4.3.2. Quasi-Static and Impact Experiments

Quasi-static and drop-hammer impact experiments, corresponding to the loading condition the of numerical simulation, were also conducted to validate numerical results to further evaluate the effectiveness of the simplified Johnson–Cook model in typical engineering structures. Quasi-static crushing tests were conducted on INSTRON 8801 (manufactured in Boston, MA, USA), where specimens were placed centrally between the polished moving platen and the stationary platen. To eliminate the influence of glass fiber panels, the platens were bigger than the specimens. All specimens were crushed under the following conditions: stroke distance, 5 mm; loading rate, 2 mm/min; and temperature, 25 ◦C. The crush-load curve with respect to the moving platen displacement was recorded automatically into a computer. A drop-hammer testing system was used for impact crushing tests to evaluate the effect of strain rate. The drop hammer, with a mass of 6 kg, was lifted by the pulley to different heights and then released through the trip gear to achieve different levels of impact energy, such as 30 and 45 J. The strain rates during impact crushing fell within the range of the SHPB experiments. The specimens were located at the center of the base of the drop-hammer testing system, directly opposite to the center of the mass of the hammer. The size of the hammer was larger than that of the specimen. A force sensor was mounted on the base to measure the impact force. The force response signals could then be recorded using a digital oscilloscope at a sampling frequency of 100,000 Hz and stored on a computer. Thus, the time history of crush load could be obtained from the recorded data. In addition, during the impact tests, a high-speed camera was used to capture the crushing deformation of the specimen with a rate of 2000 frame/s.

### 4.3.3. Numerical Simulation and Experiment Correlation

Numerical simulation of lattice structures under quasi-static and drop-hammer impact conditions, as well as the corresponding experiments, was conducted. The results are depicted in Figures 10 and 11. At a glance, an acceptable agreemen<sup>t</sup> could be observed for both quasi-static and dynamic results, indicating the validity of the simplified Johnson–Cook model. Table 3 summarizes the peak load comparison between the numerical simulation and the experiments.

**Figure 10.** Comparison between the experiment and the numerical simulation: (**a**) Crush load versus displacement curve; (**b**) deformation process.

Under quasi-static conditions, the specimen exhibited typical progressive crushing (Figure 10). When the moving platen came into contact with the specimen, the crushing load was generated and increased linearly until the peak load was reached, corresponding to the critical Euler buckling load of the truss. As compression continued, the crush load was followed by a decrease stage and kink-band formation, resulting in the development of shear stresses, as featured in Figure 10b. In Figure 10a, the crush load curves of both numerical and experimental results exhibited a highly similar trend, except that the former was slightly higher than the latter. The deformation process was also similar with each other; specifically, numerical simulation was able to well predict the kink band formation of the specimen.

**Figure 11.** Comparison of the time history of crush load and deformation obtained by FEM calculation with its counterpart from experimental measurement under different impact energy: 30 J (**<sup>a</sup>**,**b**) and 45 J (**<sup>c</sup>**,**d**).

**Table 3.** Comparison of peak load between numerical simulation and experiments.


In the drop-hammer impact experiments, dynamic crushing was highly similar to the quasi-static crushing with the same failure mechanism of Euler buckling. Figure 11 presents the time history of crush load of both the numerical and experimental results under impact energy of 30 and 45 J, and corresponding deformation results were also presented. The numerical results were close to the experimental results, with a slight difference. In addition, the peak load was significantly higher than the quasi-static crushing experiment, which illustrates the effect of strain rate. As for the lattice structure subjected to crush loading with impact energy of 30 J, the curves of both the numerical simulation and the experiment were clearly characterized by one peak corresponding to Euler buckling initiation (Figure 11a). The deformation of the numerical simulation was also consistent with that of experiments (Figure 11b). With regard to the lattice structure subjected to crush loading with an impact energy of 45 J, both curves of the numerical simulation and the experiment were clearly characterized by two peaks (Figure 11c). The first peak load also corresponded to Euler buckling initiation. The second peak load was attributed to the impact between the top and bottom panels, when higher impact energy beyond the truss bearing capacity resulted in lattice compaction (Figure 11d). The crush load from the numerical simulation could efficiently predict the experimental results, despite the slight difference with time delay of the second peak between the numerical simulation and the experiment. These differences could be attributed to the following: First, the lattice structure was manually manufactured and assembled, which inevitably introduced geometry errors, including machining errors, assembly errors, size errors, defects, and so on. Euler buckling was known to be extremely sensitive to these geometry errors, which failed to easily perform quantitative evaluation and thus was not considered in the FEM models, leading to an error in crushing response prediction. Second, the damage initiation and evolution model was not considered in the FEM model. The development of an accurate, efficient, and robust damage model remained a challenge. Accordingly, the developed simplified Johnson–Cook model without damage initiation and evolution could not obtain a highly precise failure prediction under complex contact interfaces and stress state.

However, considering the complexity of the actual structure, the accuracy of numerical simulation could be acceptable. Thus, adequate confidence in the present numerical studies with the developed simplified Johnson–Cook model could be extended to engineering structure analysis.
