## 3 Results and Discussion  
### Stress-Strain Curves and Lattice Structure Evolution of HCNNs  
It is noted that the stress-strain curves for the groups 1 to 7 HCNNs have the same trend and they just differ in the magnitude of the values. Without loss of generality, here we choose the 4 th group of HCNNs as examples to investigate the mechanical behavior and lattice structure evolution of the HCNNs during the in-plane and out-of-plane tension and compression. Figure 2a,c show the stress-strain curves of the HCNNs and Figure 2b,d show the corresponding variation of the fraction \(\eta\) of hexagonal close-packed (HCP) atoms with strain. The fraction \(\eta\) of HCP atoms is calculated by \(\eta=N_{\text{HCP}}/N_{\text{all}}\), where \(N_{\text{HCP}}\) is the total number of HCP atoms and \(N_{\text{all}}\) is the total number of atoms in the sample. In order to study the relationship between stress-strain curves and the fraction \(\eta\) of HCP atoms, Figure 2a,b are divided by dash lines **A**, **B**, **C** and **D** (with the black dash lines **A** and **C** corresponding to the in-plane direction and the red dash lines **B** and **D** corresponding to the out-of-plane direction), respectively, while Figure 2c,d are divided by dash lines **E** to **J**, noticing that lines **F** and **G** are overlapped and indicated by blue line specially. Figure 2: Stress-strain curves and the hexagonal close-packed (HCP) atom fraction \(\eta\) of group 4 for HONNs along different deformation direction. It can be seen from Figure 2a that the in-plane and out-of-plane tensile curves have the same trend. Taking the in-plane tensile curve as example, the stress-strain curve of tension can be divided into two stages (as shown in Figure 2a): (I\({}_{\text{t}}\)) initial linear elastic stage and (II\({}_{\text{t}}\)) the strain-softening and rupture. At the beginning of tension, sample enters into the linear elastic stage and reaches the peak stress (defined as the ultimate tensile strength \(\sigma_{\text{ut}}\)) (Stage I\({}_{\text{t}}\)). After that the stress decreases as the strain is further increased and finally begins to rupture (Stage II\({}_{\text{t}}\)). Dash lines **A** and **B** correspond to the peak stresses for the in-plane and out-of-plane tension at strain of 0.08 and 0.091, respectively. Figure 2b shows that the fraction \(\eta\) of HCP atoms is at a lower level when the stress reaches ultimate tensile strength \(\sigma_{\text{ut}}\). After which \(\eta\) sharply rises and reaches the peak value quickly, leading to a dramatic strain-softening (see Figure 2a) because of the accumulation of stacking faults. Figure 3 gives the atomic configurations at different stages based on the common neighbor analysis (CNA) [52]. Figure 3a,d show the atomic snapshots with the strain corresponding to the \(\sigma_{\text{ut}}\) and it can be found that few regions of the samples have transformed into plastic deformation from elastic deformation because a small amount of dislocations and stacking faults are generated. As the applied strain increases to a critical value of 0.236 (dash line **C**), the fraction \(\eta\) of HCP atoms of the in-plane tension reaches a peak value and the corresponding stress-strain curve exhibits a faster softening rate when the applied strain exceeds the critical value of 0.236. Figure 3b shows the atomic snapshot with strain of 0.236 for the in-plane tension, which is the result excluding the surface atoms. Cracks can be observed inside the ligament (marked in Figure 3b) and lots of stacking faults are formed around the cracks. As the applied strain further increases, rupture of the sample (marked in Figure 3c) occurs around the strain of 0.32. As for the out-of-plane tension in Figure 3e, a more homogeneous necking is observed compared to the in-plane tension in Figure 3b, so its stress-strain curve shows a more steadily softening rate.