# Effect of Cohesive Properties on Low-Velocity Impact Simulations of Woven Composite Shells
## 3 Results
### Effect of the Interface Stiffness
The interface can be thought of as entirely delaminated when it reaches the value of 1. The results are provided as the percentage of nodes with CSQUADSCRT = 1 and percentage of nodes with CSDMG > 0.8. The findings demonstrate that delamination only appears for cohesive stiffness values greater than 10\({}^{3}\) N/mm\({}^{3}\). In fact, the influence of delamination in the FE model simulations is hardly perceptible up to 10\({}^{5}\) N/mm\({}^{3}\). The percentage of nodes that experience damage initiation (CSQUADSCRT output variable), however, climbs sharply from 1.19% to 85.05% if the value calculated by Equation (11) is considered (2.43 \(\times\) 10\({}^{6}\) N/mm\({}^{3}\)). The observed trend reveals a direct correlation between the cohesive stiffness and the percentage of nodes exhibiting complete delamination, as indicated by the CSDMG output variable. Notably, as the cohesive stiffness value, denoted as \(k_{n,s,t}\), is increased to 10\({}^{6}\) N/mm\({}^{3}\), the proportion of totally delaminated nodes rises to 2.27% of the total number of nodes within the composite shell. However, when the cohesive stiffness is further elevated to 2.43 \(\times\) 10\({}^{6}\) N/mm\({}^{3}\), the percentage decreases to 1.09%. These findings underscore the significant impact of interface stiffness on the accurate delamination predictions. Moreover, upon analysing the calculated values of \(\alpha\) for each considered cohesive stiffness, as determined by Equation (11) and listed in in Table 3, it becomes evident that only for 2.43 \(\times\) 10\({}^{6}\) N/mm\({}^{3}\) and 10\({}^{6}\) N/mm\({}^{3}\) does \(\alpha\) exhibit significant higher values than 1, as suggested by [PERSON] et al. [30]. This underscores the importance of evaluating the value of the parameter \(\alpha\) utilised in the numerical simulations, in order to obtain proper delamination predictions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Cohesive Stiffness (\(k_{n,s,t}\))** & **Parameter \(\alpha\)** \\ \hline \hline
2.43 \(\times\) 10\({}^{6}\) N/mm\({}^{3}\) & 50 \\
10\({}^{6}\) N/mm\({}^{3}\) & 21 \\
10\({}^{5}\) N/mm\({}^{3}\) & 2.1 \\
10\({}^{3}\) N/mm\({}^{3}\) & \(2.1\times\) 10\({}^{-2}\) \\
10\({}^{1}\) N/mm\({}^{3}\) & \(2.1\times\) 10\({}^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter \(\alpha\) for the considered cohesive stiffness values (calculated from Equation (11)). Figure 6: Effect of the interface stiffness with \(\tau_{n}^{0}=15\) MPa and \(\tau_{s}^{0}=\tau_{t}^{0}=30\) MPa: (a) CSQUADSCRT output variable. (b) CSDMG output variable. The effect of the interface stiffness on the delamination predictions throughout the entire FE model, and the damage observed on the experimentally tested specimens [2] are plotted in Figures 7 and 8, respectively. In Figure 7, it is possible to observe that the FE models with cohesive stiffness values ranging from \(10^{1}\) N/mm\({}^{3}\) to \(10^{3}\) N/mm\({}^{3}\) do not present any discernible signs of delamination. However, the presence of delamination becomes increasingly apparent as the cohesive stiffness surpasses \(10^{5}\) N/mm\({}^{3}\). Notably, for a cohesive stiffness of \(10^{6}\) N/mm\({}^{3}\), the extent of delamination becomes more severe, extending beyond the impact area and propagating  
Figure 8: Damage observed on the experimentally tested specimens (visual inspection with intense backlight) [2]. along the longitudinal direction of the composite shell. However, as seen observed in Figure 6b, with a higher cohesive stiffness of \(2.43\times 10^{6}\) N/mm\({}^{3}\), the delaminated area noticeably reduces compared to the previous analysed case. It is important to note that a satisfactory agreement can be observed between the experimental evidence presented in Figure 8 and the simulation results obtained with a cohesive stiffness of \(10^{6}\) N/mm\({}^{3}\).