## 3 Classification of Core Topologies
### Core Topologies and Their Parameterisation
In its case, only a bending load orthogonal to the longitudinal axis of the cell leads to acceptable results due to the increased buckling stiffness. The performance of the rhombic pattern is almost independent of the load orientation with appropriate individual parameter selection [44]. Experiments by [PERSON] et al. [45] produced overview maps for the prediction of the relevant failure mechanisms in triangular topologies as a function of geometrical configuration and actions. As with the closed honeycomb cores, a hierarchical structure also makes it possible to improve the performance of the overall structure. To this end, [PERSON] et al. [46] designed core walls as a triangular sandwich construction (second order). While conventional structures with monolithic cell walls (first order) fail due to the buckling processes or plastic flow processes of the core components, six potential failure mechanisms are now taken into account in second-order structuring. Hierarchization results in significantly higher compressive and shear strengths for the same weight (relative core density \(\mathrm{\rho_{c}}<5\%\)). [PERSON] et al. [47] further identified the critical regions for the fatigue of diamond cores under transverse shear loads. In their study, depending on the relative density, the immediate core components in the corner regions or the connections between the core and face regions were the limiting factors. The fatigue-related failure of interfaces was observed in the course of this investigation in a number of other core types. Figure 3: Sections of prismatic closed-cell honeycomb cores with their respective unit cells. Experimental studies on sandwich specimens by [PERSON] et al. [48] indicated similar load-displacement behavior for Y-cores and triangular configurations. This was true both for a quasi-static three-point bending load with different boundary conditions and for time-independent plane indentation tests perpendicular to the sandwich faces. FE simulations by [PERSON] et al. [49] showed, in good agreement with real test results, relatively low compressive and transverse shear strengths for Y-cores compared to their longitudinal shear capacity; this result was due to the plastic bending deformations of the core components. Their energy dissipation capacity under compressive stress was much higher than that of conventional and equal-weight sandwich components with interior fillings of metal foams. [PERSON] et al. [50] recognized, for most of the Y-core variants relevant in practice, a constant load plateau with progressive compression (out-of-plane) of the sandwich construction; they confirmed its capacity for energy dissipation. Figures 5 and 6 present typical topologies from the class of two-layer prismatic and one-side-open sandwich cores, including the underlying unit cells and their geometry parameters. Figure 4: Sections of conventional prismatic open-cell cores with their respective unit cells (one layer, 1L). From top to bottom: I, Y, triangle, diamond, and container truss core. Figure 5: Sections of non-auxetic prismatic and one-side-open core structures with their associated unit cells (two-layer, 2L). From top to bottom: honeycomb, isogrid, and quadratic core. Figure 6: Sections of auxetic prismatic and one-side-open core structures with their associated unit cells (two-layer, 2L). From top to bottom: standard auxetic core (90\({}^{\circ}\) rotated), standard auxetic core, and dart core (concave deltoid). A new feature is the use of auxetic variants in Figure 6. Besides the standard auxetic cell in the upright and 90\({}^{\circ}\) rotated positions, the behavior of a core with concave deltoid cells (Figure 6, below) is of special interest due to its two incline parameters. Here, the mechanical behavior and the degree of auxeticity can be specifically controlled, within certain limits, via two independent angle settings; this offers a potential advantage over patterns with fewer influencing variables. The last category of cores consists of the lattice core variants.