## 3 Results and Discussion
### Stress-Strain Curves and Lattice Structure Evolution of HCNNs
When the applied strain increases to the value of 0.423 (dash line **D**), the fraction \(\eta\) of HCP atoms changes into a nearly steady value from a negative slope and then the corresponding stress-strain curve exhibits a slightly faster softening rate due to the rupture of the samples (marked in Figure 3f). As for compression, it can be seen from Figure 2c that the stress-strain curves of the in-plane and out-of-plane compressions also have the same trend. Taking the in-plane compression as example, the stress-strain curves of compression can be divided into four stages (as shown in Figure 2c): (I\({}_{\text{c}}\)) initial linear elastic stage, (II\({}_{\text{c}}\)) instability of pore, (III\({}_{\text{C}}\)) collapse propagation and (IV\({}_{\text{c}}\)) densification stage. At the beginning of compression, sample enters into the linear elastic stage and reaches the peak stress (defined as the ultimate compressive strength \(\sigma_{\text{uc}}\)) (Stage I\({}_{\text{c}}\)). After reaching the peak stress, the pores become unstable and begin to collapse, which shows a dramatic strain-softening in stress-strain curve (Stage II\({}_{\text{c}}\)) and then the collapse begins to propagate, which causes a plateau stage in stress-strain curve (Stage III\({}_{\text{c}}\)). Finally, the strain-hardening effect becomes noticeable in the stress-strain curves which means the sample enters into densification stage (Stage IV\({}_{\text{c}}\)). The densification strain \(\varepsilon_{\text{d}}\) can be determined roughly by the intersection of tangents to the stress-strain curve for the cell wall collapse regime and densification regime [53]. Dash lines **E** and **F** correspond to the peak stresses for the out-of-plane and in-plane compressions at a strain of 0.049 and 0.068, respectively. Similar to the tension \(\eta\)-strain curves, the fraction \(\eta\) of HCP atoms has a very small value when the stress reaches the ultimate compressive strength \(\sigma_{\text{uc}}\). From the atomic snapshots corresponding to \(\sigma_{\text{uc}}\) as shown in Figure 3g,i it can be seen that, a few regions of the sample have entered into plastic deformation from elastic deformation. And then the sample enters into Stage II\({}_{\text{c}}\) (see Figure 2c). The end of Stage II\({}_{\text{c}}\) for the out-of-plane and in-plane compressions is divided by dash lines **G** and **H** at strain of 0.068 and 0.102, respectively. Figure 3d shows that the fractions \(\eta\) of HCP atoms rise sharply during Stage II\({}_{\text{c}}\). The atomic snapshots at the strain of 0.068 and 0.102 shown in Figure 3h,k hints that more and more dislocations and stacking faults are generated during Stage II\({}_{\text{c}}\). After that the fractions \(\eta\) of HCP atoms slowly increase through the Stage III\({}_{\text{c}}\) and enter into Stage IV\({}_{\text{c}}\) eventually. The atomic snapshots at the densification strain determined by tangent corresponding to dash lines **I** and **J** are shown in Figure 3i,l, in which the void is completely filled with the atoms and the RVE is nearly densified accompanied with lots of dislocations and stacking faults.