## 3 Finite Element Model and Structural Analysis of Fixators  
Modeling a structure is the creation of an idealized and simplified presentation of the behavior of a structure exposed to various actions. This is a key step in analysis and design because errors and omissions in modeling can cause problems in the functioning of the structural system. The formulation of the model implies the choice of geometric, physical, mathematical, and, finally, numerical approximation of the phenomenon. The goals of practical (not only qualitative) analysis limit the number of possible models. There is always a dilemma when choosing a model, because more complex models are more accurate, but at the same time, less efficient. The fixator and bone model are discretized with linear (TE4) and parabolic (TE10) tetrahedron finite elements. A linear tetrahedron contains four nodes at the vertices and has a total of twelve degrees of freedom. A parabolic tetrahedron is a form of a curvilinear tetrahedron with ten nodes and a linear change of deformations within the element. The FEM model of the fixator is discretized with 120,953 TE4 finite elements (46.7%) and with 109,816 TE10 finite elements (42.4%). Both elements belong to the group of 3D isoparametric elements, i.e., solids with six edges. With isoparametric elements, the same interpolation functions and the same nodes are used to approximate their geometry and the field of basic unknowns in the element. In each node of these finite elements, there are three degrees of freedom (displacement). Connections between individual parts of the fixator structure (solid, contact, and screw connections) as well as connections for modeling the influence of the supports (sliding connection) were modeled with spider-type elements (28,232 finite elements or 10.9%). In this way, the FEM model of the fixator consists of a total of 259,001 finite elements with 262,652 nodes, which results in 787,959 degrees of freedom (number of DOF), (Figure 3). For the production of medical devices, the device from Figure 1 is completely made of stainless steel, which is modeled as an isotropic linear elastic material in the FEM analysis. In the case of isotropic materials, the constitutive relations, that is, the stress-strain relations, contain only two constants: the modulus of elasticity and Poisson's ratio, which, for the given steel, have the values E = 215 GPa and \(\upgamma\) = 0.29, respectively. The device from Figure 2 is made of stainless steel (couplings, coupling carrier, and half-pins) and composite material (fixator frame). For steel, we have already noted that in the FEM analysis, it is modeled as an isotropic linear elastic material, while the composite material is modeled as an anisotropic material, and thanks to the cylindrical symmetry of its structure, it can be viewed as an orthotropic material where the properties are defined in three planes determined with transverse, tangential, and the radial section of the frame. The models of bone segments are made of beech wood, which  
Figure 2: Sarafix fixation device with composite frame; (**a**) B50 configuration, (**b**) C50 configuration. has known mechanical characteristics (Table 1). Wood belongs to the group of anisotropic materials, but thanks to the cylindrical symmetry of its structure, it can be viewed as an orthotropic material where the properties are defined in three planes determined by the transverse, tangential, and radial cross-section of the trunk. A small rectangular segment with three axes of symmetry, longitudinal (L), radial (R), and tangential (T), can be distinguished from the truss, which are approximately perpendicular to each other. For the composite material and the material of the bone segment model, which is modeled as a 3D orthotropic linear elastic material in FEM analysis, it is common to define material parameters such as the modulus of elasticity, Poisson's ratio, and slip modulus (Table 1). During application, the fixator is exposed to a complex load that is a combination of pressure, bending, and twisting.