# Functionally Graded Additive Manufacturing: Bridging the Gap between Design and Material Extrusion
## 1 Introduction  
Additive manufacturing (AM) is a manufacturing process that creates parts by adding materials layer-by-layer. Unlike traditional manufacturing processes, AM only adds materials where it is required, thus reducing material waste. Furthermore, AM can fabricate parts with extremely complex geometry.  
Aside from homogeneous materials, the fabrication of functionally graded materials (FCMs) using AM technologies has recently been studied [1, 2]. Unlike traditional composite materials that are made by combining two dissimilar materials, either homogeneous mixtures or joined materials, to produce improved properties, FGMs are characterized by a compositional gradient of one material into another [3]. Often, in composites there are sharp transitions between dissimilar components, which can cause high-stress concentrations and even delamination under complex loading conditions [4]. Conversely, in FGM, thesharp interface is replaced by a gradient interface that is a mixture of both components, and it gradually changes inside the component. It follows that 3D printing of complexly shaped heterogeneous objects with continuously graded properties, such as mechanical property, hysteresis, and variable magnetic strength, can be realized by gradually changing the spatial volume fraction distribution of different constituents.  
The concept of FGM was first proposed in the 1980s in Japan. At that time, heat-resistant ceramics and tough metals were applied to the FGM design for a thermal barrier, with a temperature difference higher than 1000 K [5]. Nowadays, FGMs with other types of functions can be used in many areas, such as aerospace, biomedical engineering, sensors, and energy [6; 7].  
As mentioned, recent progresses in AM have allowed the production of parts using FGMs, through a process known as functionally graded additive manufacturing (FGAM) [8]. Among the AM process, as confirmed by the literature, fused deposition modeling (FDM) is a promising technology for FGAM. Indeed, FDM is one of the most popular processes, due to the possibility of processing cost-effective and non-toxic materials and making products at a lower cost, allowing for different transition types in FGMs, such as interlocking shapes, coextrusion, and mixing, where different fractions of materials are combined in the hot-end and flow in the same nozzle [9; 10; 11; 12; 13]. Nonetheless, FGAM needs an effective tool-path control that is based on a triptych \"materials-product-manufacturing\" approach [14]. The procedure for the manufacturing of FGAM parts is similar to the one employed in traditional AM, involving solid model generation using CAD (computer-aided design), slicing, conversion of the CAD file into STL file format (or other appropriate data exchange file format), verification of the STL data, determination of optimal orientation for the printing, generation of support material, toolpath calculation, fabrication, and post-processing. The main distinction is that FGAM prioritizes the description and assignment of material distribution in the design domain, which can be assigned based on functional requirements, adopting different representation schemes [15; 16].