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A Self Adaptive Global Digital Image Correlation Algorithm

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Abstract

A novel Digital Image Correlation algorithm is presented, focussing on accurately determining small strains with high strain gradients. Principles from p-adaptive finite element analysis are implemented to obtain a self adapting higher order mesh. The self adapting principle reduces the dependency of the results on the user’s input and the higher orders insure sufficient degrees of freedom. Performance of the algorithm, in terms of resolution and spatial resolution, is checked and compared to the traditional local method. The results indicate that the introduced method is appropriate for accurately measuring high heterogeneous deformations and that the obtained data is to a large extent user independent.

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Authors and Affiliations

  1. Department of Matrerials Technology, KU Leuven, Campus Ghent, Gebroeders De Smetstraat 1, 9000, Ghent, Belgium

    L. Wittevrongel, P. Lava, S. V. Lomov & D. Debruyne

Authors
  1. L. Wittevrongel
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  2. P. Lava
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  3. S. V. Lomov
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  4. D. Debruyne
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Corresponding author

Correspondence to L. Wittevrongel.

Additional information

This publication was supported by Agency for Innovation by Science and Technology in Flanders (IWT).

Appendix: Legendre Shape Functions

Appendix: Legendre Shape Functions

Legendre shape functions are a combination of function P p (χ):

$$ P_{p}(\chi ) = \frac{1}{(p-2)!2^{p-2}} \frac{d^{p-2}}{d\chi^{p-2}}[(1-\chi^{2})^{p-1}] $$
(61)

In a p-element shape functions are assigned to nodes, edges or faces identified in Fig 27.

Fig. 27
figure 27

Element nodes, edges and face

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The shape functions that can be used are shown in Table 8 with p the polynomial order.

Table 8 Hierarchical shape functions
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Wittevrongel, L., Lava, P., Lomov, S.V. et al. A Self Adaptive Global Digital Image Correlation Algorithm. Exp Mech 55, 361–378 (2015). https://doi.org/10.1007/s11340-014-9946-3

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