# Design of Fiber-Composite/Metal-Hybrid Structures Made by Multi-Stage Coreless Filament Winding
## 2 Materials and Methods  
### Object-Oriented Design and Management Tool  
This study developed a digital CFW design tool to assist during all the project phases. CFW structures are best described by a graph-theoretical [40] approach due to their shape characteristics. In the most fundamental level of detail, anchors are represented by nodes as points with cartesian coordinates, and edges as connecting lines represent the fiber bundles (Figure 2b). The undirected graph is stored as an edge list, not as an adjacency matrix [41]. This is more efficient because only a few of all possible connections are present. Self-connections (1-1, 2-2,... ) are not relevant; therefore, the diagonal of the adjacency matrix is filled with zeros. Nodes are numbered with integers and may contain data on external force inductions and the anchor orientation, both as vectors (Figure 2a). The fiber path (Figure 2c) is stored as a sequence of nodes, which is called winding syntax [42]. It is often separated into several sub-syntaxes, which start and end at the same node. It can be advantageous to define the path as a repetition of local direction statements if the syntax has a regular shape. Building upon this fundamental digital representation (node coordinates, graph, and path), several features can be implemented independently from each other to increase the level of detail and the precision of predictions:  
1. Additional control points can be implemented to connect two fibers at a crossing point properly, to deform the fiber net, or both (point 5, see Figure 2e). Nodes represent anchors, while control points do not. A single edge between two nodes or control points is called a segment, while the connection between two nodes is called a section and may contain several segments. 2. Two additional nodes (0 = pre_start_node, \(-1\) = post_end_node, see Table A1) represent the protruding segments required at the beginning and end of the CFW process (Figure 2e). The model can be adjusted to match the fabricated structure by relocating existing nodes or control points and by adding new ones. 3. A (uniform) subdivision of the segments along the fiber path can be implemented to add local information along the fiber path, such as cross-sectional parameters (Figure 2d), local fiber volume ratio (FVR) deviations, or strain-field measurements by a fiber-optical sensor (FOS) system [43]. 4. Around anchors, the actual circular fiber arrangement caused by the wrapping can be implemented with a polyline (Figure 2f). Depending on the hooking condition [44], the fiber path is longer than the direct connection, and the ends of the adjacent segments are radially offset. This lets the actual fiber net deviate from the graph for structures that are small in relation to their anchors. The developed digital design tool (Figure 3) is an object-oriented Python (version 3.7.7) script to digitally represent and analyze CFW objects. It has dependencies mainly to numpy [45], pandas [46], plotly [47], and scipy [48]. The script operates on all beforementioned levels of detail and helps during all project phases, from design, over simulation, and fabrication to managing the finished components. When adding a level of detail, the fundamental representation of the object is preserved. Figure 2: Digital representation of different levels of detail of the same winding object. (**a**) Point cloud of the nodes, containing information on the cartesian coordinates, external forces, and the anchor orientation; (**b**) Graph of the winding object; (**c**) Winding path as sequence of nodes [1, 2, 3, 4, 1, 3, 2, 4, 3, 1]; (**d**) Local information (e.g., cross-section) defined along the path; (**e**) Control point 5 at the crossing point deforms the fiber net, points 0 and \(-1\) position the fiber ends; 2–5–4 and 1–5–3 are sections, 1–5, 2–5, 3–5, and 4–5 are segments; (**f**) Nodes are represented as sleeve–washer combinations with the winding path in a discretized form.