## 1 Introduction  
Designers are able to create complex topologies and shapes, thanks to the design freedom provided by Additive Manufacturing (AM) [1, 2, 3, 4]. In our days, the design manufacturing procedures have been expanded to conventional manufacturing processes, although Design for Additive Manufacturing (DfAM) methods have to be further elaborated [5, 6, 7, 8]. Many of these methods help us to use the properties that are enabled by AM. Such methodologies are: Topology Optimization (TO), the AM manufacturability analysis, and cellular structures. Cellular structures are observed in nature: in plant stems or in bamboo microstructures [9, 10, 11]. These structures present an incline and can proceed toward better material distribution for a performance optimization. In relation to artificially designed cellular structures, the features presented are upper level, making them suitable for processes such as energy absorption or heat transfer.  
AM stands out for its ability to reduce the necessary manufacturing material when producing a part and the weight of the part itself, thanks to its nature [12, 13, 14]. AM can manufacture lightweight parts characterized by a sparse internal infill and an external skin. In regards to the fabrication process, the type of the infill is a crucial parameter, with the most reliable and fast printing infills those that are made by printing the same pattern for every layer. These are the 2D infills, and they are characterized by a vertical cross-section, which creates a geometry fertile to anisotropic structural properties [15].  
Another type of infills, that present an isotropic behavior, are the 3D infills. In particular, the infills that have a cubical symmetry are called \"cubic infills\", and they repeat in all three directions. Another type of strong and fast printing 3D infill is the mathematically based \"gyroid infill\", which can simplify the designing process. The disadvantage that comes along with 3D infills is that they are not easy to be printed and show a high complexity [16; 17].  
The final type of infills are those that cannot be characterized either as 2D infills or as 3D infills. Due to process optimization, they have a non-periodical nature, which allows them to be rich in forms. They may have internal structures containing voids, using graded infills or internal structures with repeating optimized lattice structures. These can show differing spatial properties or particular elastic properties. In an effort to stimulate the general orthotopic properties, Poisson's ratio and elastic moduli tuning, many researchers have used Topology Optimization [18; 19; 20].  
Topology Optimization is the mathematical method that can optimize the material distribution within a specific design area. Its purpose is the system performance maximization for a given set of loads. There are several TO implementations like Solid Isotropic Material with Penalization (SIMP), level set and BESO. TO is a technique via which we can remove from the structure the ineffectual material and add at the same time the proper material to the structure [21; 22; 23]. Furthermore, the MMC and the homogenization methods are used in order to produce a quickly infilling gradient microstructure [24]. The most famous method is the SIMP algorithm that calculates the element's relative density distribution in the design space [25]. Some of the topologies are limited in AM and the truss-like cellular structures in the functionally graded modeling method. There are only a few isotropic cellular structures when the established TO methods are calculated for isotropic materials. Topology Optimization and Additive Manufacturing are coupled in an efficient manner and can make the most of their potential, in order to allow for wide application prospects in modern manufacturing [26].