# Random Fiber Array Generation Considering Actual Noncircular Fibers with a Particle-Shape Library
## 1 Introduction  
Random fiber generators can provide arbitrary arrangements of fibers or fillers in a two-dimensional (2D) or three-dimensional (3D) space, which approximate the shape of the microstructure of a composite material. As a result, the representative volume elements (RVEs) simulating the real microstructure can be constructed; they have been commonly used in studying the mechanical behavior of composite materials and structures. RVEs can be an excellent micromechanical-based model that predicts equivalent physical properties, such as the strength, stiffness, coefficient of thermal expansion, and so forth of composites. However, for efficient modeling of these RVE models, there are some situations in which the shape of the fiber/filler is excessively simplified into a circle, sphere, cylinder, or disc. Sometimes, these approximations could distort the effect of stress concentration between fibers, resulting in less accurate prediction of the equivalent stiffness and strength. In addition, the actual fiber has a more complex shape due to various manufacturing defects such as waviness [1; 2], misalignment [3; 4], crater, and so forth [5; 6; 7]. In particular, in the case of unidirectional composites, unlike the cross-sections of glass fibers, which are almost circular, those of carbon fibers have been reported to have various shapes, such as circular, triangular, C-shaped, kidney-shaped, and so forth, so that the stress concentration between the fibers is complicated [8; 9; 10; 11; 12; 13; 14; 15; 16]. Moreover, it has a larger specific surface area due to its irregular shape; therefore, better mechanical properties are attained [17]. It has also been found that it is not appropriate to simplify circular fibers using the popular Hough transform when having irregular fiber shapes [18]. To construct more actual RVEs, various fiber shapes were proposed to see the effect of the shape of fibers for the mechanical properties. However, their shape was still regular because it was derived from the mathematical equation, not real experimental data [13; 14]. Thus, an algorithm based on the shape from the experimental data is urgently required to generate realistic RVEs. Recently, a shape-library approach was introduced to generate the carbon nanotube morphology from a database constructed from the experimental data through micro-computed tomography (CT) analyses to predict the electrical resistivity [19], and it turned out that a prediction with the shape-library approach was accurate as well as promising because it can reflect the experimental data into a prediction model. Similarly, 3D particle shapes were extracted from CT analysis; they were used to reconstruct many RVE samples [20; 21]. However, no studies have been reported on the generation of RVEs using a shape library composed of 2D particle shapes of unidirectional composites. The objective of this work is to generate RVEs considering the actual fiber shape of unidirectional composites with the aid of a shape-library approach. A particle-shape library was constructed by extracting fiber shapes from real microscopic images of M55J/M18 composites whose fiber shape is rather irregular using the signed-distance-based mesh trimming scheme, which we proposed in our previous work [18; 22]. Then, random sequential expansion (RSE) [23] and random fiber removal (RFR) [24; 25] algorithms were applied to generate many RVE samples with various volume fractions (\(V_{f}\)). The spatial and physical statistical metrics were calculated to confirm the randomness of the actual noncircular fiber arrangements. In addition, to compare the performance of the proposed RVEs with that of conventional RVEs with circular fibers, the effective elastic properties were compared by applying the properties of M55J/M18 and T300/PR319 composites, which are unidirectional composites showing transverse isotropy. Finally, the trend of the maximum von Mises stress in the matrix was investigated to determine the effect of shapes of fibers on the fracture strength of the material.