Skip to main content
SpringerLink
Log in

Fast Adaptive Mesh Augmented Lagrangian Digital Image Correlation

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background Digital image correlation (DIC) is a widely used experimental method to measure full-field displacements and strains. This technique compares images of speckle patterns before and after deformation to computationally infer the displacement and strain fields. Of particular interest are complex mechanical phenomena where strains are far from uniform.

Objective In such situations, it would be desirable to use an adaptive technique with higher resolution in the regions of rapidly changing strain and lower resolution elsewhere.

Methods This paper builds on the recently proposed augmented Lagrangian digital image correlation (ALDIC) method to incorporate mesh adaptivity. We call the resulting approach adapt-ALDIC.

Results We show that the structure of ALDIC makes it easy to incorporate adaptive resolution. We demonstrate through both synthetic and experimental examples that adapt-ALDIC is robust and saves significant computational time with almost no loss in accuracy. Among two types of adaptive mesh strategies, we find that adaptive quadtree mesh outperforms Kuhn triangulation mesh both in accuracy and computational cost. Indeed, we demonstrate that quadtree adapt-ALDIC provides compatible deformation and noise insensitivity typical of global DIC at the cost of local DIC.

Conclusions Adapt-ALDIC with adaptive quadtree mesh can analyze heterogeneous deformations accurately and efficiently. An open-source Matlab code is freely available through GitHub and Caltech DATA.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. We only consider FE-based global DIC in this work. It is also possible to have other basis sets for global DIC, and other approaches like dense global DIC. We do not consider them here.

  2. The introduction of the regularizer requires a boundary condition, and one can proceed analogously with displacement boundary conditions if the boundary displacements are known.

  3. In our previous work on ALDIC [25], we used finite difference discretization where the gradients are defined on the nodes.

References

  1. Sutton MA ,Orteu JJ, Schreier HW (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer-Verlag GmbH

  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 20:062001

    Article  Google Scholar 

  3. 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 47:214–228

    Article  Google Scholar 

  4. Hild F, Roux S (2008) CorreliQ4: A software for finite element displacement field measurements by digital image correlation. Rapport interne LMT Cachan 269:195

    Google Scholar 

  5. Blaber J, Adair B, Antoniou A (2015) Ncorr: Open-Source 2D Digital Image Correlation Matlab Software. Exp Mech 55:1105–1122

    Article  Google Scholar 

  6. Turner D, Crozier P, and Reu P (2015) Digital Image Correlation Engine (DICe). Sandia Report, SAND2015-10606 O

  7. Belloni V, Ravanelli R, Nascetti A, Di Rita M, Mattei D, Crespi M (2019) py2DIC: A new free and open source software for displacement and strain measurements in the field of experimental mechanics. Sensors 19:3832

    Article  Google Scholar 

  8. Chen Z, Lenthe W, Stinville JC, Echlin M, Pollock TM, Daly S (2018) High-resolution deformation mapping across large fields of view using scanning electronmicroscopy and digital image correlation. Exp Mech 58:1407–1421

    Article  Google Scholar 

  9. Bugra I, Kapan E, Turkoglu O, Aydıner CC (2019) In situ investigation of strain heterogeneity and microstructural shear bands in rolled magnesium AZ31. Int J Plasticity 118:233–251

    Article  Google Scholar 

  10. Shafaghi N, Kapan E, Aydıner CC (2020) Cyclic Strain Heterogeneity and Damage Formation in Rolled Magnesium Via In Situ Microscopic Image Correlation. Exp Mech 60:735–751

    Article  Google Scholar 

  11. Schreier HW, Sutton MA (2002) Systematic errors in digital image correlation due to undermatched subset shape functions. Exp Mech 42:303–310

    Article  Google Scholar 

  12. Wang B, Pan B (2019) Self-adaptive digital volume correlation for unknown deformation fields. Exp Mech 59(2):149–162

    Article  Google Scholar 

  13. Pierré JE, Passieux JC, Périé JN (2017) Finite element stereo digital image correlation: framework and mechanical regularization. Exp Mech 57:443–456

    Article  Google Scholar 

  14. Patel M, Leggett SE, Landauer AK, Wong IY, Franck C (2018) Rapid, topology-based particle tracking for high-resolution measurements of large complex 3D motion fields. Sci Rep 8:5581

    Article  Google Scholar 

  15. Chen Z, Daly S (2018) Deformation twin identification in magnesium through clustering and computer vision. Mater Sci Eng A 736:61–75

    Article  Google Scholar 

  16. 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 55:121–137

    Article  Google Scholar 

  17. Tadmor E, Nezzar S, Vese L (2004) A multiscale image representation using hierarchical (BV, \(\cal{L}_{2}\)) decompositions. Multiscal Model Simul 2:554–579

