## 2 Methodology
### Finite Element Analysis
Figure 7: _Cont._  
The greatest observed value of von-Mises stress near the neck of the condylar head in Ti alloy implant material is 32 MPa, as shown in Table 3, which is safe enough because the yield strength of Ti-6 Al-4V is 850 MPa. The maximum produced von-Mises stresses around the condylar area for the Co-Cr alloy material model of Customized TMJ prostheses are 45 MPa, which is likewise substantially lower than the Co-Cr alloy yield strength (448 MPa). Therefore, we can conclude that both of the material models are in the safer zone as per the design point of view of patient-specific TMJ Implant. Von-Mises stresses for the condylar component were observed to be lower in Ti alloy-based customized TMJ implants than in Co-Cr alloy-based customized TMJ implants [23]. For the fossa components corresponding to both material models, the differences in values of Von Mises stresses are very small. Further, for patient-specific TMJ prostheses, the deformation contours for Ti alloy and Co-Cr alloy are shown in Figures 8 and 9, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material Model** & **Condy** & **Condylar Screws** & **Fossa** & **Fossa Screws** \\ \hline Ti alloy & 32 & 30.48 & 7 & 18.28 \\ Co-Cr alloy & 45 & 31.62 & 8 & 22.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum von-Mises stresses values in MPa for two different materials model in customized TMJ prostheses. Figure 7: The von-Mises stress contours for (**a**) Total TMJ prostheses with mandible (**b**) Condylar and fossa parts without screws (**c**) fossa and condylar screws in case of Co-Cr alloy model of customized TMJ prostheses. Figure 8: Deformation contours for (**a**) Total TMJ prostheses with mandible (**b**) Condylar and fossa parts without screws (**c**) fossa and condylar screws in case of Ti alloy model of customized TMJ prostheses. The maximum value of deformation for the Ti alloy model and Co-Cr model of customized TMJ prostheses are 0.022 mm and 0.0113 mm, respectively, shown below in Table 4.  
Figure 9: Deformation contours for (**a**) Total TMJ prostheses with mandible (**b**) Condylar and fossa parts without screws (**c**) fossa and condylar screws in case of Co-Cr alloy model of customized TMJ prostheses. As compared to the intact mandible model, both material models of customized implant exhibit higher induced stresses and lower deformation values. The reason for this is that the Young's modulus of the jawbone is lower as compared with Ti alloy and Co-Cr alloy, therefore a flexible bone changes its shape considerably more than the other two material models when subjected to loading. Moreover, the less stiff the material, the less the resistance to the external load will be, hence the induced stress in the case of intact mandible model is lower than other two material models of customized TMJ implant. The TMJ implant must be adequately stiffer as mechanical failures can fracture the implant. The most critical safety requirements for bio-implants are mechanical strength and toughness. The TMJ Implant must be sturdy and durable enough to survive the physiological pressures placed on them, and they must be anticipated to last a long time or until they fail or require more than one surgical operation. Any prostheses or bio-implants must have a strength greater than the bone and an elastic modulus that is comparable to that of human bone to avoid stress shielding effects which in turn results in bone resorption [8]. Therefore, the outcome of our study is that our patient-specific TMJ prostheses are on the safer side from a designer's point of view. Similarly, since Ti alloy is less stiff than Co-Cr alloy; hence the maximum deformation of Ti alloy material model is greater and the maximum von-Mises stress is lesser than Co-Cr material model of customized TMJ prostheses. This observation also makes Ti-alloy (Ti-6 Al-4V) a material that could be a better choice for the condylar and ramus part of the patient-specific implant from a design perspective.