## 4 Validation I: Simulation of Open-Hole Tension Tests with Optimal GA Solution
### Simulation of Size Effects  
With confidence in the mesh-insensitive damage simulations, different hole sizes can be investigated to further assess the prediction capabilities of the GA-derived CODAM2 material model using a coarse mesh of 1 mm \(\times\) 1 mm. Table 5 shows the three different OHT test configurations where the hole diameter \(D\) varies from 8 mm to 16 mm with constant specimen width \(W\) and length \(L\). This results in varying hole-to-width ratios \(D/W\) from 0.4 to 0.8. Table 6 compares the simulated OHT strength to experimental mean values for each of the three OHT test geometries. It shows that the OHT strength can be predicted with errors \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Mesh Size**} & \multirow{2}{*}{**Characteristic Length \(l^{*}\)**} & \multicolumn{2}{c}{**Damage Saturation Strains**} \\ \cline{3-3}  & & \(\mathbf{\varepsilon_{1}^{s}}\) **(-)** & \(\mathbf{\varepsilon_{2}^{s}}\) **(-)** \\ \hline
1 mm \(\times\) 1 mm & 1.0 & 0.084 & 0.081 \\
0.5 mm \(\times\) 0.5 mm & 0.5 & 0.168 & 0.162 \\
0.25 mm \(\times\) 0.25 mm & 0.25 & 0.336 & 0.324 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of investigated mesh sizes in combination with adjusted damage saturation strains according to [PERSON]’s crack band scaling in Equation (4). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} 1 mm \(\times\) 1 mm \\ 26.40 MPa \\ \end{tabular} } & 0.5 mm \(\times\) 0.5 mm & 0.25 mm \(\times\) 0.25 mm \\
26.40 MPa & 26.42 MPa & 26.47 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulated open-hole strength in \([90/45/0/-45]_{s}\) beech veneer laminates with 8 mm hole diameter using different element sizes. Figure 7: Comparison of damage in \(0^{\circ}\)ply after simulated open-hole tension tests of \([90/45/0/-45]_{s}\) beech veneer laminates using different element sizes. of less than 8%. Note that simulations complete in 1-2 min on a conventional computer using four CPUs. Figure 8 further compares the simulated and experimental results of the size effect study to theoretical bounds. The ratio between the simulated/measured OHT notch strength \(\sigma_{\text{n}}\) from Table 6 to the experimentally measured un-notched strength \(\sigma_{\text{un}}=70.0\) MPa [6] decreases with increasing hole-to-width ratio \(D/W\). The theoretical bounds are given by ideally ductile behaviour (\(1-D/W\)) and ideally brittle fracture \(\left(\frac{1-D/W}{K_{t}}\right)\) where the stress concentration factor \(K_{t}\) is given by [35]  
\[K_{t}=3-3.14\left(\frac{D}{W}\right)+3.667\left(\frac{D}{W}\right)^{2}-1.527 \left(\frac{D}{W}\right)^{3}. \tag{7}\]  
with hole diameter \(D\) and sample width \(W=20\) mm. The results in Figure 8 show that it is possible to find reasonable lower and upper bounds by analytical models shown in Equation (7). However, it can also be seen that the presented FE simulation method on progressive damage analysis significantly improves the prediction of the OHT strength where the simulated strength ratios are much closer to experimental results compared to the theoretical bounds. The computation time of the presented FE models with less than 2 min for the simulation of one OHT test on a conventional computer is certainly larger than the evaluation of these analytical models. In contrast, the analysis of FE results offers more details, in particular the analysis of qualitative results as discussed in the following. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **OHTS \({}^{*}\)** & **OHT12 \({}^{*}\)** & **OHT16 \({}^{**}\)** \\ \hline Simulation & 26.40 & 17.69 & 8.81 \\ Experiments (CoV [\%]) & 25.53 (6.5) & 17.30 (6.9) & 9.18 (10.7) \\ \hline Difference & +3.4\% & +2.2\% & \(-4.0\%\) \\ \hline \hline \end{tabular} \({}^{*}\)based on 20 experiments, \({}^{**}\) based on 3 experiments.  
\end{table}