## 3 Results  
### Density and Dimensional Accuracy  
The results of the density measurement of the auxetic structures and the CAD-derived values are given in Figure 7. Errors in fabricated parts and \(\Delta\) are \(\pm\) 1%. From Figure 7, it can be seen that the relative density of most of the fabricated samples is greater than that calculated from the CAD models. The increase in relative density is likely due to the increase in thickness of the struts of the fabricated samples. The strut size deviations from CAD for the three struts in Samples 3 and 4 are given in Figure 8. It can be seen that for both samples, strut re-entrant 2, built at an angle of 80\({}^{\circ}\) to the build-platform, is the most accurate strut and closer to the designed thickness of 1000 \(\upmu\)m. Furthermore, as expected, re-entrant 1, which was built almost horizontally at an angle of just 10\({}^{\circ}\) to the build-platform without any support structures, has the worst dimensional accuracy, with increased thickness over the designed value, and therefore, the thickness of the strut increases as the build angle of the struts decreases. All struts, other than the re-entrant 2 struts, are thicker than the design intent, and thus account for the disparity between the CAD and actual values for apparent density in Figure 7. The fabricated samples also show a wide range of variation in relative density (0.565 \(\pm\) 0.005% to 26.5 \(\pm\) 0.4%). Those built with a re-entrant angle of 70\({}^{\circ}\) show significantly higher deviation (average of 3 \(\pm\) 2%) than those at 45\({}^{\circ}\) (average of 23 \(\pm\) 2%). The use of a higher re-entrant angle would align re-entrant strut 1 to a greater angle to the build-plate (55\({}^{\circ}\)) without compromising greatly the orientation of re-entrant strut 2 (105\({}^{\circ}\)), which in in agreement with the strut thickness trend observed for samples 3 and 4. Figure 7: Theoretical CAD relative density and measured relative density of the auxetic structures. Strut lengths were obtained from the DIC image data. An example of a DIC image used is given in Figure 9. The deviations from the nominal CAD sizes (Table 1) are given in Figure 10.  
Figure 8: Strut size deviation from CAD for samples 3 and 4. Figure 10: Unit cell dimension deviations from nominal. Figure 9: Digital image correlation (DIC) image used to measure unit cell dimensions. There was a small increase in the length of the vertical struts (\(\Delta\)H) by an average of \(2.1\pm 0.4\%\). For the re-entrant struts, there was an average deviation of \(12\pm 1\%\), which may be a result of their shallower build angle with respect to the build-plate (XY-plane) (see Figure 3 for orientation reference). An average of \(5\pm 1\%\) deviation in re-entrant angle was observed across all structures, but was considerably less for the \(70^{\circ}\) structures than for those with a \(45^{\circ}\) angle. Again, this is likely due to the increasing inaccuracy in geometry for features orientated at lower angle to the XY plane. The results of the porosity analysis are given in Figure 11.  
The relative density for all the struts is greater than \(99\%\). The re-entrant 2 struts, which are inclined at \(80^{\circ}\) to the build-plate, proved to be the best orientation, with a relative density as high as \(99.9\%\). This is similar to the findings of other work which showed that vertically oriented struts/samples provide maximum density [39]. [PERSON] also observed that struts oriented horizontally were the most affected in terms of porosity, followed by diagonal struts [39], however, in this work, the vertical strut (inclined at \(35^{\circ}\)) to the build direction (almost diagonally oriented) expressed slightly higher porosity when compared with re-entrant 1, which was inclined at \(10^{\circ}\) (almost horizontally oriented during build).