## 4 Results and Discussion
### Energy Absorption Capability of Functionally Graded TPMS Structures  
The stress-strain curves and energy absorption curves for axial compression are shown in Figure 15. The values of stress and energy absorption increase with the compression displacement. It is noteworthy that the EA of Sh-D1, Sh-D2, and Sh-D3 are very close to each other. However, Sh-D3 provides a lower initial peak force, which is 40% of that of Sh-D1, and the stress-strain curves of Sh-D1 and Sh-D2 are very close to each other, indicating that the change in the transverse gradient has very little effect on the energy absorption in longitudinal compression. The deformation processes of functionally graded sheet-TPMS structures are shown in Figure 16. The deformation patterns in the compression process differed for different forms of gradient structures. Sh-D1 compression is characterized by premature densification due to the large thickness in the middle, whereas Sh-D2 compression is characterized by convexity on both sides due to the large thickness on both sides. In Sh-D3 compression, due to the small thickness at the top, the structure is guided to deform in an orderly manner from top to bottom.  
Figure 14: (**a**) Stress–strain and (**b**) energy-absorbing curves of uniform TPMS structures.  
Figure 15: (**a**) Stress–strain and (**b**) energy absorbing curves of functionally graded TPMS structures.  
The 2D-DIC method was used to analyze the deformation patterns and strain field distributions of functionally graded TPMS structures during the loading process. As illustrated in Figure 17, it is clear from the DIC strain contours that the local deformation starts at the weakest part of the structure. Different from the uniform specimens, the Sh-D1, Sh-D2, and Sh-D3 samples showed completely different deformation behaviors. Sh-D1 showed a localized structural fracture at a location with a large thickness in the middle of the structure; Sh-D2 tended to produce an oblique shear zone during compression, and Sh-D3 showed an overall stable deformation pattern during compression and progressively collapsed from the top layer layer-by-layer. The results show that the geometric deformation gradient in the compression direction can effectively induce more collapsed layers in the early stages of compression. In the early stage of compression, more collapsed layers can be effectively induced by decreasing the thickness of the structure. In the late stage of compression, the number of collapsed layers can be reduced, and the strength can be increased by increasing the bottom structure. Interestingly, Sh-D3 exhibits trapezoidal deformation during compression, which effectively enhances the compression distance and improves energy absorption.  
As shown in Figure 18. For the same volume fraction, the SEA, EA, and MCF of the sheet-TPMS structures are higher than those of the skeletal-TPMS structures, and Sh-D exhibits a better energy absorption effect, which is related to the material distribution of the structure. Due to the non-uniform material distribution, plastic hinges formed  
Figure 16: Deformation processes of functionally graded sheet-TPMS structures.  
Figure 17: DIC strain contours of functionally graded TPMS-based cellular structures.  
at the nodes of the skeletal TPMS structure during compression, leading to the rotation and collapse of the structural struts. SEA, EA, and MCF of the gradient TPMS structure were similar to those of the uniform TPMS structure in terms of energy absorption, and the results indicated that the change in the orientation of the gradient structure did not improve the overall energy absorption of the structure for the same volume fraction and the same compression distance. It is noteworthy that Sh-D3 shows the lowest PCF value and the highest CFE value, which indicates that the compression direction is the same as the gradient direction, which can effectively reduce the initial peak force in the compression process and simultaneously improve the crushing force efficiency at the same time.