7. Fast Adaptive Global Digital Image Correlation

Digital image correlation (DIC) is a powerful experimental technique to compute full-field displacements and strains. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation, and thereby to compute displacements and strains. Since DIC is a non-contact method that gives the whole field deformation, it is widely used to measure complex deformation patterns. Finite element (FE)-based Global DIC with regularization is one of the commonly used algorithms and it can be combined with finite element numerical simulations at the same time (Besnard et al., J Strain Anal Eng Design 47(4):214–228, 2012). However, Global DIC algorithm is usually computationally expensive and converges slowly. Further, it is difficult to directly apply an adaptive finite element mesh to Global DIC because the stiffness matrix and the external force vector have to be rebuilt every time the mesh is changed.

In this paper, we report a new Global DIC algorithm that uses adaptive mesh. It builds on our recent work on the augmented Lagrangian digital image correlation (ALDIC) (Yang and Bhattacharya, Exp Mech, submitted). We consider the global compatibility condition as a constraint and formulate it using an augmented Lagrangian (AL) method. We solve the resulting problem using the alternating direction method of multipliers (ADMM) (Boyd et al., Mach Learn 3(1):1–122, 2010) where we separate the problem into two subproblems. The first subproblem is computed fast, locally and in parallel, and the second subproblem is computed globally without image grayscale value terms where nine point Gaussian quadrature works very well. Compared with current Global DIC algorithm, this new adaptive Global DIC algorithm decreases computation time significantly with no loss (and some gain) in accuracy.