## 3 Methodology
### Verification and Robustness  
The FEMU procedure is first validated using \"virtual test\" strain field data generated from FE simulation with a set of target material parameters (\(E_{11}^{target}\), \(E_{33}^{target}\), \(v_{13}^{target}\), \(G_{13}^{target}\)). An initial approximation of the material parameters is needed to initiate the non-linear least-squares optimization algorithm. For example, Figure 9 shows convergence of the parameters to their target values and the reduction of the weighted strain error with the number of iterations starting from an initial approximation of the material parameters is shown in Figure 10. Results in Figure 9 have been normalized to one by the respective target parameter. The following initial approximation of the material parameters was used, which corresponds to \(\pm\) 40% of relative error compared to the target parameters. \[ \begin{array}{l}E_{11}^{[0]}=0.6\ E_{11}^{target}\\ E_{33}^{[0]}=1.4\ E_{33}^{target}\\ v_{13}^{[0]}=0.6\ v_{13}^{target}\\ G_{13}^{[0]}=1.4\ G_{13}^{target}\end{array}  \tag{3}\]  
Similar convergence for different initial parameters up to 50% of initial relat  
Figure 10: Weighted RMS strain error for the OHC FEMU methodology using FEM-generated virtual test strain data. Figure 9: Convergence of normalized material parameters to their target value. The FEMU updating procedure is stopped when the relative change in the RMS average of the parameters between two iterations is less than 0.3%. As shown in Figures 9 and 10, convergence is quickly achieved and all parameters converge to their desired and expected target value. Figure 11 shows an example of convergence of the material parameters for the FEMU procedure using experimental DIC strain data from OHC testing of a generic carbon-epoxy unidirectional specimen. The threshold for convergence is reached after nine iterations, however effective convergence is pretty much achieved after two or three iterations, as illustrated. In this example, convergence is illustrated for a 50% maximum relative error in the initial approximation of the interlaminar Young's Modulus \(E_{33}\)[(0)] compared to its final converged value after nine iterations \(E_{33}\)[(9)]. Initial relative error for the other parameters is between 37% and 43%. Figures 12 and 13 compare the DIC-measured longitudinal normal and shear strain fields, respectively, with FEM results at the beginning and end of the updating process. It is worth noting that the DIC strain data have been mapped on the FEM node grid, as part of the FEMU methodology [(15)]. Interpolation of the DIC strains on the FEM nodes is realized at the beginning of the FEMU procedure using Abaqus Python scripting interface and the natural neighbor interpolation method implemented in Python function _griddata_ of module _SciPy_. Figure 11: Convergence of the four material parameters (**a**) \(E_{11}\), (**b**) \(v_{13}\), (**c**) \(E_{33}\) and (**d**) \(G_{13}\) extracted with the OHC-ILT FEMU methodology using DIC-measured strain data from a generic unidirectional carbon/epoxy OHC test specimen. Figure 14a shows the evolution of relative absolute strain error between FEM and DIC during the FEMU iterative procedure for the minimum longitudinal strain value in the contour plots shown in Figure 12. Figure 14b shows the relative absolute strain error for both the minimum and maximum shear strain value for the shear strain contour plots shown in Figure 13.  
Figure 14: Relative absolute strain error between FEM and DIC data for (**a**) the minimum longitudinal strain and (**b**) the maximum and minimum shear strain value in the DIC region of interest. Figure 12: Comparison of DIC-measured longitudinal strains with FE results from the OHC-ILT FEMU procedure before (iteration 0) and after optimization (iteration 9) of material parameters. Figure 13: Comparison of DIC-measured interlaminar shear strains with FE results from the OHC-ILT FEMU procedure before (iteration 0) and after optimization (iteration 9) of material parameters.