## 3 Results and Discussion
### Delamination-Buckling Simulation Results
#### 3.2.2 Influence of the Through-Thickness Position of Delamination  
The analysis concerning the through-thickness position of the initial delamination, whose results are reported in Figure 9, indicates that a delamination located closer to the magnesium skin would lead to a lower load sustaining capacity (apart from the cases where the delamination is located at any of the interfaces). This is attributed to a combination of factors. Firstly, the delamination path would become longer when it propagates towards the interface. Secondly, the skin will have higher apparent rigidity, because a thicker layer of resin is bonded to it. Lastly, a greater number of xFEM elements would have to be traversed by the delamination front, which would imply that there would be a higher number of elements with residual stress. The results, however, do not follow the mentioned pattern when the delamination is initiated within the cohesive elements. The lowest load sustaining capacity is observed when the delamination is located at the upper interface; that is because no xFEM element is affected by the delamination. When the delamination is initiated at the lower interface, it does not propagate towards the upper interface, because the stress necessary for the delamination to kink is not attained. However, as can be seen from Figure 7c, several cracks appear in the adhesive layer due to the bending (note that all the cracks are oriented normal to the delaminated surface); notwithstanding, experimental tests would be required to corroborate these findings. Another important observation exposed by the result is that xFEM elements failed at a higher stress level in comparison to the cohesive elements, despite the fact that both element types were fed the same material properties (note that both cohesive and xFEM elements were described by the same bi-linear traction-separation law, cf. Section 2.1). For practical applications, it is therefore recommended to consider a slightly larger traction when using the cohesive element in comparison to the xFEM element. The exact amount of the traction value would have to be established by tuning the numerical models with experimental data. Another interesting phenomenon observed during this phase of the study is the change in the ensuing delamination kink angle. This angle is defined as the angle between a hypothetical non-kinked delamination path and the delamination orientation after it kinks, as shown in Figure 10a. Note that for the reasons mentioned earlier, only the variation of the delamination in the xFEM elements could be considered. As seen from Figure 10b, the closer the delamination is to the interfaces, the greater is the delamination kink angle (i.e., \(\sim\)60\({}^{\circ}\)), while the minimum angle of 43\({}^{\circ}\) is observed when the delamination is located near the mid-thickness of the adhesive. This would indicate that, as the delamination becomes closer to an interface, its advancement will involve a greater presence of mode I compared to mode II. Figure 9: Axial-load shortening curves produced by the MIXED model for case studies having various through-thickness positions of the initial delamination. Note that the first portion of the graphs has been omitted for clarity, as it is the same for all the cases. This is attributed to the stress state and the difference in the deformation responses of the relatively more flexible skins and the more rigid FRP core. Therefore, this could explain why an optimal surface preparation is of paramount importance for obtaining the maximum performance in such 3D-FMLs, in particular when the constituents bonded together have low chemical compatibility ( such as in our case). It should be noted that in another work that will be soon published, we proposed a new bonding technique for improving the interface adhesion strength between magnesium and fiber-reinforced epoxy composites.