## 3 Finite Element Models  
The open-hole laminated composite plates containing 24 plies were obtained from a new stringer that was cut to a specified length, and the width and length of the specimens were 24 mm and 250 mm, respectively. An open hole with a diameter of 4.76 mm was centrally located at the laminates. The number of these laminate coupons was 8, and each specimen is numbered from 1 to 8. The composite laminate material used was T800S/3900-2B, which was widely applied to the load-bearing structure of both military and civil aircraft, and the adhesion between the fiber and matrix was good. The lamina properties, such as the elastic properties and the strength parameters, as shown in Tables 1 and 2, were provided by vendors. Each ply thickness was 0.19 mm, and the number of plies, fiber orientation and total thicknesses of the laminates are shown in Table 3.  
The matrix material was considered to be isotropic, having [PERSON]'s modulus \(E_{m}\) and a [PERSON]'s ratio \(\
u_{m}\). Transversely isotropic material was applied to the fiber constituent, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**E\({}_{1}\)/GPa** & **E\({}_{2}\)/GPa** & **E\({}_{3}\)/GPa** & **G\({}_{12}\)/GPa** & **G\({}_{13}\)/GPa** & **G\({}_{23}\)/GPa** & \(\
u_{12}\) & \(\
u_{13}\) & \(\
u_{23}\) \\ \hline
149 & 10.3 & 10.3 & 7.5 & 7.5 & 3.45 & 0.29 & 0.29 & 0.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elastic properties of the T800S/3900-2B lamina. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Width (mm)** & **Stacking Sequence** & \multicolumn{3}{c}{**Number of Plies**} & \multicolumn{3}{c}{**Thickness (mm)**} \\ \hline
24 & \([45/-45/0/-45/0/45/0/0/45/0/-45/0/-45/45]\) & 14 & 2.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stacking sequences and thicknesses of the open hole laminates. where five independent elastic parameters existed. \(E_{f11}\) represented the longitudinal modulus, \(E_{f22}\) denoted the transverse modulus, \(\
u_{f12}\) was the longitudinal Poisson's ratio, and \(G_{f12}\) was the longitudinal shear modulus. The elastic properties of fiber and matrix, as shown in Table 4, were obtained from vendor data or were partially backed out from elastic lamina properties measured for T8005/3900-2B. A fiber volume fraction of 50.4 percent was used for the current simulation models. The strengths of the composite constituents are shown in Table 5, where \(X_{fh}\) and \(X_{fc}\) represented the tensile and compressive strength of the fibers, respectively, and \(Y_{mt}\), \(Y_{mc}\) and \(T_{m}\) denoted the tensile, compressive and shear strength of the matrixes, respectively. Three-dimensional eight-node reduced integration elements (C3D8R) were used in the region around the open hole of the FEA models, and the rest region utilized C3D8 in order to guarantee the accuracy of solutions, though it was also available to choose a 2D shell element for the analysis of laminate specimens. The finite element model established is shown in Figure 2. The meshes around the open hole regions were refined in size to precisely capture the stress fields and damage states. The X-Y-Z global coordinate system was introduced with its origin located in the center of the coupons, X-axis was aligned with the direction of the \(0^{\circ}\) fiber, and Y-axis was the direction perpendicular to the \(0^{\circ}\) fiber so Z represented the direction of the ply thickness. The left edge of the simulation model was fixed so that the whole translational degrees in each node were restricted, and the horizontal edges of the model had no constraints enforced. While the right edge was only allowed to move in the X direction, and it was imposed a displacement load. Static analysis was implemented using ABAQUS/Standard, in which the coupled damage and failure models were implemented using the user subroutine UMAT, and the microlevel GMC along with the failure criteria was also included.