## 4 Application in Real Experiment  
To compare the three methods in terms of real deformation measurements near curved edges, a diametrical compression test was performed using a ring made of aluminum alloy 6061. Figure 10a and Table 1 present the ring specimen dimensions and the mechanical properties of the aluminum alloy 6061. An irregular speckle pattern was created on the specimen beforehand by spraying black and white paints on the front surface. The test was conducted on a universal WDW-50E testing machine (Figure 11). Displacement control was applied with a loading rate of 0.05 mm/min. During the loading process, an imaging system consisting of a charge coupled device (CCD) camera with a spatial resolution of 1628 \(\times\) 1236 pixels and a 50 mm fixed-focus lens was used to capture images of the specimen front surface at a speed of 1 fps. Figure 11 presents the undeformed image with an inner radius of 243 pixels and an outer radius of 486 pixels for the ring. The collected deformed images were processed using the VIC-2D software with a subset size of 47 pixels, the extrapolation method, the half-subset method, and Q8-DIC to obtain the displacement field of the front surface. The meshing scheme illustrated in Figure 10b, with a total of 42 elements and 154 nodes, was used in the Q8-DIC, and the rules for meshing in Q8-DIC referred to the papers [12; 17]. Figure 10: Diametrical compression test diagram of the aluminum ring (**a**) and meshing scheme in Q8-DIC (**b**). Figure 9: Relative errors along radius at \(\theta\) = 90\({}^{\circ}\). A 2-dimensional FE model (Figure 12) of the diametrical compression test was created by using the commercial software ABAQUS. The loading and supporting platens were modeled as analytical rigid bodies, and the frictionless contact option was used between the ring and platens. A concentrated force was applied at the reference point of the loading plate. The ring was discretized into 6000 4-node plane stress elements (CPS4R in ABAQUS notation), with 30 elements in the radial direction and 200 elements in the circumferential direction. Isotropic properties were assigned to the elements, as detailed in Table 1.  
Figure 13 presents the load-displacement curve of the indenter during the diametrical compression test. For comparison with the elastic solution obtained by the finite element analysis, the image captured at a very early loading stage (point \(A\) in Figure 13) was selected to calculate the displacement field. Figure 14 illustrates the calculated displacement fields in the vertical direction using different methods. In general, all measured displacement distributions agreed strongly with the simulated result. However, as the Q8-DIC method considered the continuity constraint for the entire field, it produced a smoother displacement field than the other two methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(d\) (mm) & \(D\) (mm) & \(b\) (mm) & **Modulus (GPa)** & **Poisson’s Ratio** \\ \hline
25 & 50 & 15 & 68.9 & 0.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specim dimensions and mechanical properties of aluminum alloy 6061. Figure 12: Finite element model of diametrical compression test. To provide an intuitive comparison of the three methods' accuracy in the deformation measurement near curved edges, the displacement distributions around 2 circles with radii of 244 and 259 pixels were plotted in Figure 15a,b, respectively. It can be observed that the Q8-DIC calculation result was always in strong agreement with that predicted by the FE model, even on the hole edge (\(r=244\) pixels). The extrapolation method could also indirectly produce the displacements on the hole edge, but with relatively large deviations from the FEM result. The half-subset method even failed to provide a reasonable displacement distribution around the hole. However, the measurement accuracy of the half-subset method improved with increasing distance from the hole edge.