Table 1 Covariance matrix \({\mathbf {H}}_{FEMU}^{-1}\) (the three parameters are ordered as: \(\frac{E_2}{E_1}\), \(\frac{G_{12}}{E_1}\), \(\nu _{12}\)), its eigenvalues \(\lambda _i\) and the associated eigenvectors \({\mathbf {w}}_i\) (same order)
From: Spline-based specimen shape optimization for robust material model calibration
| Â | Initial geometry | End of \(\pmb {1^\mathrm{st}}\) optim. step | End of \(\pmb {2^\mathrm{nd}}\) optim. step |
|---|---|---|---|
\({\mathbf {H}}_{FEMU}^{-1}\) | \(\begin{bmatrix} 27 &{} -0.50 &{} -0.047 \\ -0.50 &{} 1.6 &{} 0.0072 \\ -0.047 &{} 0.0072 &{} 0.31 \end{bmatrix}\) | \(\begin{bmatrix} 2.6 &{} -0.28 &{} 0.24 \\ -0.28 &{} 0.29 &{} -0.020 \\ 0.24 &{} -0.020 &{} 0.47\\ \end{bmatrix}\) | \(\begin{bmatrix} 0.63 &{} -0.050 &{} 0.14 \\ -0.050 &{} 0.14 &{} -0.017 \\ 0.14 &{} -0.017 &{} 0.67 \\ \end{bmatrix}\) |
\(\lambda _i\) | \(\begin{matrix} 0.31\\ 1.5\\ 27\\ \end{matrix}\) | \(\begin{matrix} 0.26\\ 0.45 \\ 2.7\\ \end{matrix}\) | \(\begin{matrix} 0.14\\ 0.51\\ 0.80\\ \end{matrix}\) |
\({\mathbf {w}}_i\) | \(\begin{bmatrix} 0.0017 &{} 0.020 &{} -1.0 \\ -0.0051 &{} 1.0 &{} 0.020 \\ 1.0 &{} 0.0051 &{} 0.0018 \end{bmatrix}\) | \(\begin{bmatrix} 0.12 &{} 0.10 &{} -0.99 \\ 0.99 &{} -0.058 &{} 0.12 \\ -0.046 &{} -0.99 &{} -0.11\\ \end{bmatrix}\) | \(\begin{bmatrix} 0.099 &{} 0.74 &{} -0.66 \\ 1.0 &{} -0.070 &{} 0.070 \\ 0.0056 &{} -0.67 &{} -0.74 \\ \end{bmatrix}\) |