4.4 Second Virtual Experiment The second virtual experiment aims to evaluate the error committed when trying to extend the measure of strain to the elements containing the crack tip. Again the FE method was used; now a quadrilateral of 8 mm side is meshed with Plane 42 elements, 0.1 mm in size, with an initial crack ranging from the middle left side to centre of the square. Plausible in-plane displacements were assigned to the external sides of the quadrilateral, determining the crack opening shown in Fig. 4.9; again, the nodal data were assumed as real data and the red square represents a typical 4 nodes element with 4 mm side that can be acquired by the optical grid method. The distribution of the first principal strain, as computed by fine meshed FEM model, is reported in Fig. 4.10a. Conversely, Fig. 4.10b shows the strain map computed by the 4 nodes element having centroid at the crack tip (yellow square in Fig. 4.9) and using the enriched shape functions given by Eq. (4.3). Analogously to error analysis shown in the previous section, the 4 nodes element can be offset in several positions, leading to different values of maximum error with respect to the “real” data. The distribution of maximum error as function of the offsets in X and Y directions is shown in Fig. 4.11. It must be noted that the error represents the maximum difference between the real strain map (Fig. 4.10a) and the strain map of the 4 nodes element, avoiding from the computation a region within 0.2 mm from the crack tip, where the strain field is singular. Fig 4.7 e1 distribution map for the simulated extended grid method of pitch 4 mm (a) crack parallel, (b) 20 rotated Fig. 4.8 e1 maximum error in the strain maps varying the grid offset (a) classic grid method, (b) extended grid method 44 M. Sasso et al.
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