## 2 Multiscale Modeling of Carbon-Fiber-Reinforced Composite
### Microscale Model Simulation Analysis
#### 2.2.1 Microscale Model Simulation Analysis Method  
The woven yarns in CFRP are composed of fiber filaments and resin, as shown in Figure 2. The cross-sectional structure of the woven yarns is observed using an electron microscope (model JSM-IT300 LA) to obtain a realistic microscale model, which is then approximated to an equivalent microscale cell through homogenization. As can be seen from Figure 2, the microscale cell is composed of carbon fiber filaments, represented by the yellow area, and resin, represented by the gray area. The geometric parameters of the microscale cell mainly include the diameter of the fiber filaments, the thickness of the cell, and the half-side length (\(x_{1}\)) of the cell. Previous literature studies have shown that the main factor affecting the elastic properties of the microscale cell structure is the fiber volume fraction (\(V_{\text{f}}\)) [21; 23]. Therefore, in this paper, while the fiber diameter and cell thickness are fixed, different \(V_{\text{f}}\) are obtained by setting different half-side lengths \(x_{1}\) for the microscale cell, that is, choosing the \(x_{1}\) of the microscale cell shown in Figure 2 as the microscale design variable. In this study, T700-12k carbon fibers are used, and the resin selected is EPOLAM 5015 RESIN epoxy. The mechanical properties of both the fibers and the resin are presented in Table 1.  
A microscale cell model, as depicted in Figure 2, was developed in ABAQUS for the predictive analysis. In this model, the fiber-reinforced phase is represented by the yellow region, while the resin matrix is indicated by the gray area, comprising a fiber volume fraction of 51%. The analysis involved constructing a finite element model of the microscale cell in ABAQUS, inputting material parameters for each component as listed in Table 1, specifying material orientations, and setting up a thermal stress analysis step. The mesh was created using C3D8R elements with a side length of 0.4 mm. A custom For \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{\(\mathbf{E_{1}/GPa}\)} & \(\mathbf{E_{2}=}\) & \(\mathbf{G_{12}=}\) & \multirow{2}{*}{\(\mathbf{G_{23}/GPa}\)} & \multirow{2}{*}{\(\mathbf{\mu_{12}=\mu_{13}}\)} & \multirow{2}{*}{\(\mathbf{\mu_{23}}\)} \\  & & & & & & \\ \hline Fiber & 227.0 & 13.4 & 6.8 & 4.8 & 0.2 & 0.25 \\ Matrix & 3.3 & - & - & - & 0.35 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of T700/EPOLAM 5015 RESIN used in the multiscale design. Figure 2: Schematic view of microscale cell. tran subroutine was developed to define specific variables, and binding contact techniques were applied to enforce periodic boundary conditions on the microscale cell. Computations were executed in ABAQUS, with Figure 3 illustrating the resultant equivalent stress distribution in the microscale cell under six distinct thermal stress scenarios. Figure 3a,b displays the tensile scenarios. Specifically, Figure 3a shows stretching along the fiber direction, with the fiber serving as the main load-bearing component. The stress levels in Figure 3b,c are nearly identical, with the primary distinction being a 90\({}^{\circ}\) rotation in the stress distribution around axis one, further validating the reliability of the thermal stress-based analysis method. Figure 3d-f illustrate shear conditions, whereas Figure 3d,e exhibits almost the same stress values, yet the stress distribution is rotated 90\({}^{\circ}\) around axis one. Post-calculation, a Python script was employed to extract the results, facilitating the determination of equivalent elastic properties for the microscale cell. Figure 3: Equivalent stress contour result of different thermal stress conditions: (**a**) \(S^{11}\); (**b**) \(S^{22}\); (**c**) \(S^{33}\); (**d**) \(S^{12}\); (**e**) \(S^{13}\); (**f**) \(S^{23}\).