## 2 Fundamental Concepts
### Three-Dimensional Printing  
The world is constantly witnessing several technological advances. These advances always require acquiring new knowledge so that they are better understood. A technology that has evolved significantly in recent decades is 3D printing [1].  
One of the significant advantages of this technology is the flexibility in producing 3D-modeled parts by computer-aided design (CAD), which, together with computer-aided manufacturing (CAM), allows for the fabrication of different geometries, complex or straightforward [8]. Additive manufacturing technology can be divided into seven families: vat photopolymerization; powder bed fusion (PBF); binder jetting (BJ); material jetting (MJ); sheet lamination (SL); material extrusion (ME); directed energy deposition (DED) [9]. In the material extrusion (ME) family, the FFF process is the most common and easily used nowadays. They are the printers that generally anyone can have at home due to their low cost and operational simplicity [10].  
In the FFF process, the raw material, in the form of a filament, is hot extruded through a nozzle on a heated table following the coordinates defined by the digital file, where the material is deposited layer by layer until the piece is obtained [2]; see Figure 1. The most common materials in this type of process are plastic filaments, such as PLA, which is a rigid material, which allows fir greater detail in the parts produced with it, and acrylonitrile butadiene styrene (ABS), which is a thermoplastic with great flexibility and has more excellent resistance to impacts. Other materials also used in this process are polyester, polypropylene (PP), polycarbonate (PC), polyamide (PA), elastomers and waxes [3; 11].  
In the 3D printing process, several parameters influence the manufactured product [12]. Therefore, to have greater control over the final part, each of these factors must be carefully analyzed. Some of these parameters are [2; 13]:  
* Construction orientation: orientation with which the part is constructed relative to the base, along the X, Y and Z axes.
* Layer thickness: height of the layer deposited by the extruder nozzle. Varies with nozzle diameter and material.
* Fill density: space between adjacent filaments in the fill region of the part.
* Fill angle: angle between the filler filament deposition and the X axis.
* Filler filament width: width of the filament used for filling. It depends on the diameter of the extruder nozzle.
* Number of contours: number of perimeters built along the part, internal and external.
* Contour filament width: width of the filament used in the contour of the part.
* Space between contour filaments: space between each of the filaments used in the contour.
* Space between contour and fill: space between the contour and the effective fill of the part.
* Extrusion speed: speed at which extruded filaments are deposited.
* Extrusion temperature: temperature at which the filament is deposited.
* Platform temperature or bed temperature: temperature of the surface of the table/bed where the printing is carried out.
* Environmental conditions: temperature and humidity of the printing environment.  
Figure 1: Three-dimensional printing process.  
Due to this large number of factors that can influence the manufacture of parts produced by 3D printing, physical and mathematical formulations become challenging to develop [14].