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Augmented Lagrangian Digital Image Correlation

  • J. Yang
  • K. Bhattacharya
Article
  • 66 Downloads

Abstract

Digital image correlation (DIC) is a powerful experimental technique for measuring full-field displacement and strain. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation, and thereby to compute the displacement and strain fields. Local subset DIC and finite element-based global DIC are two widely used image matching methods. However there are some drawbacks to these methods. In local subset DIC, the computed displacement field may not be compatible, and the deformation gradient may be noisy, especially when the subset size is small. Global DIC incorporates displacement compatibility, but can be computationally expensive. In this paper, we propose a new method, the augmented-Lagrangian digital image correlation (ALDIC), that combines the advantages of both the local (fast) and global (compatible) methods. We demonstrate that ALDIC has higher accuracy and behaves more robustly compared to both local subset DIC and global DIC.

Keywords

Digital image correlation (DIC) Augmented Lagrangian 

Notes

Acknowledgments

We are grateful to Dr. Louisa Avellar for sharing her images of heterogeneous fracture with us. We gratefully acknowledge the support of the US Air Force Office of Scientific Research through the MURI grant ‘Managing the Mosaic of Microstructure’ (FA9550-12-1-0458).

References

  1. 1.
    Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties-a review. Strain 42:69–80CrossRefGoogle Scholar
  2. 2.
    Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001CrossRefGoogle Scholar
  3. 3.
    Sutton MA, Orteu JJ, Schreier HW (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, BerlinGoogle Scholar
  4. 4.
    Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR (1983) Determination of displacements using an improved digital correlation method. Image Vis Comput 1:133–139CrossRefGoogle Scholar
  5. 5.
    Chen DJ, Chiang FP, Tan YS, Don HS (1993) Digital speckle-displacement measurement using a complex spectrum method. Appl Opt 32:1839–1849CrossRefGoogle Scholar
  6. 6.
    Dhir SK, Sikora JP (1972) An improved method for obtaining the general-displacement field from a holographic interferogram. Exp Mech 12:323–327CrossRefGoogle Scholar
  7. 7.
    Kreis T (1996) Holographic interferometry: principles and methods. In: Simulation and experiment in laser metrology: proceedings of the international symposium on laser applications in precision measurements Held in Balatonfured/Hungary, June 3-6, 1996, volume 2. John Wiley & Sons, p 323Google Scholar
  8. 8.
    Rastogi PK (2000) Principles of holographic interferometry and speckle metrology. In: Photomechanics. Springer, pp 103–151Google Scholar
  9. 9.
    Dickinson AS, Taylor AC, Ozturk H, Browne M (2011) Experimental validation of a finite element model of the proximal femur using digital image correlation and a composite bone model. J Biomech Eng 133:014504CrossRefGoogle Scholar
  10. 10.
    Franck C, Hong S, Maskarinec SA, Tirrell DA, Ravichandran G (2007) Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp Mech 47:427–438CrossRefGoogle Scholar
  11. 11.
    Franck C, Maskarinec SA, Tirrell DA, Ravichandran G (2011) Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions. PloS one 6:e17833CrossRefGoogle Scholar
  12. 12.
    Rehrl C, Kleber S, Antretter T, Pippan R (2011) A methodology to study crystal plasticity inside a compression test sample based on image correlation and ebsd. Mater Charact 62:793–800CrossRefGoogle Scholar
  13. 13.
    Daly S (2007) Deformation and fracture of thin sheets of nitinol. Phd thesis California Institute of TechnologyGoogle Scholar
  14. 14.
    Bastawros AF, Bart-Smith H, Evans AG (2000) Experimental analysis of deformation mechanisms in a closed-cell aluminum alloy foam. J Mech Phys Solids 48:301–322CrossRefzbMATHGoogle Scholar
  15. 15.
