# Mechanical and Fatigue Behavior of Cellular Structure
## 3 Result and Discussion
### Stresses in Porous Stem Layers
#### 3.2.2 Stresses in Porous Stem's Section  
The stresses within each porous layer were computed through the FEA results for the fifteen FG designs and for each of the three walking speeds (as illustrated in Figure 7). The stresses within the stem's layers are increasing radially up to reach the maximum stress at the outer stem's layer (L3). The stresses associated with layer 3 (L3) were considered for the fatigue calculations as this layer is associated with the maximum stress and on direct contact with the bone. Stresses at the outer layer (L3) of the porous stems were found to be less than the stresses generated on the bulk stem for all designs and walking speeds, which indicates that the applied loads/stresses are distributed between the femur and the stem (more stress transfer to the femur). This is attributed to the reduction of the stiffness associated with each porous stem designs in comparison with the bulk stem stiffness (114 GPa). Hence, the stress level is on the stem is affected by two factors: the applied loads associated with the walking speeds and the stiffness of the designed stems. Although the stress distribution along the FG stem's layers was varied, this is attributed to the difference in the Young's modulus of each porous layer. The yield strength was studied for each stem's porous layer and compared with the stress values computed via FEA of the stem-bone models and found that all designs are not yielding at walking speed of 1 km/h except designs 9, 12 which holds stress value at the stem's outer layer equal to the yield strength value related to 70% and 80% porosities, respectively, and design 14 which gave no results. At 3 km/h walking speed only designs 1, 3 and 8 were observed to be not yielding and safe. All designs found to be yielded at walking speed of 5 km/h as the stresses encountered are higher than the yield strength associated with the relevant porous structure of each design. stem's failure (_SF_) is calculated based on the stress ratio  
Figure 6: Stem-bone model validation of bulk stem against [PERSON] el. al. FE results [11; 19].  
between the relevant stem layer yield strength (\(Y_{sl}\)) and the maximum stress value of that layer (\(\sigma_{Lm}\)) based on Equation (8):  
\[SF=\frac{Y_{sl}}{\sigma_{Lm}} \tag{8}\]  
The design will not fail/yield if \(SF\) value > 1.0, the results are illustrated in Figure 8.  
Previous experimental study [PERSON] et al. [26] shows the superiority of the cubic porous structures over the other structures such as diamond shape structures. None of their cubic structure tested samples were failed under cyclic loading at maximum load of 80% of the relevant porous structure yield strength (0.8\(\sigma_{\rm{Ys}}\)) [26]. This finding is comparable with our computational analysis findings up to certain loading conditions as illustrated in Figure 8.  
Figure 7: Stresses within each porous layer were computed through the FEA results for the fifteen FG designs and for each of the three walking speeds: 1 km/hr, 3 km/hr, and 5 km/hr walking speed.  
Figure 8: _Cont_.