## 3 Classification of Core Topologies
### Considered Core Topologies for Numerical Studies  
The primary goal of being able to evaluate and compare numerous core topologies without an increased standardization effort led to the definition of some constant geometry parameters for all sandwich configurations in the run-up to the simulations. In addition to the fixed thickness of the face sheets, equal lateral dimensions and a constant core height were also set for all configurations. Furthermore, a constant relative density was set for all core variants; consequently, identical weights for all constructions were guaranteed. On this basis, an initial efficiency evaluation and assessment of the performance of the auxetic cores compared to conventional variants can be made according to the simulation results. The data in Tables 1-4 describe the considered core topologies and their geometry parameters. The adjustment of the wall thickness \(\mathsf{t_{c}}\) of the prismatic cores is performed automatically and--in order to maintain the weight--depends exclusively on the total cell wall area available in the interstitial space. The parameters of the conventional core geometries are based on common values for sandwich structures of this size. The data on open lattice core geometries in Table 4 also contains information on the number of unit cells and layers used. From this, the lateral dimensions of the individual spatial cells can be derived. Furthermore, the radius \(\mathsf{r_{c}}\) of the lattice bars replaces the wall thickness \(\mathsf{t_{c}}\) of the prismatic cores. The design of the cell structure is carried out here exclusively by means of circular solid cross-sections. \begin{table}
\begin{tabular}{c l c c c c c} \hline \hline
**No.** & **Designation** & \(\mathbf{h_{uc}}\) **in mm** & \(\mathbf{b_{uc}}\) **in mm** & \(\mathbf{l_{1}}\) **in mm** & \(\boldsymbol{\kappa}\) **in**\({}^{\circ}\) & \(\mathbf{t_{c}}\) **in mm** \\ \hline
01 & honeycomb & 15.00 & 17.32 & 8.66 & 120 & 0.2500 \\
02 & square-honeycomb & 2000 & 20.00 & - & - & 0.3305 \\
03 & closed isogrid core & 3000 & 34.64 & 17.32 & 60 & 0.1645 \\
04 & auxetic honeycomb (h-15) & 15.00 & 17.32 & - & 120 & 0.1895 \\
05 & auxetic honeycomb (h-20) & 20.00 & 23.09 & - & 120 & 0.2498 \\
06 & auxetic honeycomb (h-25) & 25.00 & 28.87 & - & 120 & 0.3200 \\
07 & auxetic honeycomb (h-30) & 30.00 & 34.64 & - & 120 & 0.3609 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Topology and parameters: closed prismatic honeycomb cores. See Figure 3. \begin{table}
\begin{tabular}{c l c c c c} \hline \hline
**No.** & **Designation** & \(\mathbf{h_{uc}}\) **in mm** & \(\mathbf{b_{uc}}\) **in mm** & \(\mathbf{l_{1}}\) **in mm** & \(\boldsymbol{\kappa}\) **in**\({}^{\circ}\) & \(\mathbf{t_{c}}\) **in mm** \\ \hline
08 & I-core (g = 20 mm) & 20.00 & - & - & - & 0.6610 \\
09 & Y-core (b\({}_{1}\) = 4 mm) & 20.00 & 20.00 & 8.00 & 45 & 0.3602 \\
10 & container truss core & 20.00 & 60.00 & 20.00 & 45 & 0.5476 \\
11 & triangle-core & 20.00 & 40.00 & - & 45 & 0.4674 \\
12 & diamond-core & 20.00 & 20.00 & - & 90 & 0.2337 \\
13 & square-honeycomb (2L) & 10.00 & 10.00 & - & - & 0.2203 \\
14 & square-honeycomb (4L) & 5.00 & 5.00 & - & - & 0.0944 \\
15 & honeycomb (2L) & 10.00 & 11.55 & 5.77 & 120 & 0.1808 \\
16 & honeycomb (4L) & 5.00 & 5.77 & 2.89 & 120 & 0.0864 \\
17 & open isogrid core & 10.00 & 11.55 & 5.77 & 60 & 0.0603 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Topology and parameters: one–side-open non-auvetic prismatic cell cores. See Figures 4 and 5.