###### Abstract
[21] demonstrated the capability of the tiebreak contact and xFEM for modeling crack propagation in a precracked thick beam, under mode I loading. They showed the deviation of the crack that originally started in \(0^{\circ}/90^{\circ}\) ply-interface, propagating into the adjacent \(90^{\circ}/0^{\circ}\) interface. It should be noted that in general, however, the accuracy of the results is highly dependent on the xFEM formulation, which is considerably more complex than the conventional finite element formulations [22; 23]. As a result, xFEM is not readily available in all commercial finite element software, and if it is, the formulation is usually limited to a set of element types. Moreover, it is worth mentioning that there are a few studies that have compared the integrity of the three approaches when used in simulating crack propagation. For instance, [PERSON] et al. [1] used the erosion and xFEM elements of LS-DYNA for simulating the crack propagation resulting from the impact of a rectangular cast iron specimen in three-point bending configuration. The xFEM results were found to be in excellent agreement with the experimental results, while the erosion elements could not accurately simulate the experimentally observed response. [PERSON] and [PERSON] [24] compared capabilities of the xFEM element against both cohesive and erosion elements for simulating the response of a standard double cantilever beam modeled using 3D elements in ABAQUS. They found the xFEM results to be more consistent and closer to the experiment results, and not too sensitive to mesh density. However, they observed xFEM's tendency to underestimate the fracture energy, while CZM overestimated it. As stated, all the modeling facilities mentioned above are available in LS-DYNA. In this paper, we will focus on CZM and xFEM and, more precisely, on the possibility of combining them for conducting a more accurate modeling of crack propagation resulting from delamination buckling of a relatively complex 3D hybrid composite material (i.e., a new class of FML). This new material referred to as 3D-FML, takes advantage of the properties of a lightweight magnesium alloy, coupled with a recently developed truly 3D fiberglass fabric and a light-weight foam, thus rendering a cost-effective lightweight material with remarkable stiffness, strength, and resiliency against impact [25]. However, it is well-known that the Achilles' heel of all laminated composites is their relatively weaker interlaminar strength compared to their bending and axial strengths, and the 3D-FML is no exception. The likelihood of delamination initiation in such materials becomes even greater when they become subjected to a suddenly applied axial compressive loading [26; 27; 28]. Under such a circumstance, the metallic constituent often debonds from the core section. Therefore, the presence of a delamination, even a small one, would adversely affect the performance of laminated composites and FMLs subjected to compressive loadings. The authors are, therefore, interested in better understanding the response of 3D-FMLs under compressive impact loading, and the ensuing failure mechanism during their delamination buckling in order (i) to accurately predict their behavior through numerical simulation and (ii) to enhance their load-carrying capacity of the 3D-FML by appropriate means.