# Effect of Cohesive Properties on Low-Velocity Impact Simulations of Woven Composite Shells
## 3 Results
### Effect of the Interface Stiffness  
To assess the influence of the interface stiffness on the impact response of the semicylindrical woven composite shells, simulations were carried out using cohesive stiffness values ranging from \(10^{1}\) N/mm\({}^{3}\) to \(2.43\times 10^{6}\) N/mm\({}^{3}\) (\(k_{n}=k_{s}=k_{l}\)), while maintaining the normal and shear interface strengths constant (\(\tau_{n}^{0}=15\) MPa and \(\tau_{s}^{0}=\tau_{l}^{0}=30\) MPa). Notice that the highest value considered for the cohesive stiffness, that is, \(2.43\times 10^{6}\) N/mm\({}^{3}\), was obtained by employing the equation proposed by [PERSON] et al. [30]:  
\[k=\frac{\alpha E_{3}}{t} \tag{11}\]  
where \(t\) is the thickness of each ply, \(E_{3}\) is the through-thickness elastic modulus, and \(\alpha\) is a parameter larger than 1, which, in this study, was set with a value of 50, as suggested in [30]. The cohesive stiffness proposed by [PERSON] et al. [29] (\(10^{6}\) N/mm\({}^{3}\)) was also analysed in this study. The numerical and experimental [2] force-time, energy-time, and force-displacement curves are shown in Figures 3-5, respectively. It is possible to appreciate that the cohesive stiffness has no impact on the force and energy histories for values between \(10^{3}\) N/mm\({}^{3}\) and \(2.43\times 10^{6}\) N/mm\({}^{3}\), and that there is a satisfactory numerical-experimental correlation within this range. The force-time and force-displacement response curves are significantly affected by employing smaller cohesive stiffness values, such as \(10^{1}\) N/mm\({}^{3}\), because the stiff connection between the laminate layers is not ensured. It was noted, however, that the energy-time response curve was unaffected because the numerical output results for the impact energy were calculated based solely on the mass and velocity of the impact along the established step time, which were defined on the FE models in accordance with the experimental evidence. On the other hand, high cohesive stiffness values caused convergence issues. For instance, adopting a cohesive stiffness of \(10^{9}\) N/mm\({}^{3}\) resulted in immediate convergence failure. It should be noted that these findings are in good agreement with those presented by [PERSON] et al. in [33]. If the cohesive stiffness is maintained between \(10^{3}\) N/mm\({}^{3}\) and \(2.43\times 10^{6}\) N/mm\({}^{3}\), the impact bending stiffness (IBS), which is determined by the slope of the ascending branch of the force-displacement curves represented in Figure 5[34], is also hardly affected. Once more, for \(10^{1}\) N/mm\({}^{3}\), the IBS significantly declines and completely breaks apart from the experimental evidence. It was observed that, in terms of computing efficiency, an increase in cohesive stiffness is accompanied by a significant rise in the number of increments required to compute the solution. As an example, it was observed that increasing the cohesive stiffness from \(10^{5}\) N/mm\({}^{3}\) to \(10^{6}\) N/mm\({}^{3}\) raised the computational cost of the solution by 138%. The cohesive stiffness was observed to have a limited impact on the response curves when maintained within the range of \(10^{3}\)-\(2.43\times 10^{6}\) N/mm\({}^{3}\). However, it was identified as a critical factor affecting the delamination predictions. To understand and quantify this impact, the effect of the cohesive stiffness on the delamination initiation and progression  
Figure 4: Effect of the interface stiffness on the energy–time results with \(\tau_{n}^{0}=15\) MPa and \(\tau_{5}^{0}=\tau_{l}^{0}=30\) MPa. are shown in Figure 6a,b, respectively. The damage initiation in the cohesive surfaces was measured for this reason using the output variable CSQUADSCRT. This variable shows whether or not the quadratic contact stress damage initiation threshold was met (see Equation (8)). It was anticipated that cohesive surface degradation would start when its value approached 1. The stiffness deterioration, following damage initiation, was measured using the output variable CSDMG.