## 2 Materials and Methods
### FE Modeling Approach  
The numerical model was built in ANSYS Workbench v19 software. Static analyses were performed to validate the structural strength of both metallic EF, and of the alternative EF with a 3D-printed ring from PLA-CF. Simulations were conducted using Mechanical APDL iterative solver with Large deflection option activated in order to take into account the geometric and contact nonlinearities. Several scenarios were run to achieve the objectives of the numerical analysis, as noted in Figure 1. First, to evaluate the global stiffness of the EF, the fracture line was modeled as a gap (as shown in Figure 2). This approach also enabled the computation of global displacements and stress levels for each fixator component, ensuring both the overall stability of the fixation device and compliance with strength requirements. For the early fracture healing stage (0 to 4 weeks), additional scenarios were analyzed, where the fracture was progressively filled with callus at different healing phases. Furthermore, a ring-only model was used to study various ring designs subjected exclusively to wire pre-tension loads. Initially, all scenarios were simulated for the metallic EF. The results were then compared with those obtained for the same configurations, but with the metallic ring replaced with a 3D-printed ring from PLA-CF. This comparison aimed to evaluate the impact of material change, and determine the necessary geometrical modifications to meet the strength requirements of the 3D-printed component. For consistency in the analysis, the same geometry was maintained for both metallic and 3D-printed components. The modeling approach consisted of a detailed FEM using a 3D mesh, with tetrahedral elements for the bone and clamps, as they facilitate the modeling of complex geometries, and hexahedral elements for the wires, pins, and rods, thus ensuring higher accuracy in stress calculations for anchoring components. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Tensile Ultimate** & **Tensile Yield** & **Tensile Modulus** & **Poisson Ratio** & **Failure Criteria** \\  & **Strength [MPa]** & **Strength [MPa]** & **[MPa]** & **[-]** & **(\({}^{\circ}\))** \\ \hline Kirschner Wires—Stainless Steel & 1100 & 800 & 187,500 (\({}^{\circ}\)) & 0.33 (\({}^{\circ}\)) & Normal Stress \\
316 LVM [38] & 135 (Tension) & 71.5 (Tension) & & & \\  & 205 & 115 & & & \\ Cortical Bone [35] & (Compression) & (Compression) & 16,000 & 0.3 & Tresca \\  & 65 (Shear) & 41 (Shear) & & & \\  & Cancellous Bone & - & 16.3 (\({}^{1}\)) & 1100 & 0.26 & \\  & Granulation Tissue & - & 0.5 (\({}^{2}\)) & 1 & 0.167 & \\ Callus [29; 36] & Fibrous Tissue & - & 2.8 (\({}^{2}\)) & 5 & 0.167 & VM \\  & 0.4 weeks & - & 5.5 (\({}^{2}\)) & 15 & 0.167 & \\  & Fibrous–Cratilage & - & 16.3 (\({}^{2}\)) & 125 & 0.167 & \\  & & & & & \\  & & & & & \\ EF components Steel S235 [39] & 360 & 235 & 210,000 & 0.3 & \\  & PLA-CF filament [40; 41] & 48 & 89 (\({}^{3}\)) & 4950 & 0.40 & \\ \hline \hline \end{tabular}  
* The cancellous bone is enclosed in a layer of compact bone, providing improved strength and rigidity. Conservatively, at the cancellous bone ends of tibia, the layers of compact bone are not modeled. \({}^{2}\) Yield Strength data obtained from rabbit long bone samples correlated with specific specimen prospective FE analyses. \({}^{3}\) Flexural Strength measuring the PLA-CF resistance under bending loads. \({}^{4}\) The failure criteria are provided for each component based on the theoretical considerations depicted in Section 2.1. \({}^{5}\) The Young modulus and Poisson ratio used in calculation for wires are 210 000 MPa and 0.3, respectively, as for basic structural Steel, with no significant impact on this study’s conclusions, as EF structural behavior using other metallic steel grades would be very similar.  
\end{table} 
Table 1: Materials and mechanical properties for FEA. Mapped face meshing was applied to bone hole areas to enhance contact modeling, ensuring at least one element per 45\({}^{\circ}\) around each hole.