## 3 Classification of Core Topologies  
As already explained in the previous sections, the core of a sandwich construction contributes significantly to the functional performance of the overall structure. It determines quasi-static load-bearing capacity due to its shear stiffness and buckling resistance in the vertical direction. In addition, the core topology affects system behavior in dynamic ballistic and/or blast loading scenarios. Usually, there are three fundamentally different strategies for core designs:  
1 Polymeric, ceramic, and metal foams with stochastic void distribution (open-cell foams or closed-cell foams);  
2 Periodic prismatic core geometries (open or closed);  
3 Periodic lattice-type core geometries (lattice cores).  
Figure 1 shows an example of two elementary prismatic core structures with auxetic base geometry. The design on the right belongs to the family of so-called honeycomb cores (closed-cell cores). Here, the longitudinal direction of the cells always coincides with the thickness direction of the core, and a closed, periodic interior space is created in the plane. The alternative design on the left-hand side is open on one side and allows, for example, oriented mass transport in one of the surface directions (unidirectional open-cell cores). In this case, the longitudinal direction of the cells is parallel to the two cover layers.  
A periodic core design that is open on all sides can only be realized by means of lattice-type cell elements (so-called lattice cores). Three-dimensional lattice structures provide versatile options for parameter-based topology optimization. Figure 2 illustrates a lattice core design based on a three-dimensional auxetic unit cell.  
Figure 1: Examples of prismatic core structures based on the standard auxetic topology. (**Left**) open-cell core. (**Right**) closed-cell core.  
Figure 2: Example of a lattice-type core structure based on a three-dimensional auxetic unit cell.  
The mechanical deformation behaviors and, thus, the mechanical properties of the three elementary core variants differ in fundamental ways. The manufacturing process for conventional polymeric, ceramic, and metal foam usually generates a randomly distributed void structure with irregular and corrugated cell walls or cell webs.  
During loading, these cell components are primarily subjected to bending stresses [29]. In addition, closed cells usually have very low relative membrane load-bearing capabilities and fail due to the rapid onset of buckling or cracking effects [30]. Imperfections, defects, and inhomogeneities caused by the manufacturing process lead to the comparatively low mechanical strength and stiffness of foam cores [31]. Many analyses of this foam's properties, the parameters that can be used to adjust its mechanical properties, and its use in sandwich construction exist in the literature. Therefore, foam cores are not the subject of this study.  
However, core structures with conventional periodic prismatic structures are primarily subject to a completely different deformation mechanism over wide load ranges. The regular cells provide a spatial folding structure with a dominant vertical axial orientation and components with a high relative membrane load-bearing capacity. Their mechanical properties depend primarily on the material and the buckling strength of the cell walls. In principle, this load-bearing behavior leads to higher stiffness and strength values than what is observed in foam cells that are mainly subject to bending stress.  
Similar correlations can also be deduced for the other core variants. However, the specific choice of geometry parameters for unilaterally open prismatic core cells, as well as for lattice cells, strongly affects their membrane and bending load-bearing capacities, more so than with other core types. So, it is not possible to identify a dominant load-bearing behavior in advance.