## 6 Simulation Results
At the same time, the maximum load on the bearing structure was only 40% of the reference value. Figure 15.9 Prismatic cores: normalized maximum values for displacement \(u_{3,\text{top}}\) and displacement ratio \(u_{3,\text{top}}/u_{3,\text{bot}}\). Figure 17.0 Prismatic cores: normalized maximum values for plastic dissipation energy. Conventional and auxetic topologies from the class of three-dimensional lattice cores concluded the numerical study. As already described above, the auxetic variants were able to counteract the formation of cracks even in a single-layer design due to their unusual deformation behavior and the associated reduction in tensile stress in the upper surface areas. At the same time, this led to a reduction in upper displacement compared to the non-auxetic lattice geometries; see Figure 17.1  
Figure 17.2 Three-dimensional lattice cores: normalized maximum values for displacement \(u_{3,\text{top}}\) and displacement ratio \(u_{3,\text{top}}/u_{3,\text{bot}}\). However, this effect was not accompanied by a significant reduction in the deflection of the lower cover surfaces. Irrespective of the cell angle, the displacement was, on average, about 30% greater than in the reference plate; see Figure 17.3 While both the conventional single-layer lattice cores and the prismatic cores exhibited rather soft behavior due to partial failure, the auxetic lattices achieved higher core stiffnesses. In some cases, their stiffness was comparable to that of the honeycomb cores. Due to their general position in space, a mixture of bending and membrane stresses, without the clear dominance of one type, was always present in the lattice bars, even if the cell angles were adjusted. In general, the values for plastic energy dissipation capacity were quite high, as shown in Figure 17.4 Irrespective of the sign, it tended to increase with increases in cell angle. The opposite was true for the transmitted peak load. Here, the maximum stress on the substructure decreased considerably with increases in cell angles and dropped by up  
Figure 17.5 Three-dimensional lattice cores: normalized maximum values for displacement \(u_{3,\text{bot}}\) and reaction force \(\text{RF}_{3}\). to almost 60% compared to the homogeneous monolithic reference plate. Clear trends were observed with increases in the number of layers. The absolute values for deflection, both on the bottom side and, above all, on the top surface, were reduced in multi-layer structures. Larger cell angles led to deformations on the side facing away from the load, with a simultaneous increase in deformations on the top side. The values for the bottom surface were, in some cases, only slightly above the reference value of the monolithic plate. The stiffness of the core structure (in terms of the displacement ratio between the top and bottom sides) varied by up to 35% according to the cell angle. In this case, larger angles led to larger deformations in the core area, as well as increasing energy dissipation capacities. It is noticeable that with neutral cube cells (\(\alpha~{}=~{}0^{\circ}\)), very stiff cores were created that, despite the given compressive load, expanded in some areas of the core structure in the thickness direction. A strong angular dependence, with significant internal differences of up to almost 60%, also occurred in the case of maximum load transmitted. Here again, larger angles caused a drastic reduction in the transmitted load. The two-layer auxetic configuration (\(\alpha~{}=~{}-45^{\circ}\)), for example, reduced the ambient stress by almost 70% compared to the reference value; see Figure 17.6  
Figure 17.7 Three-dimensional lattice cores: normalized maximum values for plastic dissipation energy.