## 2 Theoretical Background  
### Dic  
The DIC working principle is based on optical tracking of displacements of subsets on the specimen surface during the specimen deformation. The general 3D DIC setup is shown in Figure 2a, (only basic DIC principles are presented in this chapter without going into the details of 3D DIC and differences compared to 2D DIC, which can be found in elsewhere [3]). The DIC method consists of three steps: specimens preparation, recording images, and post processing computation. First, the pattern of points to be tracked is applied on the specimen surface during the preliminary stage of the specimen preparation, generating the so-called speckle pattern (Figure 2a). Painting the speckle dots on the specimen surface by using, for example, an air brush or a speckle pattern painting roller, is a popular method due to its simplicity and high enough quality for the DIC procedure, although other methods can be applied for specific materials (e.g., computer generated patterns printed on stickers, powder particles, laser engraving, etc.) [37]. Then, displacements of the speckle pattern points subsets are tracked with the optical cameras and recorded during the specimen deformation. Camera selection is based on the proper magnification which depends on the measuring scale of the test specimen. The specimens measuring area (FOV), camera sensor size, and the focal length of the lenses used with the camera are necessary to determine the magnification and working distance of the camera and thus its applicability for particular objects measurements [38]. Some of these parameters are shown in Figure 2b. Perfect camera focus and specimen lighting are required and can be achieved by adjusting the camera and light source to have enough exposure of the specimen (while avoiding over exposure). Some noise caused by the camera sensor, electronics, and lighting fluctuations is unavoidable, but its effect on measurement results can be minimized by a properly selected DIC setup [39]. Finally, the sequence of images recorded during the specimen testing and the corresponding speckle pattern deformation is analyzed by the DIC software during the post processing calculation stage [1,3]. The calculation procedure starts with dividing the whole FOV speckle pattern into a grid of sub-areas called subsets (see Figure 2c). The center of each subset (point \(P(x_{0},y_{0})\) in Figure 2c) is the point where the displacement assigned to each subset is calculated. After the deformation of the test specimen and speckle pattern, the subset from the deformed image is compared based on correlation criterion calculations against the subset from the reference image to find the displacement of each subset center point \(P(x_{0},y_{0})\) (Figure 2c). In order to define the position of the internal subset points \(Q(x_{i},y_{i})\) after the subset deformation, displacement mapping by using the so called \"subset shape functions\", based on deformation continuity principle is done. The subset shape function cannot be selected by the user in the VIC-3D software used in this study [40]. Figure 2: 3D DIC: (**a**) general experimental setup; (**b**) cameras and lenses parameters; (**c**) results post processing: subset tracking and displacement/strain calculation. The possibility exists that a point \(Q(x_{i},y_{i})\) in the deformed image is located between the pixels of DIC sensor, and because of this a sub-pixel interpolation is necessary to define the displacement vector of that point. Several sub-pixel displacement interpolants (4 th, 6 th, and 8 th orders polynomials) are available as user choice in the VIC-3D software [40].