    Jerabek M, Major Z, Lang RW (2010) Strain determination of polymeric materials using digital image correlation. Polym Test 29:407–416CrossRefGoogle Scholar
  16. 16.
    Wang Y, Cuitiño A M (2002) Full-field measurements of heterogeneous deformation patterns on polymeric foams using digital image correlation. Int J Solids Struct 39:3777–3796CrossRefGoogle Scholar
  17. 17.
    Zdunek J, Brynk T, Mizera J, Pakieła Z, Kurzydłowski KJ (2008) Digital image correlation investigation of portevin–le chatelier effect in an aluminium alloy. Mater Charact 59:1429–1433CrossRefGoogle Scholar
  18. 18.
    Tracy J, Waas A, Daly S (2015) Experimental assessment of toughness in ceramic matrix composites using the j-integral with digital image correlation part i: methodology and validation. J Mater Sci 50:4646–4658CrossRefGoogle Scholar
  19. 19.
    Kimiecik M, Jones JW, Daly S (2013) Quantitative studies of microstructural phase transformation in nickel-titanium. Mater Lett 95:25–29CrossRefGoogle Scholar
  20. 20.
    Chang S, Wang CS, Xiong CY, Fang J (2005) Nanoscale in-plane displacement evaluation by afm scanning and digital image correlation processing. Nanotechnology 16:344CrossRefGoogle Scholar
  21. 21.
    Erten E, Reigber A, Hellwich O, Prats P (2009) Glacier velocity monitoring by maximum likelihood texture tracking. IEEE Trans Geosci Remote Sens 47:394–405CrossRefGoogle Scholar
  22. 22.
    Rubino V, Lapusta N, Rosakis A (2012) Laboratory earthquake measurements with the high-speed digital image correlation method and applications to super-shear transition. In AGU Fall Meeting Abstracts 1:06Google Scholar
  23. 23.
    Rubino V, Lapusta N, Rosakis AJ, Leprince S, Avouac JP (2014) Static laboratory earthquake measurements with the digital image correlation method. Exp Mech, pp 1–18Google Scholar
  24. 24.
    Besnard G, Leclerc H, Hild F, Roux S, Swiergiel N (2012) Analysis of image series through global digital image correlation. J. Strain Anal Eng Des 47:214–228CrossRefGoogle Scholar
  25. 25.
    Blaber J, Adair B, Antoniou A (2015) Ncorr: open-source 2d digital image correlation matlab software. Exp Mech: 1–18Google Scholar
  26. 26.
    Jones EMC, Silberstein MN, White SR, Sottos NR (2014) In situ measurements of strains in composite battery electrodes during electrochemical cycling. Exp Mech 54:971–985CrossRefGoogle Scholar
  27. 27.
    Pan B, Wang B, Lubineau G, Moussawi A (2015) Comparison of subset-based local and finite element-based global digital image correlation. Exp Mech 55:887–901CrossRefGoogle Scholar
  28. 28.
    Correlated Solutions (2009) Vic-2d Reference ManualGoogle Scholar
  29. 29.
    Pan B, Asundi A, Xie HM, Gao JX (2009) Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements. Opt Lasers Eng 47:865–874CrossRefGoogle Scholar
  30. 30.
    Avril S, Feissel P, Pierron F, Villon P (2009) Comparison of two approaches for differentiating full-field data in solid mechanics. Meas Sci Technol 21:015703CrossRefGoogle Scholar
  31. 31.
    Zhao JQ, Zeng P, Pan B, LP Lei HFDu, He WB, Liu Y, Xu YJ (2012) Improved hermite finite element smoothing method for full-field strain measurement over arbitrary region of interest in digital image correlation. Opt Lasers Eng 50:1662–1671CrossRefGoogle Scholar
  32. 32.
    Modersitzki J (2004) Numerical methods for image registration. Oxford University Press, LondonzbMATHGoogle Scholar
  33. 33.
    Ronovskỳ A, Vašatová A (2017) Elastic image registration based on domain decomposition with mesh adaptation. Mathematical Analysis and Numerical Mathematics 15:322–330Google Scholar
  34. 34.
    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 111:123–143MathSciNetCrossRefGoogle Scholar
  35. 35.
    Merta M, Vašatová A, Hapla V, Horák D (2014) Parallel implementation of Total-FETI DDM with application to medical image registration. In: Domain Decomposition Methods in Science and Engineering XXI. Springer, pp 917–925Google Scholar
  36. 36.
