## 5 Results and Discussion
### Simulations  
Two methods mentioned above were used to carry out the finite element analysis, and the load versus displacement curve of specimen numbering \"1-5\" was represented as shown in Figure 6 due to its closest failure load compared with the average experimental ultimate load. It could be seen the numerical results matched well with the experimental data, as shown in Figure 7. The ultimate load obtained using the multiscale method GMC/Tsai-Hill was 60.80 kN, which was slightly higher than 60.03 kN acquired by using the lamina-level Hashin method. The reaction force versus displacement response obtained using both methods was also desirable. The final failure load of the specimen was determined by the 0\({}^{\circ}\) layer fiber, and the difference between the strength values obtained by the two analysis modes was quite small. On the whole, the simulation results were in good agreement with the experimental results.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Specimen Number** & **1–1** & **1–2** & **1–3** & **1–4** & **1–5** & **1–6** & **1–7** & **1–8** \\ \hline ultimate load (kN) & 61.57 & 60.34 & 59.26 & 62.51 & 60.99 & 58.09 & 63.16 & 59.98 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Ultimate loads of the composite laminate specimens.  
Figure 5: A damage contour in composite laminate specimen numbered “1–5”.  
It was observed that the failure displacement of the simulation model was smaller than that of the experimental data, which may be the reason that the effect of nonlinearity and plasticity was not taken into account in the analysis model [32]. In addition, the absence of the interface phase of composite material embedded in the GMC may be another factor contributing to the difference [33], which would be considered in our next work.  
Because the specimens tested were subjected to tensile load, tensile failure of fiber in 0\({}^{\circ}\) layers may be the main failure pattern, while the \(\pm 45^{\circ}\) layers mainly produced matrix tensile failure. Therefore, the fiber tensile failure mode of the 0\({}^{\circ}\) layer and the matrix tensile failure mode of the \(\pm 45^{\circ}\) layer were of significant concern. The failure modes and damage processes between \(-45^{\circ}\) and \(45^{\circ}\) for the damage contours plots were roughly the same, so the damage states of only 45\({}^{\circ}\) layers were represented here. It should be emphasized that a fiber subcell failure utilizing GMC/Tsai-Hill method represented the fiber failure for the whole RUC, and the matrix subcell whose failure was dominant in the three matrix subcells would be displayed for comparison and illustration. The simulation results showed that the failure of the third subcell was dominant, so in this paper, the failure of the No. 3 matrix subcell represented the failure of the matrix constituent.  
Figure 6: Load versus displacement for composite laminate specimens.  
Figure 7: Load versus displacement using both methods.  
Figures 10 and 11 were contour plots of fiber damage state for 0\({}^{\circ}\) plies in different degrees of failure using both methodologies. Fiber damage of 0\({}^{\circ}\) layers initiated when the tensile loads were 47.89 kN, as shown in Figure 10a, and continued to expand as the tensile load gradually increased. Figure 10b displayed the damage situation at 90 percent failure under the tensile load of 59 kN, after which laminated plates rapidly reached the ultimate load, and then fiber damage passed through the specimen quickly. The two methods produced different fiber failure patterns, as shown in Figure 11. A gradient of material properties due to the matrix or fiber failure could result in a bifurcated state around the open hole, but it not occurred in the experiment and the simulation by GMC/Tsai-Hill model. A similar situation existed in some of the literature [3; 34]. Hence the GMC/Tsai-Hill method could produce reasonable mechanism and physical failure, and the fiber failure path produced by GMC/Tsai-Hill was considered to be more reasonable.