## 3 Results and Discussion
### Mechanical Characterization of TPMS Structures
#### 3.1.2 Mechanical Response  
During the quasi-static compression experiment, the load and displacement data are collected by sensors, and the mechanical properties of different TPMS compression samples are evaluated by measuring the load and deformation of the samples. Reaction force and displacement data of nodes on rigid platen with different TPMS porous structures are extracted in finite element simulation (Figure 10a). The load-displacement curves obtained from three sets of quasi-static compression tests and finite element simulations for each type of TPMS sample are summarized (Figure 10b).  
After calculation, the error values between the data obtained from three sets of quasi-static compression tests on each TPMS sample and the data obtained from finite element simulation were within 5%. The load-displacement curve was obtained based on the post-processing results, and one data point is displayed for every 100 data points.  
Three-stage compression of porous TPMS structure samples: (1) first undergo the linear elastic stage; (2) then enter the platform section with load fluctuations; (3) finally, the compaction section with the load changes abruptly, and the curve changes significantly. The slope of the linear elastic segment represents the initial structural stiffness of the porous  
Figure 10: The post-processing results of quasi-static compression experiments. (**a**) The load-displacement curves based on finite element simulation results. (**b**) The multi-component waterfall diagram obtained from three sets of compression tests and finite element simulation results.  
TPMS structure. The long, stable platform segment symbolizes the excellent compression resistance of the porous TPMS structure. As the compression process proceeds, the internal stress of the porous TPMS structure reaches the ultimate strength, and the structural skeleton produces internal fracture or collapse as the load increases sharply. Finally, the structure is gradually flattened and compacted. After the test, we observed the failure parts of each sample and found that F-RD and PMY samples reach the compaction stage after experiencing smaller compression displacement, and the structures become thicker after densification. The solidity of F-RD and PMY led to greater structural stiffness during deformation, resulting in a higher average load value in its load-displacement curve.  
Observing the load-displacement curves of various TPMS porous structures during loading and compression, we found that the average load and peak load of the Gyroid structure were relatively small, and the deformation was uniform. Primitive, followed by Gyroid, yielded longer and gentler plateaus compared to other structures. The load-displacement curve obtained from the quasi-static compression simulation shows results similar to those of the uniaxial compression test, confirming the accuracy of our simulation. It proves that the established porous TPMS structure's finite element simulation model has good predictability, which lays the groundwork for crash simulation of vehicle crash box models filled with porous TPMS structure.