## 2 Experimental Implementation of DIC
### DIC Post-Processing  
The DIC method consists in determining a displacement field by comparing a distorted image to a reference one, which can be chosen arbitrarily among all the images of the sequence. In practice, the reference image is recorded before the shock. The images are considered as gray level functions, \(f\) for the reference image and \(g\) for the distorted one, spatially discretized over the pixels of the camera and taking integer values within the dynamic range of the digitisation provided by the camera (here 8 bits). Numerous formulations and implementations of DIC are available, a short review of which can be found in [14]. For the present study, the in-house software CMV has been used. This software has initially been specifically developed for micromechanical applications using scanning electron microscope (SEM) images or images recorded with optical microscopes (see, e.g., [15; 16; 17] for applications). It implements several DIC formulations and has been shown to provide results consistent with other implementations (it is one of the software packages bench-marked in [14]). In addition, some specific post-processing routines adapted to micromechanical analyses are implemented, out of the scope of the present work, as well as routines to efficiently quantify the measurement errors, including random and systematic errors [16], which will be discussed later. The particular DIC formulation used in this study consists in dividing the region of interest of the reference image into juxtaposed independent, and in practice square, correlation windows. The size of these windows needs to be sufficiently large with respect to the local gray level fluctuations of the images and sufficiently small with respect to the fluctuations of the displacement field to be investigated. Within each of these windows, the mechanical transformation \(\Phi_{0}\) is assumed to be a purely rigid translation (transformation of order 0, see [14]) characterized by two scalar components. The actual mechanical translation of the beam is estimated by maximizing the matching between the reference \(f\) and the back-translated deformed image \(g(\Phi_{0})\), the matching being quantified by the so-called zero-centered, normalized cross-correlation coefficient, \(C\), defined as:  
\[C=1-\frac{\int_{D}(f(\underline{u})-\overline{f})(g(\Phi_{0}(\underline{u}))- \overline{g})du}{\sqrt{\int_{D}(f(\underline{u})-\overline{f})^{2}du\int_{D}( g(\Phi_{0}(\underline{u}))-\overline{g})^{2}du}} \tag{1}\]  
where \(\overline{f}\) and \(\overline{g}\) are the mean values of \(f(\underline{u})\) and \(g(\Phi_{0}(\underline{u}))\) in the current window, with \(\underline{u}\) the coordinates vector, and \(\int_{D}\) refers to a summation over all pixels in the reference window. We emphasize here the fact that higher-order shape functions describing the mechanical transformation with, e.g., affine or quadratic functions were unnecessary because of the very low strains associated with the vibrations of the beam. The actual DIC errors are for the present application dominated by the so-called \"ultimate errors\" and not the shape function mismatch errors: we refer to [14] for a discussion on these two error regimes. This has been checked with a comparison of the displacements evaluated assuming a rigid transformation and those obtained when an affine transformation is assumed, whose higher-order coefficients are determined, not by optimizing the correlation coefficient (which would have lead to additional random errors, see [14]), but from a larger scale fitting using the displacements evaluated in neighbor windows (see [18] for details about such a procedure). The differences between both approaches are within the random errors, discussed hereafter. This proves that the DIC errors in our experiments are identical to those occurring when purely rigid translations are considered, i.e., DIC errors are governed by the so-called ultimate error regime [14].