# Anatomical-Based Customized Cervical Orthosis Design in Automation
## 3 Finite Element Analysis  
To ensure the strength of loading support of the 3D printing orthosis, a finite element analysis with ANSYS (version 19.2) was conducted to simulate the stress distribution in the orthosis under various loadings of postures. The coverage area on the lateral side of the orthosis includes the ribs, which provide necessary support for the orthosis. The parameters for the front and back pieces of the orthosis were 30 mm wide, with four different thicknesses of 3 mm, 4 mm, 5 mm, and 6 mm for finite element analysis. The orthosis was fabricated using an FDM 3D printer with PLA at 20% infill. The elastic modulus for 3D-printed PLA with 25%, 50%, and 75% infills are 0.866, 0.985, and 1.223 GPa, respectively, while the elastic modulus for these three infills is 31.4 MPa, 34.96 MPa, and 42.67 MPa, respectively [19]. In the finite element model, the mechanical properties for PLA with 20% infill, listed in Table 1, can be obtained by extrapolating the above measurement data reported in [19]. The boundary conditions in the finite element analysis are shown in Figure 9. For all postures, the sternum and side neck points are fixed in the front piece model, while the seventh cervical vertebra and side neck points are fixed in the back piece model. For the front piece with flexion posture, an extra fixation at the assembly points shown in Figure 9 is added due to the constraint from the back piece. Similarly, the back piece assembly points are also fixed for extension posture. The assembly points are not fixed for left and right lateral flexions. According to the moments at the seventh cervical vertebra for various postures obtained from [20,21], the equivalent forces applied on the front and back pieces of orthosis in each posture are listed in Tables 2 and 3. Tables 4 and 5 show the maximum von Mises stress of the respective front and back pieces of orthosis for various postures from finite element analysis. Figure 10 shows the stress simulation outcomes for the front and back pieces. The horizontal dashed line indicates the tensile strength, 29.58 MPa. The stress contours for cervical orthosis with a thickness of 3 mm are shown in Figure 11. The results indicate that the maximum stress decreases as the thickness increases, regardless of the neck postures. In the front piece, the maximum stress exceeds the tensile strength, 29.58 MPa, at 3 mm thickness for flexion, left lateral flexion, and right lateral flexion and 4 mm thickness for left lateral flexion. The back piece found no maximum stress exceeding the yield strength. According to the finite element analysis results, the front piece should be at least 5 mm thick, and the back piece should be at least 3 mm thick to ensure the maximum stress remains below the PLA tensile strength of 29.58 MPa. For safety reasons, it is recommended to utilize a minimum thickness of 5 mm for customized orthosis fabricated with 20% infill PLA material. \begin{table}
\begin{tabular}{c c c} \hline  & **Property** & **Value** \\ \hline Elastic modulus & 0.811 GPa \\ Poisson’s ratio & 0.33 \\ Tensile strength & 29.58 MPa \\ \hline \end{tabular}
\end{table} 
Table 1: Material properties of PLA with 20% infill [19]. \begin{table}
\begin{tabular}{c c c c} \hline  & **Flexion** & **Left Lateral Flexion** & **Right Lateral Flexion** \\ \hline Force (N) & 135.06 & 90.96 & 86.36 \\ Loading location & Chin & Left mandible angle & Right mandible angle \\ \hline \end{tabular}
\end{table} 
Table 2: Loads on the front piece of orthosis in each posture. Figure 9: Fixed points and loading points for the finite element analysis: (**a**) the front piece, (**b**) the back piece. In the finite element analysis, the magnitudes of the loads listed in Tables 2 and 3 are based on the strength of the neck muscles [20; 21]. These test data were measured from healthy persons. This means that the loads applied to the orthosis in the finite element analysis were the maximum forces a healthy person could apply.