Systematic errors in digital image correlation due to undermatched subset shape functions

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. 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. 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. 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. Finally, the relation of this work to previously published studies is discussed.