## 3 Fuselage Barrel Test Case: Geometrical Description and Finite Element Model
### Material System  
Figure 3 allows to highlight the material systems adopted for the different subcomponents of the fuselage. Three different material systems were adopted: namely a fibre-reinforced composite material system with long unidirectional fibres (UNIDIRECTIONAL UD), a woven fabric material system and AL2025 aluminium. The related material mechanical properties are introduced in the following Tables 2-4. Figure 3: Material components. Figure 2: Fuselage section components. (**A**): Frontal view. (**B**): Lateral view. (**C**): Isometric view. For the aluminium plates, a thickness of 8 mm was chosen. Table 5 shows the stacking sequences for the composites' made sub-components. A discrete coordinate system has been introduced in the numerical model for each composite barrel sub-component. Fibres are oriented according to the fuselage longitudinal direction, while the normal axis has been chosen according to the element normal direction. As already mentioned, three different material systems configurations, characterised by different fracture toughness energies, were considered for the simulations in order to assess the influence of fracture characteristics on the evolution of the damage and hence on the dynamic response of the whole fuselage. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Aluminium Al2025**} \\ \hline Young’s Modulus, E [MPa] & 70,000 \\ Poisson’s ratio, \(\
u_{12}=\
u_{13}=\
u_{23}\) & 0.33 \\ Yield stress [MPa] & 369 \\ Ultimate Tensile Stress [MPa] & 469 \\ Density [ton/mm\({}^{3}\)] & 2.7 e\({}^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Aluminium Al 2024 mechanical properties \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Fibre Composite Material**} \\ \hline Young’s Modulus, E\({}_{11}\) [MPa] & 137,500 \\ Young’s Modulus, E\({}_{22}\) [MPa] & 8200 \\ Shear Modulus, G\({}_{12}\) [MPa] & 3950 \\ Shear Modulus, G\({}_{13}\) [MPa] & 3950 \\ Shear Modulus, G\({}_{23}\) [MPa] & 3950 \\ Poisson’s Ratio, \(\
u_{12}=\
u_{13}=\
u_{23}\) & 0.35 \\ Fibre Tensile Strength F\({}_{1t}\) [MPa] & 1890 \\ Fibre Compressive Strength F\({}_{1c}\) [MPa] & 1008 \\ Matrix Tensile Strength F\({}_{2t}\) [MPa] & 86.5 \\ Matrix Compressive Strength F\({}_{2c}\) [MPa] & 112 \\ In-Plane Shear Strength, S\({}_{12}\) [MPa] & 95 \\ Out-Plane Shear Strength, S\({}_{23}\) [MPa] & 100 \\ Density [ton/mm\({}^{3}\)] & 1.9 e\({}^{-9}\) \\ Ply Thickness [mm] & 0.129 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: UNIDIRECTIONAL (UD) material system properties. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Fibre Composite Material**} \\ \hline Young’s Modulus, E\({}_{11}\) [MPa] & 137,500 \\ Young’s Modulus, E\({}_{22}\) [MPa] & 8200 \\ Shear Modulus, G\({}_{12}\) [MPa] & 3950 \\ Shear Modulus, G\({}_{13}\) [MPa] & 3950 \\ Shear Modulus, G\({}_{23}\) [MPa] & 3950 \\ Poisson’s Ratio, \(\
u_{12}=\
u_{13}=\
u_{23}\) & 0.35 \\ Fibre Tensile Strength F\({}_{1t}\) [MPa] & 1890 \\ Fibre Compressive Strength F\({}_{1c}\) [MPa] & 1008 \\ Matrix Tensile Strength F\({}_{2t}\) [MPa] & 86.5 \\ Matrix Compressive Strength F\({}_{2c}\) [MPa] & 112 \\ In-Plane Shear Strength, S\({}_{12}\) [MPa] & 95 \\ Out-Plane Shear Strength, S\({}_{23}\) [MPa] & 100 \\ Density [ton/mm\({}^{3}\)] & 1.9 e\({}^{-9}\) \\ Ply Thickness [mm] & 0.129 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Woven fabric material system properties. Each configuration, identified with a number (I,II,III), is associated to different values of the fracture toughness energies for the matrix and fibre under tensile and compression conditions for both the UNIDIRECTIONAL UD and the woven composite material systems. Moreover, tensile and compression fracture energy values for the woven fabric were assumed identical for all the considered configurations. As it can be observed from Table 6, Configuration II can be considered the most toughened configuration while configurations I is characterised by the lowest toughness.