8 Mechanical Shape Correlation: A Novel Integrated Digital Image Correlation Approach 51 8.4 Virtual Experiments Two virtual experiments are executed to test the performance of the MSC method. The first experiment concerns one of the main deformation modes of the considered stretchable electronic interconnects: double bending of beams. In this experiment the effect of masking versus no masking is examined. The second virtual experiment concerns the other main deformation mode: torsion of beams. 8.4.1 Double Bending of Beams The effect of masking is tested by means of a virtual experiment concerning a double bending beam, see Fig. 8.4. In this virtual experiment no real experiment is executed with this structure, but an FE simulation is performed and the projections made from this are used as the ‘experimental’ images. The model is an elastic model, with only one unknown model parameter: the Young’s modulus E. The value used for the virtual experiment is 69GPa, or 6:9 10 2N/ m2, since the structure is modeled in micron. This value is the solution which is attempted to be determined using the Mechanical Shape Correlation method. The same model used to create the virtual experiment is also plugged in the MSC algorithm, however a variety of initial guesses for E are given. Also the perturbation factor Pis varied. This factor is a parameter in the MSC algorithm, which originates from the derivative of the objective function being needed to minimize the residual. Since it is not possible to do so analytically, the derivative is approximated using a finite difference scheme. The step size for this calculation is taken relative to the value of the considered parameter, i.e., the perturbation factor P is introduced. The quantity of this factor affects the convergence behavior of the method and therefore different values for Pare investigated in this research. Since the real value for the Young’s modulus is known, it is possible to determine the error in this parameter. This error is plot against the number of iterations for the situation when masking is applied versus no masking, and for different values x [μm] y [μm] 0 1020304050607080 0 10 20 30 40 50 60 y [μm] x [μm] 0 1020304050607080 0 10 20 30 40 50 60 y [μm] x [μm] 0 1020304050607080 0 10 20 30 40 50 60 0 10 20 30 40 50 60 signed shortest distance to sample edge [μm] x y z z-displacement Fig. 8.4 Virtual experiment with a simple double bending beam. One end of the beam structure is constrained, while the other end is lifted with a prescribed force. The FE model is elastic with a Young’s modulus of 69GPa. Not that the xy-coordinates in the signed distance maps correspond to the yz-coordinates in the FE simulation
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