Augmented Lagrangian Digital Volume Correlation (ALDVC)

Digital volume correlation (DVC), the volumetric extension of the popular digital image correlation (DIC) technique, is a powerful experimental tool for measuring 3D volumetric full-field displacements and strains. Most current DVC algorithms can be categorized into either local or finite-element-based global methods. As with most experimental approaches, there are drawbacks with each of these methods. In the local method the subvolume deformations are estimated independently and the computed displacement field may not necessarily be kinematically compatible. Thus, the deformation gradients can be noisy, especially when using small volumetric subsets. Although the global method often enforces kinematic compatibility, it generally incurs substantially greater computational costs than its local counterpart, which is especially significant for large volumetric data sets. To address these shortcomings, we present a new hybrid DVC algorithm, called augmented Lagrangian digital volume correlation (ALDVC), which combines the advantages of both the local (fast computation time) and global (compatible displacement field) methods. This new algorithm builds on our recent work on the augmented Lagrangian digital image correlation (2D-ALDIC) technique and solves the general motion optimization problem by using the alternating direction method of multipliers (ADMM). We demonstrate that our ALDVC algorithm has high accuracy and precision while maintaining low computational cost, and is a significant improvement compared to current local and global DVC methods. ALDVC is a computationally efficient algorithm to measure 3D volumetric displacements and strains. An open-source Matlab implementation is freely available.