Systematic Errors in Digital Image Correlation Due to Undermatched Subset Shape Functions

Abstract

ABSTRACT--Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset 9 Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains.In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed 9 It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis 9 Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first-and second-order shape functions 9 Finally, the relation of this work to previously published studies is discussed 9

High Performance Digital Volume Correlation

“…In This mapping between the reference image and the deformed image is given by a shape function which defines the degrees-of-freedom (DOF) to be determined at each point. The linear shape function [12] Alternatively, the quadratic shape function results in greater accuracy in matching an underlying nonlinear deformation [48,70]. It adds second derivative terms, for a total of thirty DOF at each point.…”

“…When the shape function does not match the underlying displacement, a systematic bias error is measured by DIC, as discussed by Schreier and Sutton [70].…”

“…However, the standard deviation σ u is also larger when using quadratic shape functions [70], because the extra quadratic terms allow for more flexibility in matching the displacement. For instance, in a linear field, the quadratic terms should all be zero, but due to experimental noise will be some small but non-zero value, introducing more variability into the results.…”

On the detection of systematic errors in terrestrial laser scanning data

“…Yoon et al [20] carried out an error compensation process for detecting systematic errors at depth discontinuities. For relevant researches, we refer to Vosselman [17] and Schreier and Sutton [15].…”

A speckle texture image generator

“…As the number of influencing parameters is large, a practical approach consists in analysing computer generated images given sets of varying settings. Several authors [1][2][3][4] have used synthetic deformed speckle-pattern images for DIC evaluation, however the generated patterns are quite non realistic, often exhibit very different spectral properties as present in real speckle images, and elude potentially important effects brought by the digitization process of an imaging system. We want to produce synthetic images of a realistic speckle pattern.…”