    Article  MATH  Google Scholar 

  18. Pan B, Xie HM, Wang ZY, Qian KM, Wang ZY (2008) Study on subset size selection in digital image correlation for speckle patterns. Opt Express 16(10):7037–7048

    Article  Google Scholar 

  19. Yuan Y, Huang YJ, Peng XL, Xiong CY, Fang J, Yuan F (2014) Accurate displacement measurement via a self-adaptive digital image correlation method based on a weighted ZNSSD criterion. Opt Lasers Eng 52:75–85

    Article  Google Scholar 

  20. Zhan Q, Yuan Y, Fan XT, Huang JY, Xiong CY, Yuan F (2016) Digital image correlation involves an inverse problem: A regularization scheme based on subset size constraint. Opt Lasers Eng 81:54–62

    Article  Google Scholar 

  21. Wang B, Pan B (2019) Anisotropic self-adaptive digital volume correlation with optimal cuboid subvolumes. Meas Sci Technol 30(11):115008

    Article  MathSciNet  Google Scholar 

  22. Wittevrongel L, Lava P, Lomov SV, Debruyne D (2015) A self adaptive global digital image correlation algorithm. Exp Mech 55:361–378

    Article  Google Scholar 

  23. Yuan Y, Huang JY, Fang J, Yuan F, Xiong CY (2015) A self-adaptive sampling digital image correlation algorithm for accurate displacement measurement. Opt Lasers Eng 65:57–63

    Article  Google Scholar 

  24. Ronovskỳ A, Vašatová A (2017) Elastic image registration based on domain decomposition with mesh adaptation. Mathematical analysis and numerical mathematics 15:322–330

    Google Scholar 

  25. Yang J, Bhattacharya K (2019) Augmented Lagrangian digital image correlation. Exp Mech 59:187–205

    Article  Google Scholar 

  26. Yang J (2019) Augmented Lagrangian Digital Image Correlation Matlab code (2D_ALDIC). Caltech DATA: https://data.caltech.edu/records/1794

  27. Yang J, and Bhattacharya K (2019) Fast adaptive global digital image correlation. In L Lamberti, MT Lin, C Furlong, C Sciammarella, PL. Reu, and MA Sutton, editors, Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics, Volume 3, pages 69–73. Springer

  28. Xu XH, Su Y, Zhang QC (2017) Theoretical estimation of systematic errors in local deformation measurements using digital image correlation. Opt Lasers Eng 88:265–279

    Article  Google Scholar 

  29. https://github.com/jyang526843/adapt_ALDIC

  30. Yang J (2020) Adaptive Mesh Augmented Lagrangian Digital Image Correlation MATLAB code (adapt_ALDIC). Caltech DATA: https://data.caltech.edu

  31. Leclerc H, Périé JN, Hild F, Roux S (2012) Digital volume correlation: what are the limits to the spatial resolution? Mec Ind 13:361–371

    Google Scholar 

  32. Pan B, Wang B, Lubineau G, Moussawi A (2015) Comparison of subset-based local and finite element-based global digital image correlation. Exp Mech 55:887–901

    Article  Google Scholar 

  33. Wang TY, Qian KM (2017) Parallel computing in experimental mechanics and optical measurement: A review (II). Optics and Lasers in Engineering

  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 111:123–143

    Article  MathSciNet  MATH  Google Scholar 

  35. Fedele R, Galantucci L, Ciani A (2013) Global 2D digital image correlation for motion estimation in a finite element framework: a variational formulation and a regularized, pyramidal, multi-grid implementation. Int J Number Methods Eng 96:739–762

    Article  MATH  Google Scholar 

  36. Horn BK, and Schunck BG (1981) Determining optical flow. In 1981 Technical Symposium East, pages 319–331. International Society for Optics and Photonics

  37. Modersitzki J (2004) Numerical methods for image registration. Oxford University Press on Demand

  38. Christensen GE (1994) Deformable shape models for anatomy

  39. Fischer B, Modersitzki J (2003) Combining landmark and intensity driven registrations. PAMM 3:32–35

    Article  MATH  Google Scholar 

  40. Burger M, Modersitzki J, Ruthotto L (2013) A hyperelastic regularization energy for image registration. SIAM J Sci Comput 35:B132–B148

    Article  MathSciNet  MATH  Google Scholar 

  41. Yang J (2019) Fast adaptive augmented lagrangian digital image correlation. PhD thesis, California Institute of Technology

  42. Glowinski R (2016) ADMM and Non-convex Variational Problems. In: Glowinski R, Osher SJ, Yin W (eds) Splitting Methods in Communication. Imaging, Science and Engineering, Scientific Computation. Springer, Cham, Switzerland, pp 251–299

