# Stress Analysis on the Ankle Joint during Incline and Decline Standing
## 3 Results  
### Von Mises Stress Distribution at the Ankle Joint during Slope Standing  
The FE model developed enables von Mises stress distribution to be predicted during level and slope standing. For validation of the model, the acquired von Mises stress distribution was compared with results given in the literature that were obtained during level standing on the talus, tibia, and fibula, as shown in Table 2. The Young Modulus and Poisson Ratio for bone, cartilage, and ligaments used in the current study is similar to the compared study in the literatures [11; 15]. As seen in the table, the value of von Mises stress distributions is comparable with a slight difference. The slight difference might be due to different boundary conditions applied in developing the FE model. The FE model of the ankle on five inclination conditions was analysed and the von Mises stress distributions and maximum von Mises stress were obtained. The result of the ankle joint model was specified into the effect on bones, i.e., talus, tibia and fibula, cartilage, and ligament. The von Mises stress was analysed according to colour contour as represented in Tables 3 and 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **Maximum von Mises** \\ **Stress from the** \\ **Present Study** \\ \end{tabular} & \begin{tabular}{c} **Maximum von Mises Stress Distributions** \\ **from Literature** \\ \end{tabular} \\ \cline{2-4}  & \
\begin{tabular}{c} **[PERSON] et al. [11]** \\ \end{tabular} &
\begin{tabular}{c} **[PERSON] et al. [15]** \\ \end{tabular} \\ \hline Talus (MPa) & 1.86 & 2.07 & 2.38 \\ \hline Tibia (MPa) & 4.84 & 5.50 & 5.86 \\ \hline Fibula (MPa) & 1.18 & 1.28 & 1.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of maximum von Mises stress on ankle joint during level standing between present study and the literatures [11; 15]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Inclination** & & **Von Mises Stress** \\ \hline \multicolumn{3}{c}{**Talus**} & **Tibia** & **Fibula** \\ \hline \multicolumn{3}{c}{**Superior View**} & **Inferior View** & **Tibia** & **Fibula** \\ \hline \(-10^{\circ}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Von Misses stress distribution on bones (talus, tibia, and fibula). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Surface Inclination Angle**} & \multicolumn{2}{c}{**Von Mises Stress**} \\ \cline{2-3} \multicolumn{1}{c}{} & **Cartilage** & **Ligament** \\ \hline \(-10^{\circ}\) & & \\ \hline \(-5^{\circ}\) & & \\ \hline \(0^{\circ}\) & & \\ \hline \(5^{\circ}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Von Misses stress distribution on cartilage and ligament. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Inclination**} & \multicolumn{2}{c}{**Von Mises Stress**} \\ \hline \hline \multicolumn{1}{c}{**Talus**} & \multicolumn{1}{c}{**Tibia**} & **Fibula** \\ \hline \hline \multicolumn{1}{c}{**Superior View**} & **Inferior View** & **Tibia** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._As can be seen in Table 3, an overall blue colour contour, which represents 0-2 MPa stress, has covered all of the talus during flat standing. Instead of that, a light blue contour, which represents 2-4 MPa, was spread around the talus, and a small lighter blue contour, representing 4-6 MPa, can be observed at the edge and bottom of the talus during 5\({}^{\circ}\) and 10\({}^{\circ}\) decline standing. As for 5\({}^{\circ}\) incline standing, similar to decline standing, the talus was covered with a light blue contour (2-4 MPa) but with a larger contour at the top of the talus, and there was a small lighter blue contour, which represents 4-6 MPa, that was located at the edge and bottom of the talus. During 10\({}^{\circ}\) incline standing, a light blue contour (2-4 MPa) was more significant than another standing covered on the top surface of the talus. The stress increased until the greenish-blue contour, which represents 6-8 MPa, appeared at the edge and bottom of the talus bone.