Fractal Pattern for Multiscale Digital Image Correlation
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RESEARCH PAPER
Fractal Pattern for Multiscale Digital Image Correlation ¨ Fouque1,2 · Robin Bouclier1,3 · Jean-Charles Passieux1 · Jean-Noel ¨ Peri ´ e´ 1 Raphael Received: 2 December 2019 / Accepted: 23 July 2020 © Society for Experimental Mechanics 2020
Abstract Background: Digital Image Correlation (DIC) is based on the matching, between reference and deformed state images, of features contained in patterns that are deposited on test sample surfaces. These features are often suitable for a single scale, and there is a current lack of multiscale patterns capable of providing reliable displacement measurements over a wide range of scales. Objective: Here, we aim to demonstrate that a pattern based on a fractal (self-affine) surface would make a suitable pattern for multiscale DIC. Methods: A method to numerically generate patterns directly from a desired auto-correlation function is introduced. It is then enhanced by a Mean Intensity Gradient (MIG) improvement process based on grey level redistribution. Numerical experiments at multiple scales are performed for two different imposed displacement fields and results for one of the patterns generated are compared with those obtained for a random pattern and a Perlin noise one. Results: The proposed pattern is shown to lead to DIC errors comparable to those found with the two others for the first scales, but has much greater robustness. More importantly, the pattern generated here exhibits stable errors and robustness with respect to the scale whereas these two outputs become significantly degraded for the other two patterns as the scale increases. Conclusions: As a result, scale invariance properties of the pattern based on fractal surfaces correspond to scale invariance in DIC errors as well. This is of great interest regarding the use of such patterns in multiscale DIC. Keywords Pattern auto-correlation · Coarse-to-fine initialisation · Uncertainty quantification · Large strain · Speckle optimisation · Pattern generation
Introduction One of the most important elements in Digital Image Correlation (DIC) is the pattern deposited on test sample surfaces, as measurement accuracy depends strongly on
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11340-020-00649-7) contains supplementary material, which is available to authorized users. Rapha¨el Fouque
[email protected] 1
ICA, INSA-UPS-Mines Albi-ISAE-CNRS, Universit´e de Toulouse, Toulouse, France
2
DGA Aeronautical Systems, Balma, France
3
IMT, INSA-UT1-UT2-UT3-CNRS, Universit´e de Toulouse, Toulouse, France
specific features of this pattern [10, 20, 29, 58]. Depending on the application, suitable speckles can be generated on specimen surfaces using a wide variety of experimental methods. For instance, for large scale applications, an airbrush or marker pen may be useful [21, 22] while, for small scale applications, the focused ion beam (FIB) technique or spin coating can be used [18, 54, 57]. However, for many of these methods, the operator’s experienc
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