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Absolute Nodal Coordinates in Digital Image Correlation

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A great deal of progress has been made in recent years in the field of global digital image correlation (DIC), where higher-order, element-based approaches were proposed to improve the interpolation performance and to better capture the displacement fields. In this research, another higher-order, element-based DIC procedure is introduced. Instead of the displacements, the elements’ global nodal positions and nodal position-vector gradients, defined according to the absolute nodal coordinate formulation, are used as the searched parameters of the Newton–Raphson iterative procedure. For the finite elements, the planar isoparametric plates with 24 nodal degrees of freedom are employed to ensure the gradients’ continuity among the elements. As such, the presented procedure imposes no linearization on the strain measure, and therefore indicates a natural consistency with the nonlinear continuum theory. To verify the new procedure and to show its advantages, a real large deformation experiment and several numerical tests on the computer-generated images are studied for the standard, low-order, element-based digital image correlation and the presented procedure. The results show that the proposed procedure proves to be accurate and reliable for describing the rigid-body movement and simple deformations, as well as for determining the continuous finite strain field of a real specimen.

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  1. 1.

    Witz J, Hild F, Roux S, Rieunier J (2009) Mechanical properties of crimped mineral wools: identification from digital image correlation. In: IUTAM symposium on mechanical properties of cellular materials, IUTAM Bookseries, vol 12, pp 135–147

  2. 2.

    Zhang J, Cai Y, Ye W, Yu T (2011) On the use of the digital image correlation method for heterogeneous deformation measurement of porous solids. Opt Lasers Eng 49(2):200–209

  3. 3.

    Tarigopula V, Hopperstad O, Langseth M, Clausen A, Hild F, Lademo O, Eriksson M (2008) A study of large plastic deformations in dual phase steel using digital image correlation and FE analysis. Exp Mech 48:181–196

  4. 4.

    Hild F, Roux S (2007) Digital image mechanical identification (DIMI). Exp Mech 48(4):495–508

  5. 5.

    Perie J, Leclerc H, Roux S, Hild F (2009) Digital image correlation and biaxial test on composite material for anisotropic damage law identification. Int J Solids Struct 46(11–12):2388–2396

  6. 6.

    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(6):062,001

  7. 7.

    Cheng P, Sutton M, Schreier H, McNeill S (2002) Full-field speckle pattern image correlation with B-spline deformation function. Exp Mech 42:344–352

  8. 8.

    Sun Y, Pang J, Wong C, Su F (2005) Finite element formulation for a digital image correlation method. Appl Opt 44(34):7357–7363

  9. 9.

    Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis from digital images: application to portevin—le chatelier bands. Exp Mech 46:789–803

  10. 10.

    Elguedj T, Rethore J, Buteri A (2011) Isogeometric analysis for strain field measurements. Comput Methods Appl Mech Eng 200(1–4):40–56

  11. 11.

    Ma S, Zhao Z, Wang X (2012) Mesh-based digital image correlation method using higher order isoparametric elements. J Strain Anal Eng Des 47:163–175

  12. 12.

    Hild F, Roux S, Gras R, Guerrero N, Eugenia M, Flórez-López J (2009) Displacement measurement technique for beam kinematics. Opt Lasers Eng 47:495–503

  13. 13.

    Rethore J, Elguedj T, Simon P, Coret M (2010) On the use of NURBS functions for displacement derivatives measurement by digital image correlation. Exp Mech 50:1099–1116

  14. 14.

    Hild F, Raka B, Baudequin M, Roux S, Cantelaube F (2002) Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation. Appl Opt 41:6815–6828

  15. 15.

    Shabana A (2008) Computational continuum mechanics. Cambridge University Press

  16. 16.

    Shabana A (1998) Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dyn 16:293–306

  17. 17.

    Shabana A (1997) Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst Dyn 1:339–348

  18. 18.

    Shabana A, Mikkola A (2003) On the use of the degenerate plate and the absolute nodal co-ordinate formulations in multibody system applications. J Sound Vib 259(2):481–489

  19. 19.

    Yu L, Zhao Z, Tang J, Ren G (2010) Integration of absolute nodal elements into multibody system. Nonlinear Dyn 62:931–943

  20. 20.

    Dufva K, Shabana A (2005) Analysis of thin plate structures using the absolute nodal coordinate formulation. Proc Inst Mech Eng, Proc Part K, J Multi-Body Dyn 219:345–355

  21. 21.

    Čepon G, Boltežar M (2009) Dynamics of a belt-drive system using a linear complementarity problem for the belt-pulley contact description. J Sound Vib 319(3–5):1019–1035

  22. 22.

