# Methodology for the Concept Design of Locally Reinforced Composites
## 1 Introduction  
Composites from fiber reinforced plastics (FRP) offer high weight-saving potentials compared to isotropic materials. Due to their superior density-specific stiffness and strength, FRP are highly suitable for lightweight applications [1]. The distinctive anisotropic behavior of continuous fibers can be utilized to design load-optimized structures. To make the most of the fiber's mechanical properties, they must be locally and congruently aligned with the component's principal stresses [2]. Manipulating the fiber paths in a manner to follow the local load-paths inside the FRP component offers the opportunity for, the so-called, tailored textiles (TT). The concept of TT is to optimize the layup and fiber orientations, considering the local stress magnitude and local orientation. By applying fibers only where structurally necessary, the material usage, and hence weight and cost, can be reduced by 30% compared to conventional FRP design strategies [3]. TT aim for low manufacturing costs by combining surface covering fabrics (base-laminate) and local fiber reinforcements, such as patches. The local reinforcements are applied to highly stressed areas, whereby the base-laminate carries a lower stress. In Figure 1 the potential for material savings using TT are shown. Observing the stress distribution of a shear loaded component (Figure 1a,b), it is apparent that only a small area is highly stressed. Designing the component according to the maximum stress \(\sigma_{\text{Max}}\), results in a large demand for material. For TT, the design stress of the whole surface covering base-laminate is reduced from \(\sigma_{\text{Max}}\) to \(\sigma_{\text{Threshold}}\) by setting a limit value for the stress (stress threshold). The usually small reinforcements are applied locally, where high stresses above the limit of \(\sigma_{\text{Threshold}}\) occur. Hence, the total material demand can be reduced using TT. However, the appropriate choice of threshold (stress threshold), for splitting into high and low stress, is currently unknown, since it depends on both mechanical and economic aspects, which are discussed as follows. The base-laminate consists of semi-finished goods, based on conventional textiles, which can be produced cost-efficiently. However, the production of many, typically small, reinforcements is associated with a lower material output rate, and thus leads to an increased weight-specific cost [4]. Therefore, from an economic point of view, as much stress as possible should be carried by the cost-efficient base-laminate, to use as few expensive reinforcements as possible. In contrast, from a mechanical point of view, it makes sense to carry a larger share of the stress via the reinforcement area. The reinforcement area is divided into several clusters. These clusters have a constant fiber angle, to ensure the application of fiber composite manufacturing technologies (e.g., patches). However, the level of granularity of the clusters has a major influence on both the mechanical and economic properties of the TT. Continuously following the local principal stress orientations leads to the best mechanical properties, but would also require many small clusters, resulting in high manufacturing costs (Figure 2c) [4; 5; 6]. When using fewer but larger clusters with constant homogenized angles, the costs can be reduced (Figure 2b). However, the angle deviation of the homogenized angle in comparison to the element-wise optimal orientation of the principal stress (deviation factor) is high, and thus the mechanical properties are simultaneously reduced. Several approaches for the simultaneous consideration of the mechanical and economic properties of FRP are available in the literature [7; 8; 9]. The approaches use genetic algorithms for the complex optimization task [10; 11; 12; 13; 14; 15; 16; 17]. The appropriate formulation of complex optimization problems and the algorithm operators, as well as the execution, require a high level of effort. Other approaches deal with the design of the reinforcements.