## 3 Results  
Mesh sensitivity analysis was performed to determine the suitable element size for the femoral FE model. Based on the femoral micro images, different element sizes (20, 30, 40, 50, and 60 \(\upmu\)m) were selected to establish the femoral FE models. The fracture simulations for the five FE models were all performed based on the CDM method. The load-displacement curves predicted in the simulations with the five FE models were shownin Figure 3. The shape of the curve was similar when the material input parameters were the same. However, certain differences existed in the fracture load and time. The FE model with coarse element underwent complete fracture early because the damage variable rose faster for the large element size, resulting in a faster decrease in the structural stiffness. The predicted three curves had no obvious differences in the fracture parameters when the element size was in the range of 20-40 \(\upmu\)m. Therefore, the element size of the femoral FE models established in this study was set to 30 \(\upmu\) considering the prediction accuracy. The load-displacement curves predicted by the three numerical methods expressed different shapes even though the simulated object was the same FE model, as shown in Figure 4. The elastic stage in the curves from the EIF and XFEM simulations nearly coincided, and the apparent stiffness in the elastic stage from the CDM simulation curves gradually decreased. The CDM simulation curves showed a brief yielding phase after the elastic stage, followed by the apparent failure, whereas the EIF and XFEM simulation curves went straight from the elastic stage to the failure stage. The comparison of the predicted fracture parameters showed different simulation accuracy in the three numerical methods. In the EIF simulation, the apparent failure appeared first compared with other numerical methods; however, the fracture load was not significantly lower than the experimental result because the apparent stiffness in the load-displacement curve was not reduced during the elastic phase. The fracture time obtained from the XFEM simulation was similar to the experimental data, and the fracture load was significantly greater than the experimental results because the apparent stiffness in the curve during the elastic phase was also not reduced. In contrast, the fracture time and fracture load obtained from the CDM simulations were both in better agreement with the experimental results. Figure 5 shows the comparison of the fracture pattern in the FE model and femur sample under various numerical simulations and experiments. Figure 5a shows the fracture pattern in the EFI simulation. The main crack primarily appeared on the upper side of the middle femur and gradually propagated from the upper to lower sides until it penetrated the outer section of the cortical bone structure, finally leading to the apparent failure. The fracture patterns in the XFEM and CDM simulations were similar, but differed with the EFI simulation, as shown in Figure 5b,c. A few damaged elements first appeared in the upper side of the middle femur close to the rigid column, and then the majority of damaged elements appeared in the lower side of the middle femur with b  
Figure 3: Mesh sensitivity analysis for the rat femoral FE models with different mesh size. stage of the loading, the failed elements and the main crack gradually propagated from the lower to upper sides of the middle femur until they penetrated the cortical bone section. This fracture pattern was more similar to the experimental fracture pattern, as shown in Figure 5d. The differences between the fracture patterns predicted by the XFEM and CDM simulations lay in the number of damaged elements. In the CDM simulation, damage occurred as soon as the condition was satisfied, so a certain number of green damaged elements appeared in the constrained and loaded regions.