    Čepon G, Boltežar M (2009) Introduction of damping into the flexible multibody belt-drive model: a numerical and experimental investigation. J Sound Vib 324(1–2):283–296

  23. 23.

    Dmitrochenko O, Pogorelov D (2003) Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst Dyn 10:17–43

  24. 24.

    Sereshk V, Salimi M (2011) Comparison of finite element method based on nodal displacement and absolute nodal coordinate formulation (ANCF) in thin shell analysis. Int J Numer Meth Bio 27(8):1185–1198

  25. 25.

    Shabana A, Maqueda L (2008) Slope discontinuities in the finite element absolute nodal coordinate formulation: gradient deficient elements. Multibody Syst Dyn 20:239–249

  26. 26.

    Guo B, Giraudeau G, Pierron F, Avril S (2008) Viscoelastic material properties’ identification using full field measurements on vibrating plates, p 737565. SPIE

  27. 27.

    Avril S, Bonnet M, Bretelle A, Grédiac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48:381–402

  28. 28.

    Zienkiewicz O, Taylor R (2000) Finite element method, vol 1, 5th edn. The Basis, Elsevier

  29. 29.

    Bing P, Hui-min X, Bo-qin X, Fu-long D (2006) Performance of sub-pixel registration algorithms in digital image correlation. Meas Sci Technol 42:1615–1621

  30. 30.

    Vendroux G, Knauss W (1998) Submicron deformation field measurements: Part 2. Improved digital image correlation. Exp Mech 38:86–92

  31. 31.

    Zhu Z, Pour B (2011) A nodal position finite element method for plane elastic problems. Finite Elem Anal Des 47(2):73–77

  32. 32.

    Gonzales R, Woods R, Eddins S (2009) Digital image processing using Matlab, 2nd edn. Gatesmark Publishing

  33. 33.

    Langerholc M, Česnik M, Slavič J, Boltežar M (2012) Experimental validation of a complex, large-scale, rigid-body mechanism. Eng Struct 36:220–227

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Operation partially financed by the European Union, European Social Fund.

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Correspondence to J. Slavič.



The j-th element shape function matrix [20] is defined as

$$ \textbf{S}_j(\textbf{x}_j)=\textbf{S}_{ij}=\textbf{S}_j(x_{1ij},x_{2ij})=\left[s_{1ij}\,\textbf{I},~~s_{2ij}\,\textbf{I},~~\ldots,~~s_{12ij}\,\textbf{I}\right]~, $$

where I is 2 × 2 identity matrix, and

$$ \begin{array}{rll} s_{1ij}&=&-(\xi-1)\,(\eta-1)\,(2\,\eta^2-\eta+2\,\xi^2-\xi-1)~,\\ s_{2ij}&=&-a\,\xi\,(\xi-1)^2\,(\eta-1)~,\\ s_{3ij}&=&-a\,\eta\,(\eta-1)^2\,(\xi-1)~,\\ s_{4ij}&=&\xi\,(2\,\eta^2-\eta-3\,\xi+2\,\xi^2)\,(\eta-1)~,\\ s_{5ij}&=&-a\,\xi^2\,(\xi-1)\,(\eta-1)~,\\ s_{6ij}&=&a\,\xi\,\eta\,(\eta-1)^2~,\\ s_{7ij}&=&-\xi\,\eta\,(1-3\,\xi-3\,\eta+2\,\eta^2+2\,\xi^2)~,\\ s_{8ij}&=&a\,\xi^2\,\eta\,(\xi-1)~,\\ s_{9ij}&=&a\,\xi\,\eta^2\,(\eta-1)~,\\ s_{10ij}&=&\eta\,(\xi-1)\,(2\,\xi^2-\xi-3\,\eta+2\,\eta^2)~,\\ s_{11ij}&=&a\,\xi\,\eta\,(\xi-1)^2~,\\ s_{12ij}&=&-a\,\eta^2\,(\xi-1)\,(\eta-1)~,\\\quad \xi&=&x_{1ij}/a,~\eta=x_{2ij}/a~, \end{array} $$

where a is the rectangular plate size.

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Langerholc, M., Slavič, J. & Boltežar, M. Absolute Nodal Coordinates in Digital Image Correlation. Exp Mech 53, 807–818 (2013). https://doi.org/10.1007/s11340-012-9691-4

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  • Absolute nodal coordinate formulation
  • Digital image correlation
  • Higher-order plate element
  • Large deformation