SpatioTemporally Adaptive Quadtree Mesh (STAQ) Digital Image Correlation for Resolving Large Deformations Around Complex Geometries and Discontinuities

Abstract

Background. Digital image correlation (DIC) is a powerful experimental tool for measuring full-field material deformations. Inherent limitations of typical DIC algorithms can cause a multitude of errors when analyzing the displacement field of samples containing complex geometries or discontinuities. Most adaptations rely on either splitting or augmenting the local DIC subsets that pass through the discontinuity path. However, these methods are challenging to generalize and automate, often requiring significant user intervention. Objective. To address these shortcomings, we present a new, user-friendly automatic experimental approach for resolving the deformation fields around complex geometries and displacement discontinuities, which we call the spatiotemporally adaptive quadtree mesh (STAQ) DIC method. Methods. In this method, the adaptive quadtree mesh is automatically generated from a mask file of the DIC image itself to handle the inherent complex geometry. Subsets that span either geometric or displacement discontinuities are automatically split to improve their DIC accuracy. A binary image mask is also used to inform an interpolation scheme for displacement and strain calculations. Furthermore, we also propose a data-driven reduced order modeling (ROM) approach to further reduce the computational costs by skipping unnecessary image frames thus achieving temporal adaptability for efficiently processing large image sequences. Results. We demonstrate that our STAQ method has high accuracy in solving complex geometric and discontinuous deformation fields in an automated fashion. We find that the proposed data-driven ROM method can provide up to 60% in computational cost savings while maintaining the same level of accuracy compared to a fully processed image set. Conclusions. STAQ DIC is a computationally efficient method for accurately solving geometrically complex and discontinuous deformation fields. Using the data-driven ROM method as part of STAQ can further reduce computational costs for processing large image sequences. An open-source Matlab implementation is freely available.

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