# Static Compressive Properties of Polypropylene Fiber Foam Concrete with Concave Hexagonal Unit Cell
## 3 Results and Discussion
### Deformability Analysis
The measured longitudinal and transverse deformation is shown in Figure 5.  
Taking the sample A-0-1 as an example, the transverse deformation data were obtained from the images of the compression process by the optical experiment software COM Correlate, the curves were compiled as shown in Figure 6a, and the transverse deformation of the specimen at the time of damage was used as the equivalent transverse deformation \(\Delta\)X. Figure 6b shows the curve compiled from the longitudinal deformation data recorded by the RMT system in the static compression process. The longitudinal deformation of the specimen at the time of damage was used as the equivalent transverse deformation \(\Delta\)Y.  
Figure 5: Schematic diagram of deformation measurement of the concave hexagonal unit cell. Due to longitudinal strain, \(\varepsilon_{y}\) can be directly obtained from the recorded data of the RMT system during the static compression of the specimen, so the Poisson's ratio v of the concave hexagonal unit cell is calculated as follows:  
\[\
u=-\frac{\Delta X}{X_{0}}\cdot\frac{Y_{0}}{\Delta Y}=-\frac{\Delta X}{X_{0}} \cdot\frac{1}{\varepsilon_{y}}, \tag{1}\]  
where \(\varepsilon_{y}\) is the longitudinal strain of the concave hexagonal unit cell. Table 4 shows the Poisson's ratios of the samples of the concave hexagonal unit cell with different fiber contents, calculated from the strain data of the experimentally obtained specimens. The trend of the effect of fiber content variation on Poisson's ratio of concave hexagonal unit cells obtained by finishing is shown in Figure 7. The negative Poisson's ratio of the concave hexagonal unit cells with 0-1.5% fiber volume content increased with the increase in fiber content; the increase in fiber content over 1.5%, on the contrary, decreased the negative Poisson's ratio of concave hexagonal unit cells. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **A-0** & **A-0.5** & **A-1.0** & **A-1.5** & **A-2.0** & **A-2.5** \\ \hline
1 & \(-0.072\) & \(-0.101\) & \(-0.131\) & \(-0.149\) & \(-0.132\) & \(-0.105\) \\
2 & \(-0.068\) & \(-0.095\) & \(-0.138\) & \(-0.142\) & \(-0.129\) & \(-0.109\) \\
3 & \(-0.076\) & \(-0.099\) & \(-0.136\) & \(-0.140\) & \(-0.130\) & \(-0.106\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: [PERSON]’s ratios of different concave hexagonal cells. Figure 6: Transverse deformation curve of the concave hexagonal unit cell (A-0-1): (a) transverse deformation \(\Delta\)X; (b) longitudinal deformation \(\Delta\)Y.  
Figure 7: Effect of fiber content on Poisson’s ratio of concave hexagonal unit cells. It can be seen from Figure 7 that the addition of polypropylene fiber can reduce the Poisson's ratio of concave hexagonal cells. When the fiber content is 0-1.0%, the foam concrete has a better constraint effect, which makes the strain value of foam concrete in static compression increase, thus reducing the Poisson's ratio of concave hexagonal cells. When the volume of polypropylene fiber is increased to 1.0-1.5%, the compressive strength of foam concrete increases, and the fiber also has a good restraining effect on the material. With the increase in fiber content, the deformation at the concave point of both sides of the sample increases, thus effectively reducing the Poisson's ratio of the concave hexagonal unit cell. When the volume content of polypropylene fibers exceeds 1.5%, the strength of foam concrete weakens substantially, and its deformation ability also becomes weaker, so the Poisson's ratio of the concave hexagonal unit cell increases. In summary, the appropriate amount of polypropylene fibers can effectively increase the deformation capacity of the concave hexagonal unit cells of foam concrete, and the Poisson's ratio of the concave hexagonal unit cells of foam concrete with 1.5% polypropylene fibers is the smallest.