## 2 Materials and Methods
### Mesh Geometry Refinement for Finite Element Analysis (FEA)
All these Surface.x components, as represented in the specification tree in Figure 4, are joined into a single surface with the help of the Join tool. Its dialog box contains several options for checking and simplifying the final surface. Thus, the program checks for tangency and convexity issues while trying to simplify the resulting surface. While creating the.model file, the user decides if it is convenient for the FEA. Most of the time, it is necessary and recommended to reduce the number of triangle elements with the help of the Simplification tool. For example, the number of triangles in the guide model studied in this paper was reduced from 82,180 to 2818. This decision leads to a much faster FEA, but also to easy manipulation of the model between the workbenches of the CATIA v5 program. The applied simplification, although substantial, does not produce significant changes in the area and volume properties of the guide. Figure 4: Joining the surface elements while simplifying the resulted surface and checking for tangency and convexity issues. Figure 3: Initial mesh surface of the guide from the.stl file while it is offset to create a new surface/model in order to be recognized by the CATIA v5 program. In the third step, once the mesh surface model has been created, verified, and simplified, the Close Surface tool is applied, and a solid object is obtained by filling the surface created according to Figure 4. This solid object can receive material properties and may be involved in a finite element analysis. Numerous constraint conditions are established for certain surfaces at the base of the guide to simulate its positioning/fixing on neighboring teeth; other surfaces are loaded with forces and moments due to the contact between the guide and the body of the drill. Finite element analysis considers the worst-case scenario when the tapered shank of the drill is in contact with the corresponding surfaces of the guide. The FEA is performed in CATIA v5 after defining the following elements:  
*.stl mesh of a tooth-supported surgical guide reduced to a limited extent at the neighboring teeth, optimized, and cleaned in the open-source software MeshLab [24];
* Material properties for surgical guide manufacturing via DLP 3D printing: E-Guide Resin (EnvisionTEC GmbH, Gladbeck, Germany): Flexural strength = 79-86 MPa; Poisson Ratio = 0.3; Density = 1.12 g/cm\({}^{3}\); Young Modulus = Tensile Modulus = Elastic Modulus = 2.6 GPa = 2600 MPa;
* Mandibular bone properties [27; 28; 29]: Density = 1.2 g/cm\({}^{3}\); Young Modulus = 15-30 GPa; Poisson Ratio = 0.3; Hardness (HB) = 56; Flexural strength = 70-150 MPa;
* The mesh used to discretize the guide's 3D model is composed of 90,217 finite elements (tetrahedrons), connected by 145,237 nodes. The 3D model is discretized using a minimum mesh size of 0.5 mm and an absolute sag (minimum distance between nodes and boundary) of 0.2 mm. For higher accuracy in the complex mesh, the finite element type is parabolic. An additional refinement of the mesh network with a smaller size of the finite elements is not necessary and does not offer important changes to the analysis results, but it would significantly increase the resources required for the FEM computations [30]. Based on the specialized literature [31; 32] and on several clinical tests/protocols recommended by the manufacturers of dental implants, the authors propose relations and values for the most important parameters used in the process of drilling the mandible bone. Some of these parameters and their coefficients are experimentally determined; they have moderate values, which ensure a safe drilling of the bone. The authors recommend using higher values with caution for the feed ratio speed, cutting speed, and axial cutting force. The moderate/safe values are because the mandible bone differs from one patient to another depending on gender, age, various health conditions, and also on the drilling protocol.