posed problems with a prescribed bound. SIAM J Math Anal 1(1):52–74. doi: 10.1137/0501006 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Passieux JC (2015) Quelques outils numériques pour la simulation et la mesure en mécanique des structures. Habilitation à diriger des recherches de l’université de Toulouse 122p.
  14. 14.
    Passieux JC, Bugarin F, David C, Périé JN, Robert L (2015) Multiscale Displacement Field Measurement Using Digital Image Correlation: Application to the Identification of Elastic Properties. Exp Mech 55 (1):121–137. doi: 10.1007/s11340-014-9872-4 CrossRefGoogle Scholar
  15. 15.
    Passieux JC, Périé JN, Salaün M (2015) A dual domain decomposition method for finite element digital image correlation. Int J Numer Methods Eng 102(10):1670–1682. doi: 10.1002/nme.4868 MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Passieux JC, Réthoré J, Gravouil A, Baietto MC (2013) Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver. Comput Mech 52(6):1381–1393. doi: 10.1007/s00466-013-0882-3 CrossRefzbMATHGoogle Scholar
  17. 17.
    Pierré JE, Passieux JC, Périé JN, Bugarin F, Robert L (2016) Unstructured finite element-based digital image correlation with enhanced management of quadrature and lens distortions. Opt Lasers Eng 77:44–53. doi: 10.1016/j.optlaseng.2015.07.008 CrossRefGoogle Scholar
  18. 18.
    Roux S, Hild F (2006) Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches. Int J Fract 140(1-4):141–157. doi: 10.1007/s10704-006-6631-2
  19. 19.
    Roux S, Réthoré J, Hild F (2009) Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2d and 3d cracks. J Phys D: Appl Phys 42(21):214,004. doi: 10.1088/0022-3727/42/21/214004 CrossRefGoogle Scholar
  20. 20.
    Réthoré J (2010) A fully integrated noise robust strategy for the identification of constitutive laws from digital images. Int J Numer Methods Eng 84(6):631–660. doi: 10.1002/nme.2908 CrossRefzbMATHGoogle Scholar
  21. 21.
    Réthoré J (2015) Automatic crack tip detection and stress intensity factors estimation of curved cracks from digital images: AUTOMATIC CRACK TIP DETECTION AND SIF ESTIMATION OF CURVED CRACKS. Int J Numer Methods Eng 103(7):516–534. doi: 10.1002/nme.4905 CrossRefzbMATHGoogle Scholar
  22. 22.
    Réthoré J, Muhibullah, Elguedj T, Coret M, Chaudet P, Combescure A (2013) Robust identification of elasto-plastic constitutive law parameters from digital images using 3d kinematics. Int J Solids Struct 50(1):73–85. doi: 10.1016/j.ijsolstr.2012.09.002 CrossRefGoogle Scholar
  23. 23.
    Sun Y, Pang JHL, Wong CK, Su F (2005) Finite element formulation for a digital image correlation method. Appl Opt 44(34):7357–7363. doi: 10.1364/AO.44.007357 CrossRefGoogle Scholar
  24. 24.
    Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR (1983) Determination of displacements using an improved digital correlation method. Image Vis Comput 1 (3):133–139. doi: 10.1016/0262-8856(83)90064-1
  25. 25.
    Sutton MA, Yan JH, Tiwari V, Schreier HW, Orteu JJ (2008) The effect of out-of-plane motion on 2d and 3d digital image correlation measurements. Opt Lasers Eng 46(10):746–757. doi: 10.1016/j.optlaseng.2008.05.005 CrossRefGoogle Scholar
  26. 26.
    Sztefek P, Olsson R (2008) Tensile stiffness distribution in impacted composite laminates determined by an inverse method. Compos A: Appl Sci Manuf 39(8):1282–1293. doi: 10.1016/j.compositesa.2007.10.005 CrossRefGoogle Scholar
  27. 27.
    Sztefek P, Olsson R (2009) Nonlinear compressive stiffness in impacted composite laminates determined by an inverse method. Compos A: Appl Sci Manuf 40(3):260–272. doi: 10.1016/j.compositesa.2008.12.002
  28. 28.
    Triggs B, McLauchlan PF, Hartley RI, Fitzgibbon AW (2000) Bundle adjustment—a modern synthesis. In: Vision algorithms: theory and practice. Springer, pp 298–372Google Scholar

Copyright information

© Society for Experimental Mechanics 2016

Authors and Affiliations

  1. 1.Institut Clément Ader, CNRS UMR 5312Université Fédérale Toulouse Midi-PyrénéesToulouseFrance

Personalised recommendations