## 2 Performance Metrics, Geometry, and Material Properties
### Cellular Structure Geometry  
Figure 4 shows the geometry of the cellular structure. The unit cell is a hexagon connected to a \(10\times 10\) mm square from its six corners. The sides of the square are considered walls whereas the hexagon and the lines extending from its corners are considered struts. The cellular structure is made from stacks of unit cells. The volume of the cellular structure is \(50\times 50\times L\) mm. The length (\(L\)) is increased from 50 to 150 mm (increments of 50 mm) for studying the effects of length scaling. The struts, walls, and stacks are assigned thicknesses in four different ways as discussed below.  
The uniform shell thickness (UT) is shown in Figure 5 where the struts and the walls have the same shell thickness. There is no variation in shell thickness in different stacks or elsewhere for UT. In the strut-wall shell thickness (SWT) type, the struts and the walls have varying shell thickness assignments. As shown in Figure 6, the walls have a thickness of \(T_{2}\) while the struts have a thickness of \(T_{1}\) different from the former. Figure 7 shows the alternating shell thickness (AT) type where the struts and walls alternate between two thicknesses \(T_{1}\) and \(T_{2}\). Starting with the left-most unit cell at the bottom stack, the struts are assigned a thickness of \(T_{1}\). The next group of struts on its right is  
Figure 4: (**a**) Honeycomb design in nature, (**b**) nature-inspired cellular structure design for this study. The novelty is through the addition of walls and struts to the honeycomb design.  
assigned \(T_{2}\), etc. For the wall thickness, the whole cellular structure is considered instead of the unit cell. The bottom wall of the bottom stack is assigned \(T_{I}\) and the top wall of the bottom stack is assigned \(T_{2}\). This pattern is repeated for all the horizontal walls. The first vertical wall of the first column-stack is assigned \(T_{I}\) and the second vertical wall of the first column stack is assigned \(T_{2}\), etc. The gradient shell thickness (GT) type has an incremental shell thickness based on the stacking levels. As depicted in Figure 8 the lowest stack has a thickness of \(T_{I}\) and it increases as we move up along the stacks until we reach the top-most stack, which has a thickness of \(T_{2}\).  
Figure 5: Uniform thickness with an isometric view (**left**) and front view (**right**). Thickness assignments to the walls (\(T_{2}\)) and the struts (\(T_{I}\)) are equal.  
Figure 6: Strut-wall thickness with an isometric view (**left**) and front view (**right**). Thickness assignments to the walls (\(T_{2}\)) and the struts (\(T_{I}\)) are different.  
Figure 7: Alternating thickness with an isometric view (**left**) and front view (**right**). Thickness assignments indicate the maximum (\(T_{2}\)) and minimum (\(T_{I}\)) values.  
Table 1 summarizes the geometric parameters we have discussed thus far. It also specifies the values that we have considered for these parameters. There are four geometric parameters: Strut thickness, wall thickness, gradient thickness, and length. The struts and walls can have either 0.2, 0.4, or 0.6 mm thickness for UT, SWT, and AT. Whereas the stacks are assigned a gradient thickness for GT which is calculated by (\(T_{2}\)\(-\)\(T_{1}\))/\(L\). For each of these geometric types, the length can be 50, 100, or 150 mm. These all together result in 45 simulations as indicated in Table 2.