## 3 Finite Element Model and Structural Analysis of Fixators
In most studies of external fixation devices, using the finite element method and/or experimental tests, separate tests are performed on axial load with compressive force and sagittal or anterior-posterior (AP) bending and twisting [22,23]. In this study, the external fixation device was tested for anterior-posterior bending. An FEM model was developed that simulates an experimental test on anterior-posterior bending, taking into account the complete geometry of the fixator and the bone model, the connections between the components, the applied load, and the applied restrictions. The structural analysis of AP bending of the FEM model of the Sarafix fixator prototype was performed by making two flat surfaces for support on the models of the upper and lower segment of the bone, i.e., the cylindrical bone models were leveled at the places of support. The support is achieved by utilizing contact with virtual parts attached to the flat surfaces on the bone segment models (Figure 3). The structural bending analysis of the fixator model was performed with a concentrated load at the fracture site, the maximum value of which was 500 N, i.e., 250 N at both ends of the bone model segment symmetrically. To prevent the movement of the model in space, three translations are prevented on one of the support surfaces on the bone  
Figure 3: FEM model of the Sarafix device—preprocessing; (**a**) B50 configuration, (**b**) C50 configuration. model segment, while two translations are prevented on the other bone segment model. The load intensity corresponds to the physiological load of the fixator after its application in the patient and is defined based on the results of in vivo tests [7; 24]. The structural analysis was carried out with the following assumptions concerning the actual situation: the load is quasi-static, the support is modeled with appropriate frictionless joints and supports, the connection between the half-pins and the bone is solid, and the characteristics of the material for the bone model correspond to the mechanical characteristics of beech wood. During the structural analysis, the displacement values at the point of loading were monitored (Figure 4), based on which the stiffness of the fixator structure is defined as the relationship between the load and the displacement of the bone at the point of impact of the load. The stiffness of the fixator structure according to AP bending (Cp) is calculated using the following relation [25]:  
\[C_{s}=\frac{F_{s}}{\delta_{s}}\ [\frac{N}{mm}] \tag{1}\]  
where \(F_{s}\) is the bending force (N) and \(\delta_{s}\) is the deflection due to load (mm). When defining fracture stiffness, displacements in the \(x\), \(y\), and \(z\) direction of a pair of adjacent points on the end planes of the proximal (upper) and distal (lower) segment of the bone model at the fracture site were determined, for which the vector of the resulting relative displacement (\(R\)) has a maximum value. The intensity of the maximum interfragmentary displacement vector at the fracture site \(R\) is defined by [26]:  
\[R=\sqrt{\left(r_{D(x)}\right)^{2}+\left(r_{D(y)}\right)^{2}+\left(r_{D(z)} \right)^{2}} \tag{2}\]  
The relative displacements of a pair of observed points on the end planes of the proximal (upper) and distal (lower) segments of the bone model in the \(x\), \(y\), and \(z\) directions are determined as [27]:  
\[r_{D(x)}=D_{p(x)}-D_{d(x)}\]  
\[r_{D(y)}=D_{p(y)}-D_{d(y)} \tag{3}\]  
\[r_{D(z)}=D_{p(z)}-D_{d(z)}\]  
where \(r_{D(x)}\), \(r_{D(y)}\), and \(r_{D(z)}\) are the relative displacements of the bone segment points in the \(x\), \(y\), and \(z\) directions (mm), \(D_{p(x)}\), \(D_{p(y)}\), and \(D_{p(z)}\) are the displacement of the proximal bone segment in the \(x\), \(y\), and \(z\) directions (mm), and \(D_{d(x)}\), \(D_{d(y)}\), and \(D_{d(z)}\) are the displacement of the distal bone segment in the \(x\), \(y\), and \(z\) directions (mm). Figure 4: FEM model of the Sarafix device (C50)—postprocessing. location MM+ (Table 2).