# Delamination Effect on the Buckling Behaviour of Carbon-Epoxy Composite Typical Aeronautical Panels
## 3 Test Case
### FEM Model  
The reinforced composite panel was modelled using the parametric design language of the Ansys software version R18.0 (APDL). The global-local approach was used to reduce the computational effort. Hence, a coarse mesh was used for the panel, representing the global model, while the zone interested by the circular delamination and the propagation area, representing the local model, was finely discretised and connected to the global model through contact elements, as shown in Figure 2.  
The elements used for the discretisation were a combination of solid and shell. In detail, SOLID186 elements, defined by 20 nodes each having three degrees of freedom, were chosen for the stringers, the underlying skin, the delaminated area and the propagation zone. The layered structural solid option was set to properly assign the composite materials and stacking sequence. The remaining panel was modelled as a bidimensional part and meshed with layered shell elements.  
The detail of the delamination and the area eventually affected by the propagation were modelled with two overlying solids that were equal but distinct. In particular, the thickness of the solid on the top was determined by the number of layers under which the delamination was placed (e.g., if the delamination was located under three layers, the upper solid thickness was 3 \(\times\)_ply thickness_), while the remaining thickness was determined by the layers underneath the delamination (lower solid). The circular delamination was simulated by a zone whose nodes were related by simple contact elements that prevented penetration, while the nodes of the propagation ring were initially bonded and were allowed to separate if and when the propagation criterion in Equation (2) was met. The detail of the local model is shown in Figure 3.  
\begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{**Property**} & \multicolumn{2}{c}{**Carbon Fibre/Epoxy Resin Material Properties**} \\ \multicolumn{1}{c}{**Value**} & \multicolumn{1}{c}{**Description**} \\ \hline E\({}_{11}\) & 122, 000 MPa & Young’s modulus in the fibres’ direction \\ E\({}_{22}\) = E\({}_{33}\) & 6265 MPa & Young’s modulus in the transverse directions \\ G\({}_{12}\) = G\({}_{13}\) & 4649 MPa & Shear modulus in the 1–2 and 1–3 planes \\ G\({}_{23}\) & 4649 MPa & Shear modulus in the 2–3 plane \\ v\({}_{12}\) = v\({}_{13}\) & 0.3008 & Poisson’s ratio in the 1–2 and 1–3 planes \\ v\({}_{23}\) & 0.02 & Poisson’s ratio in the 2–3 plane \\ Glc & 180 J/m\({}^{2}\) & Mode I critical energy release rate \\ GIIc = GIIIc & 1900 J/m\({}^{2}\) & Mode II and Mode III critical strain energy release rate \\ h\({}_{\text{h}}\) & 0.165 mm & Ply thickness \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties.  
Figure 2: Global–local approach.  
The stiffened panel was analysed under compression in the stiffeners' direction. According to Figure 4, the nodes belonging to one panel edge were fully constrained, i.e., all of the translational and rotational degrees of freedom were suppressed, while on the other side of the panel, compressive displacement was applied and the other degrees of freedom were clamped.  
First, linear eigenvalue buckling analyses were conducted to assess the buckling load of the circular delamination, the buckling load of the skin and finally the global buckling load, also involving the stiffeners. Then, non-linear static analyses, under the displacement control mode, were performed using the SMXB procedure in order to determine the delamination propagation initiation load and the final delamination status for all of the sixteen configurations.