## 3 Results and Discussion
### Delamination-Buckling Simulation Results
#### 3.2.3 Influence of the Strength Ratio and the Reference Strength  
The choice of adhesive type is of primordial importance to guarantee a sound 3D-FML. However, an adhesive with excellent bonding capabilities may not have an adequate strength, and a very strong adhesive may succumb to interfacial failure because of the lack of adhesion compatibility with the mating adherends. Therefore, another aspect that was investigated was the influence of the ratio of the cohesive strength of the adhesive (modeled using xFEM) to the interfacial strength (modeled using CZM). Surprisingly, no significant difference was observed in the resulting axial-load shortening curves among all the considered cases; therefore, these results are not reported.  
However, the influence of the reference (or the maximum traction) strength was investigated. For that, values of 0.016, 0.032, 0.08, and 0.8 GPa were considered. The results are illustrated in Figure 11. The following conventions are used to distinguish the models' results. In the figures, \"c\" and \"x\" refer to the results produced by the cohesive and xFEM elements, respectively. The numbers appearing after \"c\" and \"x\" signify the value (multiplier) by which the base strength (traction) value reported in Table 13 was increased. For instance, c-100 references to the COHESIVE model with the base strength of 0.8 GPa (i.e., 0.008 GPa \(\times\) 100).  
Figure 10: (**a**) Kinking of the delaminated front predicted by the MIXED model (initial delamination at the mid-height); (**b**) delamination kink angles for various through-thickness positions of the delamination, for the specimen under impact.  
As seen, the higher is the adhesive strength, the more difficult would be for the delamination to propagate along the interface. This results in the evolution of successive cracks, all having the same inclination. However, an apparent limit is reached when the base strength approaches a relatively large value (i.e., c-100), in which case the delamination would no longer propagate longitudinally, leading to extensive local damage at the delamination tip. Note that the delamination initially kinks towards the upper interface but could not propagate within the cohesive elements due to the high traction strength. Moreover, due to the limitation of the xFEM formulation, the delamination was not capable of propagating along the interface of xFEM/cohesive elements either. This resulted in the development of successive delaminations parallel to the initial delamination. Of interest is also the behaviors of models x-2 to x-10. In these models, the delamination propagated towards the interface, and then traveled along that interface in both forward and reverse directions. This response became increasingly noticeable as the base strength was increased, which is facilitated by the comparatively lower interface strength. In the extreme case (x-100), where the interface strength is significantly weaker than the traction strength, the adhesive detaches almost completely from both neighboring materials. Note that the minute interpenetration seen in model x-100 (see Figure 11h) is the result of the failure of the cohesive elements, and the absence of a contact algorithm. It should be noted that incorporation of an  
Figure 11: Influence of the base (traction) strength on delamination propagation captured by the MIXED model when the strength of the cohesive elements is 2-100 times greater than the strength of the xFEM elements (subfigures (**a**) to (**d**), respectively) and when the strength of the xFEM elements is 2-100 times greater than the strength of the cohesive elements (subfigures (**e**) to (**h**), respectively).  
appropriate contact algorithm would have increased CPU consumption significantly, resulting in no appreciable benefit in terms of further understanding of the behavior.