    Passieux JC, Perie JN, Salaun M (2015) A dual domain decomposition method for finite element digital image correlation. Int J Numer Methods Eng 102:1670–1682MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Wang TY, Qian KM (2017) Parallel computing in experimental mechanics and optical measurement: a review (ii) Optics and Lasers in EngineeringGoogle Scholar
  38. 38.
    Nocedal J, Wright S (2006) Numerical optimization. Springer, BerlinzbMATHGoogle Scholar
  39. 39.
    Conn AR, Gould NIM, Toint PL (1991) A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J Numer Anal 28:545–572MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Afonso MV, Bioucas-Dias JM, Figueiredo MAT (2011) An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans Image Process 20:681–695MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Simo JC, Laursen TA (1992) An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42:97–116MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Michel JC, Moulinec H, Suquet P (2000) A computational method based on augmented Lagrangians and fast Fourier Transforms for composites with high contrast. CMES-Computer Modeling in Engineering & Sciences 1:79–88MathSciNetGoogle Scholar
  43. 43.
    Goldstein T, O’Donoghue B, Setzer S, Baraniuk R (2014) Fast alternating direction optimization methods. SIAM J Imag Sci 7:1588–1623MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2010) Distributed optimization and statistical learning via the alternating direction method of multipliers. Mach Learn 3:1–122CrossRefzbMATHGoogle Scholar
  45. 45.
    Yang JF, Zhang Y (2011) Alternating direction algorithms for l(1)-problems in compressive sensing. SIAM J Sci Comput 33:250–278MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Afonso MV, Bioucas-Dias JM, Figueiredo MAT (2010) Fast image recovery using variable splitting and constrained optimization. IEEE Trans Image Process 19:2345–2356MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Glowinski R, Le Tallec P (1989) Augmented Lagrangian and operator-splitting methods in nonlinear mechanics SIAMGoogle Scholar
  48. 48.
    Pan B, Xie H, Wang Z (2010) Equivalence of digital image correlation criteria for pattern matching. Applied optics 49:5501–5509CrossRefGoogle Scholar
  49. 49.
    Simon B, Iain M (2004) Lucas-kanade 20 years on a unifying framework. International journal of computer vision 56:221–255CrossRefGoogle Scholar
  50. 50.
    Réthoré J, Hild F, Roux S (2007) Shear-band capturing using a multiscale extended digital image correlation technique. Comput Methods Appl Mech Eng 196:5016–5030CrossRefzbMATHGoogle Scholar
  51. 51.
    Réthoré J, Hild F, Roux S (2008) Extended digital image correlation with crack shape optimization. International Journal for Numerical Methods in Engineerin 73:248–272MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Reu PL, Toussaint E, Jones E, Bruck HA, Iadicola M, Balcaen R, Turner DZ, Siebert T, Lava P, Simonsen M (2017) Dic challenge developing images and guidelines for evaluating accuracy and resolution of 2d analyses experimental mechanicsGoogle Scholar
  53. 53.
    Bornert M, Doumalin P, Dupré JC, Poilâne C, Robert L, Toussaint E, Wattrisse B (2017) Shortcut in DIC error assessment induced by image interpolation used for subpixel shifting. Opt Lasers Eng 91:124–133CrossRefGoogle Scholar
  54. 54.
    Avellar L, Ravichandran G (2016) Deformation and fracture of 3d printed heterogeneous materials Society for Experimental Mechanics Annual ConferenceGoogle Scholar
  55. 55.
    Hackbusch W (2003) Multi-grid method and applications. Springer, BerlinGoogle Scholar
  56. 56.
    Yang J, Bhattacharya K (2018) Combining image compression with digital image correlation. Experimental MechanicsGoogle Scholar
  57. 57.
    Yang J, Bhattacharya K (2019) Fast adaptive global digital image correlation. In: Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics, volume 3. Springer, pp 69–73Google Scholar

Copyright information

© Society for Experimental Mechanics 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of WisconsinMadisonUSA
  2. 2.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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