8 Mechanical Shape Correlation: A Novel Integrated Digital Image Correlation Approach 49 after deformation. A Finite Element (FE) simulation is performed which represents the experiment, in which some model parameters of interest are the unknowns in the correlation procedure. The resulting displacement field from this simulation is used to back-deform the deformed images, such that if the displacement field is calculated correctly the back-deformed image matches the undeformed, reference, image. The difference between these images is denoted as the residual, which naturally approaches zero if a good correlation is obtained. If this is not the case, the unknown model parameters are updated and the procedure is repeated. The difference in MSC is that the displacement field resulting from the FE simulation is not used to create back-deformed images, but projections, i.e., images, are generated from the model itself at different time increments. This image type is introduced in the next section. These FE images are correlated to similar projections that are made from the experimental images at the same time steps. Again, the residual is defined as the difference between these images. Similar to I-DIC the model parameters are updated iteratively to obtain a good correlation between the experiment and the simulation, as shown in Fig. 8.1. 8.3 Images In conventional digital image correlation methods contrast in the images is usually provided by some sort of speckle pattern, either naturally present due to the specimen texture or artificially applied with, e.g., spray paint. In the Mechanical Shape Correlation technique the images consist of a projection of the specimen outline. The most elementary projection one could think of is the binary projection, where the background is assigned a contrasting color with respect to the structure itself, e.g., black and white, see Fig. 8.2a. However, since large parts of the image are monochromatic, the residual will only be non-zero in a relatively small area even if correlation is not achieved. This results in a low overall residual and the method will converge too soon. Therefore, the projection chosen for MSC is the signed distance map, i.e., the value for each pixel represents the closest distance to the sample contour, see Fig. 8.2b. With these images the whole field is affected if the unknown parameters in the FE simulation do not characterize the experimentally observed kinematics correctly. Therefore, the residual field is more likely to direct the algorithm to the correct solution. 8.3.1 Projection of Finite Element Simulation A common type of elements used in FE simulation is shell elements. It deserves some attention as to how to create the projection images from these simulations. Since shell elements are infinitely thin, a projection perpendicular to the structure will not incorporate the real thickness of the sample. Therefore, this thickness should be artificially included in creating the 0 20 40 60 80 100 120 −20 −10 0 10 20 30 40 50 60 70 x [μm] y [μm] (a) 0 20 40 60 80 100 120 −20 −10 0 10 20 30 40 50 60 70 x [μm] y [μm] 0 5 10 15 20 25 30 35 40 45 50 distance to sample edge [μm] (b) Fig. 8.2 Projection images used for the Mechanical Shape Correlation method. Two options are shown: on the left a binary projection in which the background is black and the structure itself is white. On the right a signed distance map is shown, where the colors indicate for each pixel the closest distance to the edge of the structure. (a) Binary image. (b) Signed distance map
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