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Convolution finite element based digital image correlation for displacement and strain measurements

Ye Lu, Weidong Zhu

TL;DR

The proposed DIC method has been tested by several representative examples, including the DIC challenge 2.0 benchmark problems, with comparison to the usual FE based DIC.

Abstract

This work presents a novel global digital image correlation (DIC) method, based on a newly developed convolution finite element (C-FE) approximation. The convolution approximation can rely on the mesh of linear finite elements and enables arbitrarily high order approximations without adding more degrees of freedom. Therefore, the C-FE based DIC can be more accurate than {the} usual FE based DIC by providing highly smooth and accurate displacement and strain results with the same element size. The detailed formulation and implementation of the method have been discussed in this work. The controlling parameters in the method include the polynomial order, patch size, and dilation. A general choice of the parameters and their potential adaptivity have been discussed. The proposed DIC method has been tested by several representative examples, including the DIC challenge 2.0 benchmark problems, with comparison to the usual FE based DIC. C-FE outperformed FE in all the DIC results for the tested examples. This work demonstrates the potential of C-FE and opens a new avenue to enable highly smooth, accurate, and robust DIC analysis for full-field displacement and strain measurements.

Convolution finite element based digital image correlation for displacement and strain measurements

TL;DR

The proposed DIC method has been tested by several representative examples, including the DIC challenge 2.0 benchmark problems, with comparison to the usual FE based DIC.

Abstract

This work presents a novel global digital image correlation (DIC) method, based on a newly developed convolution finite element (C-FE) approximation. The convolution approximation can rely on the mesh of linear finite elements and enables arbitrarily high order approximations without adding more degrees of freedom. Therefore, the C-FE based DIC can be more accurate than {the} usual FE based DIC by providing highly smooth and accurate displacement and strain results with the same element size. The detailed formulation and implementation of the method have been discussed in this work. The controlling parameters in the method include the polynomial order, patch size, and dilation. A general choice of the parameters and their potential adaptivity have been discussed. The proposed DIC method has been tested by several representative examples, including the DIC challenge 2.0 benchmark problems, with comparison to the usual FE based DIC. C-FE outperformed FE in all the DIC results for the tested examples. This work demonstrates the potential of C-FE and opens a new avenue to enable highly smooth, accurate, and robust DIC analysis for full-field displacement and strain measurements.
Paper Structure (18 sections, 41 equations, 23 figures, 3 tables)

This paper contains 18 sections, 41 equations, 23 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Convolution finite element approximation
  3. Convolution finite element for digital image correlation
  4. Problem formulation
  5. Convolution FE discretization
  6. Smoothed grayscale interpolation
  7. Convolution shape function based interpolation
  8. Spline interpolation with separation of variables
  9. Discussion on the potential adaptivity
  10. Numerical experiments
  11. Example 1: synthetic image with large spots
  12. Example 2: synthetic image with random spots
  13. Example 3: DIC Challenge 2.0 star1
  14. Example 4: DIC Challenge 2.0 star2
  15. Discussion on the computational cost
  16. ...and 3 more sections

Figures (23)

  • Figure 1: Supporting nodes for finite element and convolution finite element approximations
  • Figure 2: Illustration of different patch sizes and the influencing domain of kernel function defined by the dilation
  • Figure 3: Illustration of the convolution finite element shape function, where the patch size $s=2$, the support nodes locate at $\{-5,-3,-1, 1, 3, 5\}$, $p$ denotes the polynomial order of $W$. The original FE shape function remains linear for all the cases, whereas the convolution shape function is nonlinear with higher-order smoothness.
  • Figure 4: C-FE shape functions over the element region $[-1,1]$. Left: C-FE with $s=2, p=1, a=1$, Right: FE.
  • Figure 8: Support nodes for FE-Q4 and FE-Q8 with different $h$
  • ...and 18 more figures