## 3 Results
Figure 7: Comparison of analytical ([PERSON] and [PERSON]) and numerical values of Poisson’s ratio for different unit cell types: (**a**) BCC, (**b**) diamond, (**c**) hexagonal packing, (**d**) rhombicuboctahedron, (**e**) truncated cube, and (**f**) truncated octahedron. Figure 8: Comparison of analytical (Euler–Bernoulli and [PERSON]) and numerical values of yield stress for different unit cell types: (**a**) BCC, (**b**) diamond, (**c**) hexagonal packing, (**d**) rhombicuboctahedron, (**e**) truncated cube, and (**f**) truncated octahedron. Similarly, the maximum differences between Euler-Bernoulli analytical Poisson's ratio and corresponding numerical values for BCC, diamond, hexagonal packing, rhombicuboctahedron, truncated cube, and truncated octahedron are, respectively, 3.07%, 27.69%, 28.00%, 21.54%, 73.58%, and 40.51%. The corresponding differences between the Timoshenko analytical relationships and the numerical values for the noted geometries are, respectively, 0.133%, 0.826%, 0.899%, 6.24%, 1.36%, and 0.498%, which shows a significant improvement in the accuracy of the analytical relationships. As can be seen in Figures 6-8, the numerical/analytical discrepancy for the case of Timoshenko beam theory is significantly less (around 1/10) than that of Euler-Bernoulli beam theory. As for the yield stress (Figure 8), the analytical Euler-Bernoulli and Timoshenko relationships are identical for BCC, diamond, and truncated cube unit cells. The reason is explained in Section 4.3. However, for three other geometries, namely hexagonal packing, rhombicuboctahedron, and truncated octahedron, the analytical relationships based on Euler-Bernoulli differ from the relationships obtained based on Timoshenko beam theory. Nevertheless, for all the cases, the Timoshenko analytical yield stress curve has exceptionally good agreement with numerical results (Figure 8). For BCC, diamond, and truncated cube unit cells (the geometries that have the same yield stress analytical relationships for Euler-Bernoulli and Timoshenko beam theories), the maximum difference between analytical and numerical values is less than 0.25%. As for the three other geometries, the maximum difference between Euler-Bernoulli analytical normalized yield stress and corresponding numerical values for hexagonal packing, rhombicuboctahedron and truncated octahedron are, respectively, 21.25%, 3.02%, and 7.52%. However, such differences for the analytical relationships based on Timoshenko beam theory and numerical values are, respectively, 9.49%, 0.09%, and 0.162%, which shows a significant improvement in the accuracy of the analytical relationships. As for the proximity of the analytical/numerical elastic modulus and yield stress values to the experimental data, the experimental data points have been presented in Figures 6 and 8 for rhombicuboctahedron, truncated cube, and diamond unit cells only, as in the literature, there are experimental measurements for such unit cells only [41]. As for the elastic modulus, converting the analytical relationships from Euler-Bernoulli to Timoshenko has led to closer proximity of analytical and experimental values (Figure 6b,d,e). As for the yield stress, for the three geometries for which experimental data points are available (diamond, rhombicuboctahedron, and truncated cube), the analytical relationships based on Euler-Bernoulli and Timoshenko are identical or almost overlapping, and both are in good agreement with experimental data points (Figure 8b,d,e).