## 3 Classification of Core Topologies
### Core Topologies and Their Parameterisation
Like the prismatic versions, these cores have high weight-related strengths with low relative densities, as well as a high specific energy absorption capacity. Furthermore, the fully open core area creates a great deal of additional functionality. Application capabilities, including as a heat exchanger with a cooling medium flowing through it or as a storage structure for electrical energy (in which the core topology serves as one of the electrodes), are described in the literature; in addition, the manufacturing costs are lower than those of conventional honeycomb cores [51]. Overviews of the multifunctional application possibilities and the application-related design requirements of these cores were presented by [PERSON] et al. [52; 53]. So far, the lattice topologies shown in Figure 7 are mainly used in practical applications. Not listed are the square and rhombic lattice cores, whose mechanical properties were described by [PERSON] et al. [54; 55]. For lattice cores, the structural behavior under compressive loading is characterized by elastic buckling processes and under shear loading by tensile failure in the lattice bars. When the bars are designed as silicon carbide-titanium composites, even higher shear strengths can be achieved than with honeycomb cores made of carbon-fiber-reinforced polymer (CFRP). The performance capabilities in compression processes are comparable. However, the increase in load-bearing capacity is accompanied by a loss of ductility and the risk of spontaneous failure. A comparison of the two lattice geometries finds higher shear strength but lower tensile strength (in-plane) for diamond lattices [56]. Under compressive loading (out-of-plane), both variants react similarly. Sandwich elements subjected to bending stress achieve better performance due to the more favorable shear behavior when using diamond-shaped cells. Figure 7: Sections of conventional one-layer 3D lattice core variants with their associated unit cells. From top to bottom: pyramidal core, tetrahedral core, and 3D Kagomé core [57]. Studies by [PERSON] et al. focused on determining the mechanical properties of sandwich constructions with pyramid-shaped lattice core structures. The behavior of these sandwich structures under vertical compressive loading, as well as under longitudinal and transverse shear loading, was documented in detail [58; 59]. In addition, the geometry-dependent failure patterns were investigated in [60], taking into account multi-layer core assemblies under in-plane compressive forces. An increase in the mechanical performance of most lattice core structures can be achieved by using circular hollow sections for the lattice bars [61]. Similarly, the use of carbon-fiber-reinforced polymer as a core material promises higher performance potential [62]. Cyclic loading shows that, under shear stress, there is a high susceptibility to fatigue and failure in the brazed or welded connection areas between the core and the cover surface. However, hardly any structural problems were observed during compression processes [63]. Studies on the imperfection sensitivity of the core geometry confirmed the joints as critical regions. Deliberately introduced imperfections in the connection regions led to a loss of shear strength and shear stiffness but did not show any effects in the case of vertical compressive stresses [64]. Since finite-element-based simulations of complex core structures are very computationally expensive in terms of time and CPU capacity, the number of topologies considered in this contribution had to be limited. For this reason, a direct comparison with the previously described variants is not possible for the lattice cores. Rather, the focus here is on a subset of the novel cell geometries shown in Figure 8. The uppermost topology corresponds to the equivalent of a three-dimensional honeycomb cell and is characterized by positive values of the lattice cell angle \(\alpha\). With \(\alpha~{}=~{}0^{\circ}\), cube-shaped cells without inclined cell components are created.