In using subset/subvolume-based digital image/volume correlation (DIC/DVC), proper shape functions must be defined to depict the underlying displacement of the target subsets/subvolumes to be tracked. Because the local deformation in a subset/subvolume cannot be known a priori, mismatched problems (i.e. undermatched or overmatched) unavoidably occur, which induce either remarkable systematic errors for undermatched cases or doubled random errors for overmatched cases in detected displacements. Also, the use of high-order shape functions (e.g. second-order shape functions) would lead to greatly increased computational complexity since more deformation parameters need to be solved. In this work, a novel and simple quasi-Gauss point DIC/DVC method that only uses first-order shape functions is proposed, which can completely avoid or significantly compromise the systematic errors due to undermatched shape functions. Specifically, based on rigorous theoretical analysis, we find that specific positions (designated as quasi-Gauss points) in a subset/subvolume deliver accurate displacement results even when undermatched issues are present. This new finding inspires us to output the displacements at these specific points rather than subset/subvolume center points. Numerical simulations with different deformation modes validate that the proposed approach can effectively reduce or even eliminate the undermatched error in these deformation modes in both DIC and DVC measurements.
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This work is supported by the National Key Research and Development Program of China (2018YFB0703500), and the National Natural Science Foundation of China (NSFC) (11872009, 11632010).
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Pan, B., Zou, X. Quasi-Gauss Point Digital Image/Volume Correlation: a Simple Approach for Reducing Systematic Errors Due to Undermatched Shape Functions. Exp Mech (2020). https://doi.org/10.1007/s11340-020-00588-3
- Digital image/volume correlation
- Systematic error
- Undermatched systematic error
- Shape functions