## 3 Results and Discussion
### Case Studies
#### 3.2.3 Influence of Constituent Materials on the Shear Correction Factor
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Material**} & \(\eta 1\) & \(-75\) & \(-60\) & \(-45\) & \(-30\) & \(-15\) & \(0\) & \(15\) & \(30\) & \(45\) & \(60\) & \(75\) \\ \hline Al-WC & 1 & 0.5978 & 0.6123 & 0.6219 & 0.6196 & 0.6010 & 0.7692 & 0.6010 & 0.6196 & 0.6219 & 0.6123 & 0.5978 \\  & 1.25 & 0.5987 & 0.6102 & 0.6202 & 0.6186 & 0.6008 & 0.7692 & 0.6008 & 0.6186 & 0.6202 & 0.6102 & 0.5987 \\  & 1.5 & 0.6001 & 0.6082 & 0.6186 & 0.6176 & 0.6006 & 0.7692 & 0.6006 & 0.6176 & 0.6186 & 0.6082 & 0.6001 \\  & 1.75 & 0.6018 & 0.6066 & 0.6171 & 0.6166 & 0.6004 & 0.7692 & 0.6004 & 0.6166 & 0.6171 & 0.6066 & 0.6018 \\  & 2 & 0.6037 & 0.6051 & 0.6157 & 0.6157 & 0.6002 & 0.7692 & 0.6002 & 0.6157 & 0.6157 & 0.6051 & 0.6037 \\ \hline Al-SiC & 1 & 0.6736 & 0.6621 & 0.6605 & 0.6608 & 0.6659 & 0.7698 & 0.6659 & 0.6608 & 0.6605 & 0.6621 & 0.6736 \\  & 1.25 & 0.6759 & 0.6625 & 0.6607 & 0.6609 & 0.6661 & 0.7698 & 0.6661 & 0.6609 & 0.6607 & 0.6625 & 0.6759 \\  & 1.5 & 0.6783 & 0.6630 & 0.6609 & 0.6611 & 0.6662 & 0.7698 & 0.6662 & 0.6611 & 0.6609 & 0.6630 & 0.6783 \\  & 1.75 & 0.6807 & 0.6635 & 0.6612 & 0.6613 & 0.6663 & 0.7698 & 0.6663 & 0.6613 & 0.6612 & 0.6635 & 0.6807 \\  & 2 & 0.6833 & 0.6640 & 0.6614 & 0.6614 & 0.6665 & 0.7698 & 0.6665 & 0.6614 & 0.6614 & 0.6640 & 0.6833 \\ \hline Al-Al\({}_{2}\)O\({}_{3}\) & 1 & 0.7690 & 0.6623 & 0.6540 & 0.6556 & 0.6871 & 0.7860 & 0.6871 & 0.6556 & 0.6540 & 0.6623 & 0.7690 \\  & 1.25 & 0.8080 & 0.6650 & 0.6552 & 0.6564 & 0.6882 & 0.7860 & 0.6882 & 0.6564 & 0.6552 & 0.6650 & 0.8080 \\  & 1.5 & 0.8618 & 0.6679 & 0.6564 & 0.6572 & 0.6892 & 0.7860 & 0.6892 & 0.6572 & 0.6564 & 0.6679 & 0.8618 \\  & 1.75 & 0.9404 & 0.6709 & 0.6576 & 0.6580 & 0.6903 & 0.7860 & 0.6903 & 0.6580 & 0.6576 & 0.6709 & 0.9404 \\  & 2 & 1.0642 & 0.6740 & 0.6589 & 0.6589 & 0.6914 & 0.7860 & 0.6914 & 0.6589 & 0.6589 & 0.6740 & 1.0642 \\ \hline Al-ZrO\({}_{2}\) & 1 & 0.5609 & 0.5603 & 0.5671 & 0.5654 & 0.5549 & 0.8146 & 0.5549 & 0.5654 & 0.5671 & 0.5603 & 0.5609 \\  & 1.25 & 0.5640 & 0.5590 & 0.5658 & 0.5646 & 0.5549 & 0.8146 & 0.5549 & 0.5646 & 0.5658 & 0.5590 & 0.5640 \\  & 1.5 & 0.5675 & 0.5578 & 0.5646 & 0.5639 & 0.5549 & 0.8146 & 0.5549 & 0.5639 & 0.5646 & 0.5578 & 0.5675 \\  & 1.75 & 0.5712 & 0.5569 & 0.5635 & 0.5632 & 0.5549 & 0.8146 & 0.5549 & 0.5632 & 0.5635 & 0.5569 & 0.5712 \\  & 2 & 0.5751 & 0.5562 & 0.5626 & 0.5626 & 0.5549 & 0.8146 & 0.5549 & 0.5626 & 0.5626 & 0.5562 & 0.5751 \\ \hline \end{tabular}
\end{table} 
Table 6: Shear correction factor for different FGM auxetic beams with \(\eta 3=0.01\) as a function of \(\theta\) and \(\eta 1\). Figure 13: Shear correction factor for different FGM auxetic beams with a/h = 10 and unit cells with \(\eta 1=1\) and \(\eta 3=0.01\). From the results in Table 7, we conclude that, for the present case, the non-dimensional maximum static deflection decreases when \(\eta 1\) increases (in absolute value). This is true for any angle \(\theta\) and for any aspect ratio \(\eta 3\). We can also conclude that, for a specific pair of aspect ratios \(\eta 1\) and \(\eta 3\), this deflection gradually increases up to a maximum value correspondent to \(\theta=0^{\circ}\) and starts decreasing after that, with minor values obtained for the angles \(\theta=-75^{\circ}\) and \(\theta=75^{\circ}\). For these latter cases, the cells present a \"flattened\" configuration. From the table, it is also visible that, as expected, the non-dimensional maximum static deflection decreases as the ratio \(\eta 3\) increases. Figures 14 and 15 illustrate the non-dimensional maximum static deflection for the discrete values in the sets of geometrical parameters \(\theta\) and \(\eta 1\) and for the two limit values of \(\eta 3\). These values correspond to the thinner (\(\eta 3=0.01\)) and thicker