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Experimental Mechanics

, Volume 58, Issue 7, pp 1195–1206 | Cite as

A Space-Time PGD-DIC Algorithm:

Application to 3D Mode Shapes Measurements
  • J.-C. Passieux
  • R. Bouclier
  • J. N. Périé
Article
  • 217 Downloads

Abstract

The aim of this study is to develop a new regularized Digital Image Correlation (DIC) method for time dependent measurements. The correlation problem is written as a minimization problem over the space-time domain in a general formulation including 2D-DIC and Stereo DIC (SDIC). The unknown time-resolved displacement field is found as a sum of products of space and time functions, similarly to the Proper Generalized Decomposition in computational mechanics. It is shown that the space fields are less sensitive to noise as time regularity acts as a physical regularization of the space fields. The proposed method is illustrated by vibration measurement under harmonic excitation in 2D-DIC and SDIC.

Keywords

Digital image correlation Proper generalized decomposition Vibrations Dynamics 

References

  1. 1.
    Helfrick MN, Niezrecki C, Avitabile P, Schmidt T (2011) 3D digital image correlation methods for full-field vibration measurement. Mech Syst Signal Process 25(3):917–927CrossRefGoogle Scholar
  2. 2.
    Beberniss T, Eason T, Spottswood S (2012) High-speed 3d digital image correlation measurement of long-duration random vibration; recent advancements and noted limitations. In: International conference on noise and vibration engineering (ISMA). Katholieke Universiteit Leuven, BelgiumGoogle Scholar
  3. 3.
    Reu PL, Rohe DP, Jacobs LD (2016) Comparison of {DIC} and {LDV} for practical vibration and modal measurements. Mechanical Systems and Signal ProcessingGoogle Scholar
  4. 4.
    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 77:44–53CrossRefGoogle Scholar
  5. 5.
    Balcaen R, Reu P, Lava P, Debruyne D (2017) Stereo-dic uncertainty quantification based on simulated images. Exp Mech 57(6):939–951CrossRefGoogle Scholar
  6. 6.
    Warren C, Niezrecki C, Avitabile P, Pingle P (2011) Comparison of FRF measurements and mode shapes determined using optically image based, laser, and accelerometer measurements. Mech Syst Signal Process 25:2191–2202CrossRefGoogle Scholar
  7. 7.
    Fruehmann RK, Dulieu-Barton JM, Quinn S, Tyler JP (2015) The use of a lock-in amplifier to apply digital image correlation to cyclically loaded components. Opt Lasers Eng 68:149–159CrossRefGoogle Scholar
  8. 8.
    Siebert T, Wood R, Splitthof K (2009) High speed image correlation for vibration analysis. J Phys: Conf Ser 181(1):012,064Google Scholar
  9. 9.
    Vanlanduit S, Vanherzeele J, Longo R, Guillaume P (2009) A digital image correlation method for fatigue test experiments. Opt Lasers Eng 47(3–4):371–378CrossRefGoogle Scholar
  10. 10.
    Wang W, Mottershead JE, Siebert T, Pipino A (2012) Frequency response functions of shape features from full-field vibration measurements using digital image correlation. Mech Syst Signal Process 28(0):333–347CrossRefGoogle Scholar
  11. 11.
    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):789–803CrossRefGoogle Scholar
  12. 12.
    Sun Y, Pang J, Wong CK, Su F (2005) Finite element formulation for a digital image correlation method. Appl Opt 44(34):7357–7363CrossRefGoogle Scholar
  13. 13.
    Dufour JE, Beaubier B, Hild F, Roux S (2015) Cad-based displacement measurements with stereo-dic. Exp Mech 55(9):1657–1668CrossRefGoogle Scholar
  14. 14.
    Pierré JE, Passieux JC, Périé JN (2017) Finite element stereo digital image correlation: framework and mechanical regularization. Exp Mech 53(7):443–456CrossRefGoogle Scholar
  15. 15.
    Serra J, Pierré JE, Passieux JC, Périé JN, Bouvet C, Castanié B (2017) Validation and modeling of aeronautical composite structures subjected to combined loadings: the vertex project. part 1: Experimental setup, fe-dic instrumentation and procedures. Compos Struct 179:224–244CrossRefGoogle Scholar
  16. 16.
    Bouclier R, Passieux JC (2017) A domain coupling method for finite element digital image correlation with mechanical regularization: Application to multiscale measurements and parallel computing. Int J Numer Methods Eng 111(2):123–143MathSciNetCrossRefGoogle Scholar
  17. 17.
    Leclerc H, Périé JN, Roux S, Hild F (2009) Integrated digital image correlation for the identification of mechanical properties. Lect Notes Comput Sci 5496:161–171MathSciNetCrossRefGoogle Scholar
  18. 18.
