## 3 Methodology and Guidelines
### Preliminary Analysis of AM Constraints  
Following the flow in Figure 1, the next step of the process is the Preliminary Analysis, which is a rough examination of main manufacturing constraints to exclude unfeasible applications. Three aspects have been identified as overwhelming limitations that could impede the usage of AM. Even if the three evaluations can be regarded as subjective and depending on the evolution of the technologies, it is reasonable to evaluate them early and to skip the process from the beginning if one of them cannot be surely met by the application:  
* Lack of a material with some mandatory properties;
* Excessively large or small product dimensions for currently available technologies;
* Excessively large production batches. In Figure 3, the sub-steps of the Preliminary Analysis are presented:  
1. Screening of materials compatible with the given constraints (i.e., minimum stiffness, minimum yield strength, electric conductibility, etc.);
2. Computation of a set of indices according to Ashby [36] for each compatible material;
3. Definition of index weights using AHP and computation of an overall Compliant Index (_CI_) for each material through WSM normalization;
4. Materials ranking;
5. Selection of possible printers proceeding in the sorted list of materials;
6. Check of printer capabilities according to required volume and batch size.  
Figure 3: Workflow of the preliminary analysis of AM constraints.  
Therefore, the first step is to identify suitable materials out of a list. The materials database is built from data provided by technology suppliers, mostly available on the web [36], where the value range of properties of available materials is reported. It is possible that only a few or no materials are compatible if numerous and strict constraints are imposed, making AM an impractical solution for the imposed requirements.  
A list of seven indices, drawn from Ashby [37], are suggested to evaluate the materials. The selected indices are:  
1. \(\mathrm{I1}=\sigma\mathrm{r}/\rho\)
2. \(\mathrm{I2}=\sigma\mathrm{y}/\rho\)
3. \(\mathrm{I3}=\sigma\mathrm{f}/\rho\)
4. \(\mathrm{I4}=\mathrm{E}/\rho\)
5. \(\mathrm{I5}=\mathrm{E}^{\prime}(1/2)/\rho\)
6. \(\mathrm{I6}=\sigma\mathrm{y}/(\rho^{\star}\mathrm{C})\)
7. \(\mathrm{I7}=\mathrm{E}/(\rho^{\star}\mathrm{C})\)  
where \(\sigma\)= ultimate tensile strength (N/mm\({}^{2}\)), \(\sigma\)y = yield strength (N/mm\({}^{2}\)), of = fatigue strength (N/mm\({}^{2}\)), E= yield modulus (GPa), \(\rho\) = density (kg/cm\({}^{3}\)), C = raw material cost (EUR/kg).  
The first four indices are related to the mechanical performance of the material, the fifth index refers to the vibration behaviour, while the last two indices consider the cost. The relative weight of the indices must be assigned by the user according to company production range and company strategy. Such indices are normalized to calculate a _CI_ for each material through the WSM. The index weights are determined by the AHP method according to design strategies. Then, the materials are ranked from best (high _CI_) to worst (low _CI_). This process is summarized in Figure 4.  
Printers compatible with the selected material are then listed, verifying the production requirements relating to the volume of the product and the batch size. Additionally, the designer must consider the intrinsic material anisotropy of AM processes, the bounding surface weakness between two different materials [12] and the technology deposition maturity, thus selecting the most suitable printer. If no printer is compatible with the production requirements, the next material in the ranking is selected, repeating the check of the compatibility of available printers with the imposed constraints. A printer database is built for this purpose from data available on the web [36] or from supplier's data. If a valid combination of material and printer is found that meets the defined requirements, Potential Analysis is performed.  
Figure 4: Materials ranking process.