The errors in digital image correlation due to overmatched shape functions

Abstract

In subset-based digital image correlation (DIC), a proper shape function must be chosen to approximate the underlying displacement field of the target subsets to ensure an accurate subset matching. Shape functions with varying orders of Taylor’s expansions (e.g. zero-, first- and second-order) have been proposed. However, since the actual deformation occurring in the deformed subsets cannot be known a priori in most practical measurements, problems of mismatch (undermatched or overmatched) inevitably arise, which lead to additional errors in the measurement displacements. Although systematic errors due to undermatched shape functions have been thoroughly studied, the displacement errors associated with overmatched shape functions are still not sufficiently clear to us. In this paper, the systematic and random errors caused by the use of overmatched shape functions are first examined using numerical translation tests with precisely controlled subpixel motions. The results reveal that overmatched shape functions will not introduce additional systematic error but can induce increased random error, while the latter is negligibly small when a larger subset is used. Thus, it can be made explicit that second-order shape functions, capable of depicting more complex local deformation, can be used for practical DIC applications as a default, because this effectively eliminates the possible systematic error associated with the use of first-order shape functions, while the possibly increased random errors are small enough if using a relatively larger subset. Two sets of images with inhomogeneous deformation are also used to verify the accuracy of DIC measurements using second-order shape functions.