Finite element formulation for a digital image correlation method

Abstract

A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust.

A Space-Time PGD-DIC Algorithm:

“…In this section, particular care is taken to provide a global formalism that is suitable for both standard Finite Element Digital Image Correlation (FE-DIC [35,7]) and the newly developed Finite Element Stereo Digital Image Correlation (FE-SDIC [13,28,33]). …”

“…is a set of n s well chosen basis functions and q k i denote the corresponding degrees of freedom (dof) at time step k. In this paper, finite element shape functions are used in order to benefit from a common formalism with numerical simulation [35]. By introducing this approximation into the linearized minimization problem and performing the differentiation, we finally obtain the following linear system to be solved at each iteration of the Gauss-Newton algorithm and for each time step k:…”

“…Here, we propose to use a Finite Element based Digital Image Correlation (FE-DIC) method. The recent developments in the field of FE-DIC [35,7] and the even more recent advances in Finite Element Stereo DIC (FE-SDIC) [13,29,28,33] allow a direct link with the simulation tools. It is thus possible to share the same FE mesh during the calculation and the measurement, in the aim of (a) greatly simplifying the bridge between simulation and experimentation, and (b) limiting the uncertainties associated with reprojection.…”

Investigation of Strain Measurements using Digital Image Correlation with a Finite Element Method

“…Xiang [10] used the moving least-squares (MLS) method to smooth the displacement field followed by a numerical differentiation of the smoothed displacement field to get the strain fields. Different from above pointwise algorithms, the Q4-DIC developed by Besnard [11] and the finite element method proposed by Sun [12] can be classified as a continuum method, in which the surface deformation of the sample is measured throughout the entire image area. These techniques ensure the displacement continuity among pixel points.…”

Shear-band capturing using a multiscale extended digital image correlation technique

“…Many correlation algorithms rely on the local analysis of subsets subjected to different kinematics and gray level interpolations (Sutton et al, 1983(Sutton et al, , 2000. More recently, continuous displacement field basis have been introduced in the general framework of maximization of the correlation between the reference and the displacementcorrected strained image such as B-splines (Cheng et al, 2002), polynomials or finite element interpolation functions (Sun et al, 2005). Alternative approaches based on a direct use of the optical flow conservation allow naturally for continuous displacement fields determination, as shown for Fourier series (Wagne et al, 2002), or finite element shape functions (Besnard et al, 2006).…”