## 4 Summary and Conclusions  
In this study, the integrity and efficiency of the two modelling approaches used for assessing crack and delamination propagations in hybrid composites were examined. The approaches involved the use of cohesive and extended finite element (xFEM) elements available through the commercial finite element software LS-DYNA. More specifically, two separate case-studies were considered. First, crack propagation in a double cantilever beam (DCB) test specimen formed by two dissimilar adherends was considered. Then, delamination buckling response of a 3D fiber-metal laminate, subjected to a compressive impact loading, was simulated. The study also examined the integrity of a mixed approach; that is, the use of xFEM and cohesive elements within a single model. In the latter analysis, the cohesive elements were used to simulate the adhesive/adherent interface, while the xFEM elements were used to simulate the bulk portion of the adhesive. The summary of our findings is as follows:  
* LS-DYNA's shell elements could be used to simulate plane strain conditions in circumstances when plane strain elements cannot be used to conduct the analysis. * The analysis of the DCB specimens using the combined xFEM and cohesive approach proved that the crack kinking that was experimentally observed to occur within the adhesive could be simulated precisely. The model that used only the xFEM elements could not capture the phenomenon. * The above-mentioned combined approaches could also successfully simulate the delamination buckling response of the FML model with good accuracy. The delamination was demonstrated to change its propagation path that was initially within the adhesive (i.e., through the xFEM elements) towards the adhesive/metal interface, and subsequently propagating along the interface (i.e., through the cohesive elements). The delamination path deviation response highlights the importance of the role of surface preparation (i.e., interfacial integrity) in enhancing the performances of such FMLs under compressive loading states. * Using the same material model and properties, the model constructed using only xFEM elements appeared to overestimate the energy required for the crack/delamination to propagate in comparison with the model constructed with the cohesive elements. * The use of xFEM elements resulted in more accurate predictions of crack initiation and propagation. However, from a solution time perspective, especially when large complex geometries are to be modeled, the use of cohesive elements is deemed preferable, so long as the crack or delamination path is known a priori. In closing, while the potentials of the different numerical approaches were demonstrated throughout this study, nonetheless, further effort is necessary to establish the accuracy of the solutions that are produced by these approaches. For instance, the future works should consider (i) precise calibration of the cohesive parameters required by the methods by experimental means, including investigation of strain effect on the properties, and (ii) verify the accuracy of the numerical results by comparing them with consistent experimental results. Another aspect that requires further investigation is understanding the origins of the numerical instabilities that at times halt and limit such solution processes. Finally, it would be worth exploring the capabilities of the element-free approaches, such as the element-free Galerkin (EFG) method and the discrete element method (DEM). These approaches have been proven to be efficient in simulating crack propagation [32; 34] and are available through LS-DYNA for both 2D and 3D simulations. [PERSON] constructed and run the models, analyzed the data and wrote the draft manuscript. [PERSON] provided the idea, guided the research and edited the manuscript. This research was supported by the National Sciences and Engineering Research Council of Canada (NSERC) and the MITACS Globalink fellowship program.