    Google Scholar 

  43. 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 3:1–122

    MATH  Google Scholar 

  44. Bangerth W, Joshi A (2008) Adaptive finite element methods for the solution of inverse problems in optical tomography. Inverse Prob 24:034011

    Article  MathSciNet  MATH  Google Scholar 

  45. Nochetto RH, Siebert KG, and Veeser A (2009) Theory of adaptive finite element methods: an introduction. In Multiscale, nonlinear and adaptive approximation, pages 409–542. Springer

  46. Dörfler W, Rumpf M (1998) An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation. Mathematics of Computation of the American Mathematical Society 67:1361–1382

    Article  MathSciNet  MATH  Google Scholar 

  47. Moore DW (1992) Simplical mesh generation with applications. Technical report, Cornell University

  48. Popinet S (2003) Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J Comput Phys 190:572–600

    Article  MathSciNet  MATH  Google Scholar 

  49. Reddy (1993) An introduction to the finite element method, volume 2. McGraw-Hill New York

  50. Gupta AK (1978) A finite element for transition from a fine to a coarse grid. Int J Numer Methods Eng 12:35–45

    Article  MATH  Google Scholar 

  51. Stefan AF, Anja S (2020) Adaptive mesh refinement in 2D: An efficient implementation in Matlab. Computational Methods in Applied Mathematics 20:459–479

    Article  MathSciNet  MATH  Google Scholar 

  52. Reu PL, Toussaint E, Jones E, Bruck HA, Iadicola M, Balcaen R, Turner DZ, Siebert T, Lava P, Simonsen M (2018) DIC challenge: Developing images and guidelines for evaluating accuracy and resolution of 2D analyses. Exp Mech 58:1067–1099

    Article  Google Scholar 

  53. Saraswathibhatla A, and Notbohm J (2017) Applications of DIC in the mechanics of collective cell migration. In International Digital Imaging Correlation Society, pages 51–53

  54. Saraswathibhatla A, and Notbohm J (2020) Tractions and stress fibers control cell shape and rearrangements in collective cell migration. Phys Rev X 10:011016

  55. Zhang ZY, James RD, Múller S (2009) Energy barriers and hysteresis in martensitic phase transformations. Acta Mater 57:4332–4352

    Article  Google Scholar 

  56. Song YT, Chen X, Dabade V, Shield TW, James RD (2013) Enhanced reversibility and unusual microstructure of a phase-transforming material. Nature 502:85

    Article  Google Scholar 

  57. Stebner AP, Bigelow GS, Yang J, Shukla DP, Saghaian SM, Rogers R, Garg A, Karaca HE, Chumlyakov Y, Bhattacharya K et al (2014) Transformation strains and temperatures of a nickel-titanium-hafnium high temperature shape memory alloy. Acta Mater 76:40–53

    Article  Google Scholar 

  58. Bhattacharya K (2003) Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect, vol 2. Oxford University Press

  59. Yang J, Hazlett L, Landauer AK, Franck C (2020) Augmented lagrangian digital volume correlation. Exp Mech 60:1205–1223

  60. Landauer AK, Patel M, Henann DL, Franck C (2018) A q-factor-based digital image correlation algorithm (qDIC) for resolving finite deformations with degenerate speckle patterns. Exp Mech 58:815–830

    Article  Google Scholar 

  61. 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 47:427–438

    Article  Google Scholar 

  62. Réthoré J, Hild F, Roux S (2008) Extended digital image correlation with crack shape optimization. Int J Numer Methods Eng 73:248–272

    Article  MathSciNet  MATH  Google Scholar 

  63. Poissant J, Barthelat F (2010) A novel subset splitting procedure for digital image correlation on discontinuous displacement fields. Exp Mech 50:353–364

    Article  Google Scholar 

  64. Rubino V, Rosakis AJ, Lapusta N (2019) Full-field ultrahigh-speed quantification of dynamic shear ruptures using digital image correlation. Exp Mech 59:551–582

    Article  Google Scholar 

  65. Tal Y, Rubino V, Rosakis AJ, Lapusta N (2019) Enhanced digital image correlation analysis of ruptures with enforced traction continuity conditions across interfaces. Appl Sci 9:1625

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to Prof. Jacob Notbohm and Aashrith Saraswathibhatla who shared their experimental data 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).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Madison, WI, 53706, Madison, USA

    J. Yang

  2. Division of Engineering and Applied Science, California Institute of Technology, CA, 91125, Pasadena, USA

    K. Bhattacharya

Authors
  1. J. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Bhattacharya.

Ethics declarations

Conflicts of Interest

The authors declare that they have no conflict of interest.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 6670 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, J., Bhattacharya, K. Fast Adaptive Mesh Augmented Lagrangian Digital Image Correlation. Exp Mech 61, 719–735 (2021). https://doi.org/10.1007/s11340-021-00695-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00695-9

Keywords

Search

Navigation