## 3 Results and Discussion  
### Double Cantilever Beam Simulation Results  
The simulations of the DCB were conducted to examine the feasibility and advantage of the proposed combined simulation methods (i.e., combined xFEM and cohesive elements). It is noted that the DCB tests were conducted under static loading scenario, which differs from the loading states our 3D-FML specimens were subjected to. However, as briefly stated earlier, the accuracy of the results is not a focus of this preliminary stage of our research, since the main objective was to examine the capabilities of the various approaches used here to model the crack propagation within a complex hybrid system subjected to a critical loading state (i.e., impact). The predicted crack propagation paths are reported in Figure 5. Note that LS-DYNA's post-processor exhibits the crack propagation path captured by XFEM models by a change in the elements' color, while the deleted-element scheme exhibits the path in the case of COHESIVE models. In the COHESIVE model, as expected, the crack propagated in a straight path along the cohesive elements. In the XFEM model, the crack did not propagate when the same magnitude of displacement as applied in the case of the COHESIVE model was used. However, upon the application of a greater magnitude of displacement (i.e., +45% for initiating the crack and +1132% at the end of calculations), the crack started propagating and deviated  
Figure 4: Geometry and boundary conditions of the partially delaminated fiber metal laminates (FML) specimen (not to scale): (**a**) Sketch of the actual specimen (not to scale) (**b**) model used for numerical analysis, and the zoom-up views of the mesh around the delamination-tip in (**c**) the COHESIVE model and (**d**) the MIXED model. from its course towards the upper adherend/adhesive interface, traveling along that interface. At that stage, a second crack appeared at the initial kink location, propagating along the direction of the lower interface. It should be noted that the simulated crack propagation is not consistent with the experimental observations. Moreover, the resistance of crack to propagate led to an exaggerated opening of the delaminated portions of DCB when compared to the COHESIVE model. It should be noted that, when a combination of the elements was used (i.e., the MIXED model), the resulting crack propagation path was found to be yet different, as shown in Figure 5c. In that case, first the crack propagated through one element, and then it diverted towards the upper interface and propagated along that interface. It subsequently changed its path towards the lower interface and traveled along that interface. The total length of propagation during the described event was limited to 6 mm, after which the simulation was halted due to computational issues caused by the development of a negative volume in one of the elements; nevertheless, the approach illustrates the potential of the method. The initial stage of crack propagation obtained with the MIXED model is compared to that observed during the static testing of the DCB described in Section 2.2, as illustrated in Figure 6. Note that the tested adhesive layer of 1 mm is greater than the actual thickness of 0.2 mm used in the actual test. The change in the thickness had to be done to resolve the extremely fine mesh that would have been required, had we used the 0.2 mm thickness. In addition, it is necessary to mention that the hybrid DCB specimen was designed so that the difference in flexural stiffness between the two cantilever beam portions of DCB specimen was relatively equal (in fact, they differed by a mere 2%, and the variation of longitudinal strain induced by the applied load was limited to 8%). This unconventional DCB specimen was constructed for the sole purpose of being able to obtain  
Figure 5: Qualitative comparison of the crack propagation under the DCB test predicted by the various models (**a**) COHESIVE, (**b**) XFEM, and (**c**) MIXED. For the sake of clarity, only the zone near the crack tip is shown.