# On the Impact of Additive Manufacturing Processes Complexity on Modelling
## 5 Conclusions  
To summarize, a heuristic metric for the complexity of a process has been suggested and applied in the case of various AM processes. This metric has been proved to be quite useful towards forming a metamodeling framework for processes that includes the machine aspect (i.e., through path and speed selection) on attributes/performance indicators (i.e., part quality). In particular, all the goals towards successful AM modeling are summarized in the following points and can be facilitated through the current framework:  
* Development of process models for the increase in AM part quality;
* Consideration and investigation of the effect of the head movement on part quality (path and speed);
* Increase in the practicality of simulations for AM;
* Enabling the practical evaluation of alternatives to achieve higher part quality;
* Achieving the simulation of the entire process time. In particular, the path of the head directly affects the thermal gradients by inducing thermal stresses and deformations. Thus, the general principles concerning head path planning that have been drawn from the investigation conducted on metal-based AM can be applied to the remaining thermal-based AM processes, such as plastic-based PBF (FDM). Also, for the AM process groups that there is material flow from the head to the machine platform, coordination between the flow rate and the change in speed is required in order to maintain part quality. In such a case, the conclusions drawn in both cases are applicable and should be considered. It should be noted that the control of the energy flow (i.e., change in laser power) has a faster response rate; thus it is easier to be achieved than the control of the flow of the material. In addition, the response rate becomes lower for greater flows from nozzles of larger diameters. Moreover, it can be concluded easily that in the case of direct energy deposition, the complexity is even higher, thus more elaborated modelling should be performed. The reason is that the flow of the powder itself is an extra process parameter that has to be taken into consideration. Finally, as far as the practicality of the modelling procedure in industrial applications is concerned, MBSE could benefit from such metrics, as the added value of a model that can be adapted to different levels of detail could be based on such metrics. For instance, the model development time can be predicted through such a complexity metric. Then, by comparing this time against the monetary benefits derived from the corresponding modelling, i.e., due to zero-defect policies, one could decide on what level of detail to adopt. Regarding future work, metamodeling frameworks need to keep being enhanced, so that both conceptual and mathematical modeling are facilitated; the key concept seems to be that of level-of-detail, so everything has to be performed in accordance to MBSE and hierarchical modelling. Also, it has to be mentioned that metrics need to include somehow the complexity of the equations, without neglecting the function \(\eta\) above in Section 5. Potentially, the solution times of the models as well as the dimensionless constants could be integrated to this end. This direction will help also towards achieving further aspects of practicality, since a more accurate in-advance estimation of modelling development time would be achieved. **Author Contributions:** Conceptualization, A.P. and P.S. ; methodology, A.P. ; formal analysis, P.F. ; writing--original draft preparation, P.F. ; writing--review and editing, A.P. and P.S. All authors have read and agreed to the published version of the manuscript. **Funding:** This work is conducted under the framework of EU Project AVANGARD. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 869986. The dissemination of results herein reflects only the authors' view and the Commission is not responsible for any use that may be made of the information it contains.