# Static Compressive Properties of Polypropylene Fiber Foam Concrete with Concave Hexagonal Unit Cell
## 3 Results and Discussion
### Energy Absorption Capacity  
The influence of different fiber contents on the peak stress and strain of the concave hexagonal unit cell of foam concrete was obtained through the previous analysis. Figure 9 shows the stress-strain relationship curve in the static compression experiment of the concave hexagonal unit cell samples. The energy absorption efficiency is used to evaluate the energy absorption capacity of the test specimen. The commonly used parameters are energy absorption efficiency, energy absorption capacity of foam concrete per unit volume \(w\), total energy absorption \(E_{a}\), specific energy absorption \(E_{sa}\), etc. \[E_{f}(\varepsilon_{a})=\frac{1}{\sigma_{a}}\int_{0}^{\varepsilon_{D}}\sigma( \varepsilon)d\varepsilon,0\leq\varepsilon\leq 1, \tag{2}\]  
where \(\varepsilon_{a}\) is the strain value of the specimen at a certain moment, \(\sigma_{a}\) is the stress value corresponding to it, and \(\varepsilon_{D}\) is the compaction strain, i.e., the strain corresponding to the maximum value of energy absorption efficiency. In practical application, it is necessary to combine the actual foam concrete stress-strain curve to determine the compaction strain of the specimen. The energy absorption capacity \(w\) per unit volume of foam concrete is defined as:  
\[w=\int_{0}^{\varepsilon_{D}}\sigma(\varepsilon)d\varepsilon, \tag{3}\]  
The total energy \(E_{a}\) absorbed by the foam concrete specimen was obtained by calculating the area enclosed by the load-displacement curve of the specimen, the significance of which is that the greater the total energy absorbed, the better the impact resistance of the material:  
\[E_{a}=\int_{0}^{l}Pdl, \tag{4}\]  
where \(l\) is the displacement value corresponding to \(\varepsilon_{D}\), and \(p\) is the magnitude of the load corresponding to the displacement of \(l\). The ratio of the total energy absorbed by the test block to its mass, i.e., the specific absorbed energy \(E_{sa}\), is calculated by:  
\[E_{sa}=\frac{E_{a}}{m}, \tag{5}\]  
Figure 9: Stress-strain relationship curve of concave hexagonal unit cell specimen. Since, in this experiment, the specimen was judged to be damaged when it was sharply deformed, the energy absorbed by the specimen compressed to the peak strain was used here as a judgment index to judge the energy absorption capacity of the specimen. According to Equation (4), the total energy of the hexagonal specimen during compression deformation was obtained, and the specific energy absorption was calculated by using Equation (4) in combination with the mass of the sample, weighed before the experiment. The masses and energy absorption indexes of different hexagonal unit cells are shown in Table 5.  
The total energy absorption and specific energy absorption of the concave hexagonal unit cell with 0.5% fiber content are larger than those with other fiber content. In static compression tests, the total energy absorbed by concave hexagonal cells with 0.5% fiber content increased by 12.98% compared to concave hexagonal cells without fibers, indicating that a small amount of polypropylene fibers (about 0.5%) contributed to the higher amount of energy absorbed by concave hexagonal cells. Figure 10 was obtained by collating the average values of total and specific absorbed energy for each group of specimens, demonstrating that when the polypropylene fiber content exceeds 0.5%, the total and specific absorbed energy of the concave hexagonal unit cells decreases with the increase in fiber content. The concave hexagonal unit cell mainly transforms energy into the rupture energy of the foam pore wall and the bending deformation energy of the cell wall in the process of structural deformation. During the static ballast process, the concave portion of the cell wall of the hexagonal specimen has the main role in energy absorption. As the load strength increases, the specimen deforms, and the concave portion of the cell wall shrinks inward, deforms, and bends, which makes the foam concrete subject to force.