# Investigating the Poisson Ratio of 3D Printed Concrete
## 4 Discussion  
It is evident from the results that this study's hypothesis was evidenced to be correct. By analysing the \(\mu\)-CT scanning data rigorously, it was demonstrated that the specimens tested for Poisson's ratio in this study do contain oblate voids, aligning with the printing direction, whereas the conventionally cast specimen contains mostly spherical voids, as deduced from Figures 9-12 and the summary in Table 6. The Poisson ratio for the conventionally cast concrete specimen was determined as 0.18, which is close to the lower bound of the typical Poisson ratio for cast concrete of 0.15, possibly ascribed to the total aggregate volume fraction of the mixture [6]. All the 3D printed specimens were found to have higher Poisson ratios than the cast specimen, confirming that adopting the Poisson ratio of conventionally cast concrete (even if the material is 3D printable and has been pumped and extruded) is inaccurate. Additionally, there is a directional dependency to the Poisson ratio of printed concrete; hence, it can be accepted as an anisotropic material property. In this study, specimens tested perpendicular to the printing direction (containing oblate voids, denoted OI) yielded a Poisson ratio of 0.21. Furthermore, specimens tested parallel to the printing direction (containing prolate voids, OIII) yielded a Poisson ratio of 0.24. This is the highest of all tested configurations, which is postulated to be due to the slender vertical concrete material located between the predominantly prolate voids experiencing increased lateral deformation under axial loading, similar to that of slender structural columns, but on a microscale. The opposite is also postulated to hold, i.e., the flat oblate voids in OI experience increased axial deformation under axial loading, due to the high tensile stress concentrations at the lateral sides of the flat voids, resulting in a lower Poisson ratio that that of OIII. This postulation can, at this stage, not be experimentally tested since \(\mu\)-CT scanning is performed in a closed environment where a load cannot be applied to the specimen. The authors are uncertain at this stage why the Poisson ratio of the cast specimen is lower than both the 3D printed specimens when it would be expected to have a Poisson value between that of OI and OIII based on the fact that the voids in these specimens are predominantly spherical, i.e., between oblate and prolate. Interestingly, the OI and OIII \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & **Cartesian** & **Regression Model** & **Normalised Gradient** & **Normalised Variance** & **Normalised 3D** \\
**Configuration** & **Direction** & **Gradient** & **Normalised Gradient** & **Void Graphic** \\ \hline \multirow{3}{*}{CAST-CM} & X & 0.7835 & 1.00 & \multirow{3}{*}{0.007} \\  & Y & 0.7876 & 1.01 & & \\  & Z & 0.6931 & 0.88 & & \\ \hline \multirow{3}{*}{CAST-3 DCP} & X & 0.7265 & 1.00 & \multirow{3}{*}{0.010} \\  & Y & 0.6637 & 0.91 & & \\  & Z & 0.6467 & 0.89 & & \\ \hline \multirow{3}{*}{3 DCPOIB} & X & 0.7839 & 1.00 & \multirow{3}{*}{0.084} \\  & Y & 0.7158 & 0.91 & & \\ \cline{1-1}  & Z & 0.4699 & 0.60 & & \\ \hline \multirow{3}{*}{3 DCPOIT} & X & 0.7740 & 1.00 & \multirow{3}{*}{0.044} \\  & Y & 0.7160 & 0.93 & & \\ \cline{1-1}  & Z & 0.5521 & 0.71 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Normalised 3D voids for each configuration based on their regression model gradients. Normalisation performed with respect to the x-direction (printing direction). Poisson ratios do still fall within the typical Poisson ratio range for conventionally cast concrete of 0.15-0.25. The OI and OIII Poisson values were found to be 17% and 33% higher than their cast equivalents in this study. Although only five specimens were tested per configuration, the ANOVA results indicate that there is a statistically significant difference between the means of the three configurations, as per Table 4, with a \(p\)-value an order of magnitude smaller than the significance value of 0.05.