## 2 State of the Art  
Due to the high level of numerical effort involved, some authors refrain from an exact modeling of resolved core structures and describe their behaviors with the help of homogenization techniques [13; 14; 15]. Such continuum mechanical approaches inevitably lead to simplified representations of the relevant behaviors and failure mechanisms, with an associated loss of accuracy. For example, these approaches cannot capture local (buckling) phenomena over the core height or their influence on overall structural behavior. In addition, the homogenized input parameters of any core variants must be determined and calibrated at great expense, either by means of experimental data or detailed mapped and meshed unit cells. In addition, simplified analytical approaches exist to describe core geometry and core properties. [PERSON] and [PERSON] [16; 17; 18], for example, used analytical models for the description of the structural response of sandwich beams under blast or impact loading. They investigated different core topologies (honeycomb, pyramidal, prismatic diamond, and metal foam) and characterized the different variants on the basis of their transverse compressive strength (out-of-plane) and their tensile strength in the longitudinal direction as a function of the relative density. Comparisons with finite element calculations show good agreement. However, the analytical models often underestimate (especially at high core strengths) the maximum deformations of the backside and provide overly high values for the reaction forces in the supporting substructure [19]. The focus on a beam-like system additionally limits the general validity. Due to increased computer capacities, complete topology models of the discrete sandwich structures were considered in recent studies [20; 21; 22]. These studies focused primarily on the investigation of various core topologies, the recording of fluid-structure interactions in a fully coupled analysis, and the description of the failure mechanisms of the core and top surface areas as well as the connecting regions. Comparative studies by [PERSON] et al. [23; 24] illustrated the superior properties of several core topologies (honeycomb, prismatic, and pyramidal truss cores) in sandwich structures over monolithic panels when subjected to impulsive loading in water. With a relative density of about five percent, the best variants reduced the forces transmitted to the substructure by 25% compared to a monolithic panel of the same weight. Moreover, pyramid-shaped lattice core structures embedded in a multi-layer design achieved up to 30% lower values [24]. In addition, the adjustment of the relative core density allowed selective control of the transferred pressure [25; 26], whereby lower densities tended to mean lower amounts. Homogenization approaches and simplified load-modeling strategies (uniform initial velocity of the outer face) show acceptable agreement with the results of comparative experiments carried out under planar pressure blast loading after calibration has taken place [23; 24]. [PERSON] et al. provided a comprehensive study of auxetic double arrowhead honeycomb core sandwich panels for performance improvement under air-blast loading [27]. Their numerical results reproduced former experimental investigations [28] and confirmed the material concentration effect of auxetic double arrowhead honeycomb cores induced by a negative Poisson's ratio. According to the simulation results, the best design strategy for improving the blast performance of this kind of auxetic core structure depends upon core relative densities. The adoption of more highly inclined angles could reduce the level of deflection for the panel center more efficiently at a low relative density. For higher levelsof relative core density, it is more efficient to decrease the horizontal distance instead of increasing the incline of the angles.