## 3 Results
### TFP Process  
#### 3.2.1 TFP Pattern  
In order to determine the fiber path pattern in the final TFP preform, with particular focus on enabling the flexible behavior of the bending zones, the anisotropic nature of the fibrous composite material required combining the results of the above-mentioned simplified optimization process with an interpretation of classical lamination theory (CLT) [17; 18]. Figure 8: Topological optimization iterations. The finished TFP preform, after resin infusion process and complete curing, was supposed to be formed into a single curved surface and serve as the integrated frame in a later winding process. This required planning a diversified fiber path layout, which would reinforce and stiffen the seating area and leg endings, while guaranteeing a necessary flexibility of the composite material in the areas where the TFP preform was supposed to be bend (Figure 9). Consequently, fiber paths in the seating area, oriented at \(-45^{\circ}\), \(0^{\circ}\), and \(45^{\circ}\), aim at creating a quasi-isotropic layup sequence, resulting in constant stiffness of the material regardless of the force direction, yet offering minimal elasticity of the surface for the purpose of seating comfort. Starting from the leg tips, in the leg areas, fiber paths were oriented, at \(-75^{\circ}\) and \(75^{\circ}\), thus almost parallel to the leg axis, in order to use material properties to the maximum when trying to develop a stiff structure that would not deflect under load. However, the closer to the hinge area, the more the fiber path angles smoothly translated to more perpendicular orientation, reaching \(-15^{\circ}\) and \(15^{\circ}\) in the center of the hinge areas. Secondly, this core fiber path topology, designed according to structural performance of the stool model, was complemented with additional paths, which constituted further reinforcement and design details needed at a later stage of fiber winding. The complete design of the fiber paths in the final TFP preform structure had to be adjusted to the fabrication requirements of the machine. Thus, according to the role each fiber path fragment played in both in the fabrication process, as well as later in the structural performance of the stool, they were grouped into three layers, which were fabricated consecutively one on top of the other, using 1200 TEX and 2400 TEX flax fibers by the embroidery machine. Figure 9: Final TFP pattern and interpretation of CLT. The final TFP pattern consisted of three layers:  
1. Winding Pins Layer (Figure 10a). This layer was of special importance, since it provided the interface for the CFW process. The challenge at this step was determining the appropriate size of the pins. In order to guarantee visual integration of the pins in the final design of the FlexFlax, their dimensions should remain as modest as possible, but, at the same time, should be above the minimum fabrication size requirements of the TFP machine. The chosen geometry was a trapezoid of 2 cm (long base), 1 cm (short base), and 2 cm (height). To provide a delicate cross-section, a TFP machine preset of 1.5 mm stitch width was used for 1200 Tex flax fiber rovings. To guarantee the resolution of the winding pins, a 1 mm stitch length was set. Consequently, flax roving was sewn to the substrate with a higher number of stitches. However, this compromise resulted in a significantly longer production time for this stage of the TFP process. 2. Surface Layer (Figure 10b). The surface layer, containing the fiber layout for the bending zone, was formed from 1200 Tex Flax roving with a stitch width of 1.5 mm and a stitch length of 7 mm. 3. Structural Layer (Figure 10c). The structural layer was fabricated using 2400 Tex roving, with a cross-sectional dimension of 3.6 mm (stitch width). In this final layer, a boundary curve was embedded in order to reinforce the thinner rovings during the fabrication process. The final TFP pattern was sewn into a cotton substrate of \(1000\times 1400\) mm.