Fast Adaptive Augmented Lagrangian Digital Image Correlation

Abstract

Digital image correlation (DIC) is a powerful experimental technique for measuring full-field displacement and strain. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation in order to compute the displacement and strain fields. Local Subset DIC and finite element-based Global DIC are two widely used image matching methods; however there are some drawbacks to these methods. In Local Subset DIC, the computed displacement field may not satisfy compatibility, and the deformation gradient may be noisy, especially when the subset size is small. Global DIC incorporates displacement compatibility, but can be computationally expensive. In this thesis, we propose a new method, the augmented-Lagrangian digital image correlation (ALDIC), that combines the advantages of both the local (fast and in parallel) and global (compatible) methods. We demonstrate that ALDIC has higher accuracy and behaves more robustly compared to both Local Subset DIC and Global DIC. DIC requires a large number of high resolution images, which imposes significant needs on data storage and transmission. We combined DIC algorithms with image compression techniques and show that it is possible to obtain accurate displace- ment and strain fields with only 5 % of the original image size. We studied two compression techniques – discrete cosine transform (DCT) and wavelet transform, and three DIC algorithms – Local Subset DIC, Global DIC and our newly proposed augmented Lagrangian DIC (ALDIC). We found the Local Subset DIC leads to the largest errors and ALDIC to the smallest when compressed images are used. We also found wavelet-based image compression introduces less error compared to DCT image compression. To further speed up and improve the accuracy of DIC algorithms, especially in the study of complex heterogeneous strain fields at various length scales, we apply an adaptive finite element mesh to DIC methods. We develop a new h-adaptive technique and apply it to ALDIC. We show that this adaptive mesh ALDIC algorithm significantly decreases computation time with no loss (and some gain) in accuracy.