## 3 Results and Discussion
### Assessment of Stress Shielding and Micromotions
Detection of a stem's failure (FS) is calculated as the ratio between the maximum stress found within the stem's layer (YLmax) and the yield strength associated with the porosity value assigned to the referenced stem's layer (YsL):  
\[\text{FS}=\text{YLmax}/\text{YsL} \tag{3}\]  
An FS value > 1 for any of a stem's layers implies that the stem will fail/yield. Micromotion at the stem-femur interface was studied for the proposed designs, this information being vital to evaluate bone tissue ingrowth, a micromotion value of more than 150 \(\upmu\)m being considered excessive and liable to result in the instability of the implant [6, 9]. The average micromotion of the proposed designs is illustrated in Figure 13. Stem designs with an average porosity of 70% showed the maximum micromotion values to be greater than 150 \(\upmu\)m at 3 km/h and 5 km/h walking speeds besides the design with 50% porosity at 5 km/h, which is attributed to the low stiffness values of the higher porosity stems and the loading conditions associated with the walking speed. These findings agree with the previous studies [8, 25]. These designs are highly susceptible to aseptic loosening, which may lead to premature failure of the stem. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \hline
**Design** & **Location** & **G 1** & **G 2** & **G 3** & **G 4** & **G 5** & **G 6** & **G 7** \\ \hline
30\% Porosity & \
\begin{tabular}{c} Tracbecular bone \\ 50\% Porosity \\ 70\% Porosity \\ \end{tabular} &
\begin{tabular}{c} 27.1\% \\ 70\% Trabecular bone \\ \end{tabular} & 9.4\% & 2.5\% & 1.2\% & 4.9\% & 10.4\% & 35.9\% \\
35.8\% &
\begin{tabular}{c} 12.2\% \\ 46.1\% \\ \end{tabular} & 4.5\% & 1.8\% & 6.6\% & 16.1\% & 48.1\% \\
30\% &
\begin{tabular}{c} 48.1\% \\ \end{tabular} & 20.3\% & 6.6\% & 2.8\% & 8.6\% & 22.3\% & 62.6\% \\ \hline \hline \end{tabular}  
\begin{tabular}{c c c c c c c c} \hline \hline
**Design** & **Location** & **G 1** & **G 2** & **G 3** & **G 4** & **G 5** & **G 6** & **G 7** \\ \hline
30\% Porosity & \begin{tabular}{c} Tracbecular bone \\ 50\% Porosity \\ \end{tabular} & \begin{tabular}{c} 21.8\% \\ 70\% Porosity \\ \end{tabular} & \begin{tabular}{c} 9.5\% \\ 70\% Trabecular bone \\ \end{tabular} & \begin{tabular}{c} 2.2\% \\ 31.8\% \\ 41.4\% \\ \end{tabular} & \begin{tabular}{c} 1.5\% \\ 12.3\% \\ 19.8\% \\ \end{tabular} & \begin{tabular}{c} 5.2\% \\ 4.3\% \\ 6.6\% \\ \end{tabular} & \begin{tabular}{c} 10.2\% \\ 3.3\% \\ 3.5\% \\ \end{tabular} & \
\begin{tabular}{c} 36.1\% \\ 9.1\% \\ \end{tabular} &
\begin{tabular}{c} 36.1\% \\ 22.1\% \\ \end{tabular} \\ \hline \hline \end{tabular}  
\begin{tabular}{c c c c c c c c} \hline \hline
**Design** & **Location** & **G 1** & **G 2** & **G 3** & **G 4** & **G 5** & **G 6** & **G 7** \\ \hline
30\% Porosity & \begin{tabular}{c} Tracbecular bone \\ 50\% Porosity \\ \end{tabular} & \begin{tabular}{c} 20.3\% \\ 70\% Porosity \\ \end{tabular} & \begin{tabular}{c} 10.5\% \\ 70\% Trabecular bone \\ \end{tabular} & \begin{tabular}{c} 2.2\% \\ 30.5\% \\ 40.0\% \\ \end{tabular} & \begin{tabular}{c} 2.2\% \\ 12.9\% \\ 19.2\% \\ \end{tabular} & \begin{tabular}{c} 5.8\% \\ 4.1\% \\ 6.8\% \\ \end{tabular} & \begin{tabular}{c} 9.9\% \\ 4.1\% \\ \end{tabular} & \begin{tabular}{c} 36.6\% \\ 3.3\% \\ \end{tabular} & \begin{tabular}{c} 36.6\% \\ 7.8\% \\ 7.8\% \\ \end{tabular} & \
\begin{tabular}{c} 15.9\% \\ 15.9\% \\ \end{tabular} &
\begin{tabular}{c} 49.2\% \\ 49.2\% \\ 64.9\% \\ \end{tabular} \\ \hline \hline \end{tabular}  
\end{table} 
Table 4: Stress transfer percentages of the functionally graded porous stems in comparison to the bulk Ti (reduction in stress shielding). Figure 12: [PERSON] stresses at the FG stems’ layers and the bulk Ti stem: at (**a**) 1 km/h, (**b**) 3 km/h, and (**c**) 5 km/h walking speeds. Figure 13: _Cont._