# Thermoforming Simulation of Woven Carbon Fiber Fabric/Polyurethane Composite Materials
## 1 Introduction
The continuous method [10; 11; 12; 13; 14; 15; 16; 17] treats thermoplastic composites as continuous, uniform, and macroscopic materials, using conventional shell or membrane elements. This method considers the shear and bending behavior of the combination of fiber and resin, but in fact, the large sliding and rotation between fibers are not considered. In comparison, the discrete method [18; 19; 20] treats the woven fabric as a micro-mechanical materials model that has the behavior of fiber reorientation, a trellis mechanism, and viscoelasticity. In addition, the resin is modeled separately and combined with the fabric model to simulate the thermoforming process of thermoplastic composites. This method covers the full mobility of the fabric's microstructure and effectively represents the macroscopic behavior of the composite. Through this model, the influence of different material properties on macroscopic behavior can be studied. Furthermore, this method can also reveal large deformation, localization, and damage-related behaviors. However, because of the micro-mechanical models, a lot of fiber and resin parameters are needed, and some of them may be difficult to accurately obtain. One alternative selection to maintain the advantage and avoid the disadvantages of the above two methods is the semi-discrete method [21; 22], in which special continuous elements are developed and affected by the micro-mechanical behavior. The most important part of the discrete method is to describe the movement of both the fill yarn and the warp yarn in a fabric. A hyperelastic model was proposed by [PERSON] et al. [23] to predict the deformed geometry of a woven fabric under external loads. They conducted the experiments of both shear test and biaxial tension to validate the model. A special hexahedral finite element, in which a hyperelastic constitutive law was used to simulate the transverse properties of segment yarns, was developed by [PERSON] et al. [24]. Under a non-isothermal forming process, [PERSON] et al. [25] used a hybrid-unit-cell model in which beam elements and shell elements were combined to predict the fiber behavior. For the stamping of a preform using a spherical punch, [PERSON] et al. [26]demonstrated the applicability of a combination model consisting of truss elements for the tow scissoring and sliding and shell elements for the tow friction and angle jamming. In this work, the thermoforming behavior of composite structures composed of woven carbon fiber fabric/polyurethane was simulated by a finite element method and compared with experimental results. To characterize the thermoplastic composite, differential scanning calorimeter and dynamic mechanical analyses were performed. To simulate the deformation conditions of the composite sheets, the above-mentioned discrete method, wherein the woven carbon fabric and resin were described using different material models, was utilized. To verify this finite element simulation, bias extension tests under three constant temperatures were executed and compared numerically and experimentally. After that, the woven carbon fiber fabric/polyurethane thermoplastic composite sheets were pressed into a U-shaped structure or small luggage under temperature and pressure control. The deformed profile and fiber-included angles were the main points for the comparison between the simulation and experiment.