    Réthoré J (2010) A fully integrated noise robust strategy for the identification of constitutive laws from digital images. Int J Numer Meth Eng 84(6):631–660CrossRefGoogle Scholar
  19. 19.
    Réthoré J, Thomas Elguedj M, Coret M, Chaudet P, Combescure A (2013) Robust identification of elasto-plastic constitutive law parameters from digital image using 3D kinematics. Int J Solids Struct 50:73–85CrossRefGoogle Scholar
  20. 20.
    Besnard G, Guerard S, Roux S, Hild F (2011) A space-time approach in digital image correlation: Movie-dic. Opt Lasers Eng 49:71–81CrossRefGoogle Scholar
  21. 21.
    Besnard G, Leclerc H, Roux S, Hild F (2012) Analysis of image series through digital image correlation. J Strain Anal Eng Des 47(4):214–228CrossRefGoogle Scholar
  22. 22.
    Passieux JC, Périé JN (2012) High resolution digital image correlation using Proper Generalized Decomposition: PGD-DIC. Int J Numer Methods Eng 92(6):531–550MathSciNetCrossRefGoogle Scholar
  23. 23.
    Gomes Perini L, Passieux JC, Périé JN (2014) A multigrid PGD-based algorithm for volumetric displacement fields measurements. Strain 50(4):355–367CrossRefGoogle Scholar
  24. 24.
    Warburton JR, Lu G, Buss TM, Docx H, Matveev MY, Jones IA (2016) Digital image correlation vibrometry with low speed equipment. Exp Mech 56(7):1219–1230CrossRefGoogle Scholar
  25. 25.
    Lucas B, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: Proceedings of imaging understanding workshop, pp 121–130Google Scholar
  26. 26.
    Sutton M, Wolters W, Peters W, Ranson W, McNeill S (1983) Determination of displacements using an improved digital correlation method. Image Vis Comput 1(3):133–139CrossRefGoogle Scholar
  27. 27.
    Garcia D, Orteu JJ, Penazzi L (2002) A combined temporal tracking and stereo-correlation technique for accurate measurement of 3d displacements: Application to sheet metal forming. J Mater Process Technol 125-126:736–742CrossRefGoogle Scholar
  28. 28.
    Sutton M, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New YorkGoogle Scholar
  29. 29.
    Fehrenbach J, Masmoudi M (2008) A fast algorithm for image registration. C R Math 346(9-10):593–598MathSciNetCrossRefGoogle Scholar
  30. 30.
    Neggers J, Blaysat B, Hoefnagels JPM, Geers MGD (2016) On image gradients in digital image correlation. Int J Numer Methods Eng 105:243–260MathSciNetCrossRefGoogle Scholar
  31. 31.
    Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newtonian Fluid Mech 139(3):153–176CrossRefGoogle Scholar
  32. 32.
    Bouclier R, Louf F, Chamoin L (2013) Real-time validation of mechanical models coupling pgd and constitutive relation error. Comput Mech 52(4):861–883MathSciNetCrossRefGoogle Scholar
  33. 33.
    Chinesta F, Leygue A, Bordeu F, Aguado J, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) Pgd-based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 20(1):31–59MathSciNetCrossRefGoogle Scholar
  34. 34.
    Ladevèze P, Passieux JC, Néron D (2010) The LATIN multiscale computational method and the proper generalized decomposition. Comput Methods Appl Mech Eng 199(21):1287–1296MathSciNetCrossRefGoogle Scholar
  35. 35.
    Nouy A (2007) A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Comput Methods Appl Mech Eng 196(45-48):4521–4537MathSciNetCrossRefGoogle Scholar
  36. 36.
    Zou X, Conti M, Díez P, Auricchio F A nonintrusive proper generalized decomposition scheme with application in biomechanics. International Journal for Numerical Methods in Engineering p. online first.  https://doi.org/10.1002/nme.5610 MathSciNetCrossRefGoogle Scholar
  37. 37.
    Neggers J, Hoefnagels JPM, Geers MGD, Hild F, Roux S (2015) Time-resolved integrated digital image correlation. Int J Numer Methods Eng 103(3):157–182MathSciNetCrossRefGoogle Scholar
  38. 38.
    Passieux JC, Ladevèze P, Néron D (2010) A scalable time-space multiscale domain decomposition method: adaptive time scale separation. Comput Mech 46(4):621–633MathSciNetCrossRefGoogle Scholar
  39. 39.
    Mathieu F, Leclerc H, Hild H, Roux S (2015) Estimation of elastoplastic parameters via weighted FEMU and intergrated DIC. Exp Mech 55(1):105–119CrossRefGoogle Scholar
  40. 40.
    Beaubier B, Dufour J, 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):329–341CrossRefGoogle Scholar
  41. 41.
    ABAQUS/Standard User’s Manual (2009) Version 6.9 Providence, Simulia, RIGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2018

Authors and Affiliations

  1. 1.Institut Clément Ader (ICA), INSA-UT3-ISAE-Mines Albi-CNRSUniversité de ToulouseToulouseFrance
  2. 2.IMTUniversité de Toulouse, UPS, UT1, UT2, INSA, CNRSToulouseFrance

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