Abstract
In this paper, we propose to investigate the potential improvement of using Non-Uniform Rational B-Spline (NURBS) functions for displacement measurements by digital image correlation (DIC). The aim is at improving the performance of DIC to capture with low uncertainty and low noise levels not only the displacement field but also its derivatives. Indeed, when the displacement field is used to feed constitutive law identification procedures, displacement derivatives are required and thus may be measured with robustness. Two examples illustrate the potential of NURBS for DIC: a compressive test on a wood sample and a bending test on a steel beam. For the latter, beam kinematics are adopted and NURBS are used in order to capture the variation of the curvature (second derivative of the displacement) along the beam axis. For these two examples, an error study based on a decomposition of the error into the correlation error and the interpolation error, is carried out and shows the great potential of NURBS functions for DIC.
Similar content being viewed by others
Notes
Note that in standard FE analysis, Lagrange polynomials are used, which are different from the C 0 functions used here but produce similar results.
References
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):133–139
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
Roux S, Hild F (2006) Stress intensity factor measurement from digital image correlation: post-processing and integrated approaches. Int J Fract 140(1–4):141–157
Réthoré J, Hild F, Roux S (2007) Extended digital image correlation with crack shape optimization. Int J Numer Methods Eng 73(2):248–272. doi:10.1002/nme.2070
Farin G (1995) NURBS curves and surfaces: from projective geometry to practical use. A.K. Peters, Natick
Piegl L, Tiller W (1997) The NURBS book (monographs in visual communication), 2nd edn. Springer, New York
Cohen E, Riesenfeld R, Elber G (2001) Geometric modeling with splines: an introduction. A.K. Peters, Wellesley
Rogers D (2001) An introduction to NURBS with historical perspective. Academic, San Diego
Hughes T, Cottrell J, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195
Bazilevs Y, Calo V, Cottrell J, Hughes T, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197(1–4):173–201
Bazilevs Y, Calo V, Hughes T, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms and computations. Comput Mech 43(1):3–37
Akkerman I, Bazilevs Y, Calo V, Hughes T, Hulshoff S (2008) The role of continuity in residual-based variational multiscale modeling of turbulence. Comput Mech 41(3):371–378
Gomez H, Calo V, Bazilevs Y, Hughes T (2008) Isogeometric analysis of the Cahn-Hilliard phase field model. Comput Methods Appl Mech Eng 197:4333–4352
Auricchio F, da Veiga LB, Buffa A, Lovadina C, Reali A, Sangalli G (2007) A fully locking-free isogeometric approach for plane linear elasticity problems: a stram function formulation. Comput Methods Appl Mech Eng 197:160–172
Elguedj T, Bazilevs Y, Calo V, Hughes T (2008) B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity based on higher-order NURBS elements. Comput Methods Appl Mech Eng 197:2732–2762
Hughes T, Reali A, Sangalli G (2008) Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. Comput Methods Appl Mech Eng 197(49–50):4104–4124
Sutton M, Cheng M, Peters W, Chao Y, McNeill S (1986) Application of an optimized digital image correlation method to planar deformation analysis. Image Vis Comput 4(3):143–150
Sutton M, McNeill S, Helm J, Chao Y (2000) Photomechanics. In: chap Advances in two-dimensional and three-dimensional computer vision. Springer, New York, pp 323–372
Cheng P, Sutton MA, Schreier HW, McNeill SR (2002) Full-field speckle pattern image correlation with b-spline deformation function. Exp Mech 42(3):344–352
Réthoré J, Hild F, Roux S (2007) Shear-band capturing using a multiscale extended digital image correlation technique. Comput Methods Appl Mech Eng 196(49–52):5016–5030. doi:10.1016/j.cma.2007.06.019
Hild F, Roux S, Gras R, Guerrero N, Marante M, Florez-Lopez J (2009) Displacement measurement technique for beam kinematics. Opt Lasers Eng 47(3–4):495–503
Author information
Authors and Affiliations
Corresponding author
Additional information
Color figures available in online version at (location).
Rights and permissions
About this article
Cite this article
Réthoré, J., Elguedj, T., Simon, P. et al. On the Use of NURBS Functions for Displacement Derivatives Measurement by Digital Image Correlation. Exp Mech 50, 1099–1116 (2010). https://doi.org/10.1007/s11340-009-9304-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11340-009-9304-z