# Methodology for the Concept Design of Locally Reinforced Composites
## 2 Approach and Models
### Mechanical Model  
In Section 1 it was pointed out that the mechanical model needs to be already applicable in the concept phase, in which limited information is usually available. The following approach satisfies these requirements, as no additional data is required, except for the part dimensions, load case, and material data, as well as the main parameters of stress threshold and deviation factor (see Section 3). Furthermore, this mechanical model can be automatically executed, to rapidly generate a reproducible concept. The mechanical model calculates the location, shape, and proposed fiber angles of reinforcements, as well as information about the design stress for the base-laminate as outputs. The detailed steps performed in this model are shown in Figure 3, and described as follows. The basis for all the subsequent steps is an isotropic FEA of the initial geometry (step 1). Although the final material is anisotropic, it is mandatory to start the process with an isotropic material, since the load paths and corresponding principal stress angles need  
Figure 3: Illustration of the key steps performed in the mechanical model. to be determined without being influenced by the anisotropic material. If an anisotropic material (i.e., composite) is applied in this step, an initial fiber orientation needs to be defined manually, which significantly influences the load paths depending on the user input [25; 26; 27]. After performing the FEA, areas near boundary conditions, such as screw holes, are excluded from further analysis (step 2). For these areas, prefabricated and predefined catalogue elements, such as patches, are recommended [1]. For the remaining areas, the magnitudes of principal stresses, in the 1 st and 2 nd principal stress directions, are calculated from the stress tensor for each element (step 3). The mechanical model focuses on planar 2D components, thus it is assumed that the 3 rd principal stress direction can be omitted. Tailored textiles consist of a surface-covering base-laminate (usually fabrics) and local fiber patches (reinforcements). The split into base-laminate and reinforcements is performed in step 4, based on the parameter stress threshold (0% < 00%) and the maximum stress in the entire component \(\sigma_{\text{max}}\). Elements with stresses below the limit \(\sigma_{\text{max}}\cdot(100\%\ -\ \mu)\) are defined as base-laminate, elements above the limit are defined as reinforcements. The higher the value of the stress threshold chosen, the more of the stress is carried by the reinforcements. Figure 4 shows an example for \(\mu\) = 40% and \(\mu\) = 60%. For \(\mu\) = 40%, the highest 40% of the stresses are carried by the reinforcements and the lowest 60% by the base-laminate. For \(\mu\) = 60%, respectively, the highest 60% are carried by the reinforcements and the other 40% by the base-laminate. This characteristic can be described by \(\sigma_{\text{i}}=\sigma_{\text{b}}+\sigma_{\text{r}}\), where \(\sigma_{\text{i}}\) denotes the elementwise stress and \(\sigma_{\text{b}}\) and \(\sigma_{\text{r}}\) the design stress for the base-laminate and reinforcements. Figure 4: Schematic illustration of the split into base-laminate and reinforcement area for stress thresholds \(\mu\) = 40% (**a**) and \(\mu\) = 60% (**b**). The area of the reinforcements depends on the stress threshold, whereas the base-laminate always covers the entire surface of the part. However, there is normally no linear relationship, since the stress distribution in the parts is usually not linear (e.g., Figure 1b). Thus, doubling the stress threshold does not generally lead to a doubling of the reinforced surface area. The following steps focus on designing the reinforcements, since the base-laminate can be designed using conventional methods. From a mechanical point of view, the best reinforcement can be achieved by locally rotating each element, with the characteristic orthotropic material behavior of FRP, in the direction of the maximum principal stress [6; 28].