## 2 Materials and Methods
### Finite Element Analysis  
The model (see Figure 4) reproduced by following the approach presented in Section 2.1 has been used for the FEM simulations and the next 3D printing of both the concept and the functional impellers. In particular, the study of the stresses and deformations of the materials was carried out through the finite element analysis (FEA) Autodesk Nastran-In-CAD 2019 software, within the Autodesk Inventor 2019 environment. In particular, three different  
Figure 4: Modelling process of the impeller: (**a**) surface of revolution from the 2D sketch of the lower flared part; (**b**) surface revolution of the upper flared part; (**c**) thickening of the walls and definition of the geometry of a blade; (**d**) reproduction of the blades around the profile of the impeller; (**e**) creation of the central hole and of the wear ring at the base of the impeller; and (**f**) resulting 3D model. All the dimensions are expressed in mm. configurations of materials and techniques for making the impeller were studied (see Table 3 for the details):  
1. AISI 304 stainless steel sheet work-hardened by plastic deformation through molding;
2. PET for the 3D printing of the concept model through fused deposition modelling (FDM);
3. AISI 316L stainless steel for the 3D printing of the functional model through selective laser melting (SLM). The first adopted configuration considers the original material of the Grundfos impeller (i.e., AISI 304 stainless steel), while for the 3D printing technique SLM is the AISI 316L stainless steel. The choice of the AISI 316L stainless steel comes from the availability of the material as a metal powder for the SLM technology and due to the fact that the presence of molybdenum as an alloying element, which is absent in the grade 304, is more suitable for corrosive and humid environments. For both metal materials (i.e., AISI 304 and AISI 316L), a linear analysis under the hypothesis of small displacements was carried out. Conversely, since the polymeric \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Young’s** & **Tensile** & **Yield Strength** & **Poisson’s** & **Density** \\  & **Modulus [GPa]** & **Strength [MPa]** & **[MPa]** & **Coefficient** & **[kg/dm\({}^{3}\)]** \\ \hline AISI & 195 & 505 & 215 & 0.290 & 8 \\
304 & PET & 2.758 & 55.1 & 54.4 & 0.417 & 1.541 \\ AISI & 165.8 & 602.2 & 504.1 & 0.352 & 7.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main properties of the adopted materials for the finite element analysis. The values reported for the AISI 304 and PET are those suggested by the Autodesk Inventor 2019 software, while for the AISI 316L the typical average values evaluated after the SLM printing process [44] have been accordingly added. Figure 5: Topographic optimization and modification of the flared parts and blades for improving the resistance of the impeller and guarantee the success of the SLM printing process: (**a,b**) complete filling of the upper flared part; (**c,d**) simplification of the blade hanging by removing the bended flap. material is subject to non-linear deformation, a non-linear analysis was performed for the PET. The analysis was limited to an impeller blade as the most stressed part. A shell-type idealization was chosen since, the thickness of the component being much smaller than the other two dimensions, it fairly faithfully represents the behavior of the solid model. The mesh was set with a characteristic size of 1 mm of the triangular element of the grid. Such a dimension was chosen according to that one able to reduce the solution error to values lower than \(10^{-13}\). Constraints were imposed, and placed on the upper and lower edges of the impeller blade, as shown in Figure 5(a,b). A pressure load of 3 MPa on the external blade surface was assumed, represented in Figure 5(c) with the green arrow. This value corresponds to the pressure produced by the maximum water column that lifts the electric pump equipped with this type of impeller.