## 3 Results and Discussion
### Assessment of Stress Shielding and Micromotions  
The stress shielding assessment was performed to evaluate the performance of the stems based on stress distribution along the Gruen zones resulting from the load transfer from the implanted stem to the femur bone. The maximum von Mises stresses for the cortical bone (1-7 Gruen zones) and trabecular bone (1, 2, 6, and 7 Gruen zones), which have direct contact with the stem, were indicated. In general, to reduce stress shielding, an implant should transfer some of the stresses to the bone. The stresses obtained for the 15 functionally graded (FG) designed stems and bulk Ti stem implanted in the femur for the three different walking speeds (1, 3, and 5 km/h) are shown in Figure 11. From these plots, it can be seen that porous Ti stems perform better than bulk Ti stem in terms of reducing stress shielding (high stress values in the bone). There was almost no obvious difference between the FG designs for each average porosity used (30, 50, and 70%), regardless of the walking speed for both areas of the cortical and trabecular bone. The stress transfer to the bone and percent of the reduction in stress shielding is obvious, as shown in Figure 11 and indicated in Table 4. Stress shielding was calculated based on the percent of stress transfer to the bone of the designed FG stems compared with the bulk stem. The transfer of the stresses at the trabecular bone from the designed FG and homogeneous porous stems was more than double that in the bulk stem, indicating a sufficient reduction in stress shielding. It can be concluded from Figure 11 and Table 4 that the stress transfer from the stem to the bone at Gruen zone 7 increases as the porosity increases, which is associated with lower stiffness at a higher volumetric porosity percentage. These findings agree with previous studies [8, 24, 34]. It is also evident that the highest stress transfer to the bone at the proximal area is depicted at Gruen zone 7 for all porous stem designs, which is highly required to avoid failure of the hip stem due to stress shielding [21, 43], as this zone is susceptible  
Figure 10: Stem–bone assembly validation. to bone resorption [44]. The distal parts of the stems have higher stress values than the proximal parts, with the maximum value of the stress transfer to the bone for all porous stem designs being found in Gruen zone 4, which is in agreement with the results reported in the literature [21; 22; 25; 43; 45]. The inadequate stress transfer to the bone for all porous stem designs at zones 3, 4, and 5 is attributed to the proximal load transfer to the bone, and there is no direct contact with the stem at these areas, this being attributed to torsional stress induced by the applied load [21]. Figure 11: Stresses at Gruen zones of the functionally graded porous stems and the bulk Ti stem for proposed designs for different walking speeds: (**a**) 1 km/h, (**b**) 3 km/h, (**c**) 5 km/h. The stresses in the FG stems' assigned radial layers L1, L2, and L3 (Figure 5) for all proposed 15 FG designs, and the bulk Ti stem are shown in Figure 12. It can be observed that the stresses in the bulk Ti stem are higher than the stresses in the FG stems; however, the stress distributions along the FG stems' layers were varied, which is attributed to the difference in the Young's modulus of each porous layer. By studying the yield stress values for each of the stems' layers, all FG designs were found safe at a walking speed of 1 km/h, except for design D12, in which the stress value at the outer layer is equal to the yield stress associated with 80% porosity. Designs 1, 3, and 8 are safe at 3 km/h walking speed and none of the fifteen designed stems were found to survive at the 5 km/h walking speed due to high stress values which exceeded the yield stresses associated with the porous layers. Most patients receiving THAs usually have a gait speed of less than 2 km/h [46, 47].