Meshfree Digital Image Correlation Using Element Free Galerkin Method: Theory, Algorithm and Validation

Abstract

Abstract Background The association of advanced digital image correlation (DIC) and numerical simulation has been widely used for inverse parameter identification. Objective It is attractive to develop an accurate DIC method sharing the common features with numerical simulation, which can lead to better synergy between experiments and simulations. Methods A new meshfree digital image correlation (MF-DIC) using element free Galerkin method (EFGM) is proposed for deformation measurement. The EFGM is a classical meshfree method in numerical studies, and it is directly used to construct the shape function in MF-DIC from a set of scattered nodes for image matching. The MF-DIC is principally different from the classical local DIC and global DIC since it does not rely on the concept of a subset or an element. Results In MF-DIC, the $${C}^{1}$$ C 1 -continuous displacement for every point is constructed based on a group of scattered nodes in a small support domain surrounding it. The continuous strain map can then be directly derived from the displacement, instead of using an additional smoothing technique as required in classical local DIC or post-processing used in global DIC. A performance assessment based on the Metrological Efficiency Indicator (MEI), as defined in DIC Challenge 2.0, shows that the proposed MF-DIC yields an excellent balance between spatial resolution and measurement resolution for both displacement and strain measurements. Conclusions Given that the proposed MF-DIC shares common features with the classical meshfree method in computational mechanics, it paves the way for an enhanced synergy between experiments and simulations required for robust inverse parameter identification methods.