50 S.M. Kleinendorst et al. 0 20 40 60 80 100 120 −20 −10 0 10 20 30 40 50 60 70 x [μm] y [μm] thickness extension Fig. 8.3 Determination of the sample contour from an FE simulation. In the case of shell elements, all element corner nodes located on the perimeter of the structure have in common that they are only shared by two or three elements, while nodes located in the center share four elements. Based on this characteristic it is possible to follow the contour of the structure, by starting at some point at the perimeter and repeatedly searching for the next node that satisfies this feature. After the perimeter is determined, the thickness of the specimen is artificially incorporated signed distance maps. The first step is to determine the perimeter of the model, see Fig. 8.3. This is done by starting at an arbitrary point on the contour, however, it is easiest is to start at a corner. A node in the corner appears in only one elements, hence it is easy to search for such a node. Next all other nodes in this one element are scanned. The characteristic of the nodes located on the model perimeter is that they are shared by only two or three elements (or only one for the corners), while nodes in the center of the structure are shared by four elements. The node in the current element that satisfies this characteristic is the next in line on the contour. Furthermore, it is part of the next element in line, which is then scanned for the next node on the perimeter. This process is repeated until the starting node is attained again. Note that the assumptions made for this method only hold for rectangular elements, for other types the procedure should be adjusted accordingly. Also note that only the corner nodes of the elements are taken into consideration; the nodes at the edge centers, which are present for quadratic elements, are ignored. The next step is to construct the sample edge location more accurately, by defining more points (denser than the number of pixels on this distance). Interpolation using the FE shape functions (e.g., linear or quadratic, depending on the element type) is used to determine the positioning of these points. Now that the sample contour is accurately defined, the thickness can be incorporated. The rotation information of all nodes, resulting from the FE simulation, is taken into account to determine the locations of the virtual bottom and top contour, see the right part of Fig. 8.3. Now when a projection is made using these edges, and also the side edges connecting the top and bottom contours, the thickness of the sample is incorporated. 8.3.2 Masking As can be seen from the extended structure in Fig. 8.3 many lines are crossing inside the structure, while we are only interested in the total outline since that is the only information that can be obtained from real experimental images. Because the determined edges consist of many points, which can be very close together for sharp edges, it is difficult to determine the convex hull of the shape to locate the outer contour and eliminate the internal curves. Therefore the signed distance map for the pixels located inside the sample geometry can not be accurately determined. Furthermore, even if the signed distance map could be determined accurately, a small deviation in the calculation of the displacement field results in a relatively large effect in the signed distance map and hence the residual inside the structure, since the distances inside the structure are very small. This can lead to numerical instability and poor convergence. An elegant solution is to mask the structure itself and correlate only on the area outside the structure. The impact of masking on the method’s performance is tested by means of a virtual experiment in the next section.
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