## 1 Introduction  
Cortical bone is regarded as a load-bearing material, and its fracture performance directly determines the mechanical properties of bone structure and the fracture risk [1]. Therefore, the premise for exploration of the methods to prevent and treat fracture is a thorough understanding of the failure process in cortical bone structure under different loading conditions [2]. Many experimental studies have focused on the cortical bone failure process in the past. They observed the entire process from elastic deformation to fracture and depicted the load-displacement curve in the cortical bone structure, and calculated the fracture parameters based on the mathematical methods, which assisted in the investigation of the cortical bone fracture performance [3, 4].  
The cortical bone sample is relatively difficult to obtain, and the experimental research has the inconvenience of not being able to observe the internal mechanical state of the structure in real-time [5]. With the development of fracture mechanics and finite element (FE) method, the number of fracture simulation studies for cortical bone increased gradually. The linear elastic fracture model based on the virtual crack closure technique was used to simulate in the early stage, and the model was suitable for brittle fracture simulation, but the fracture path needed to be defined [6, 7, 8]. Because the damage and failure process in cortical bone structure is difficult to determine in advance, this poses a certain obstacle to practical application. Current fracture simulations for cortical bone structure are mainly based on three numerical methods. The first is the element instantaneous failure (EIF) method. This method directly reduces the stiffness of the element to zero when it reaches the failure condition, and simulates the apparent fracture in bone structure through the accumulation of the failed elements; it is easy to implement and reach convergence [9, 10]. The second is the continuum damage mechanics (CDM) method. This method allows the stiffness to gradually decrease in the damaged element and simulates the apparent fracture in bone structure through the accumulation of the failed elements, but the damage evolution law in the damaged element is difficult to determine [11, 12]. The third is the extended finite element method (XFEM). This method extends the degrees of freedom by using a special displacement function to allow the existence of discontinuous fields within the damaged element, and the crack can be arbitrarily extended along the damage evolution law which is based on the traction-separation mechanical behavior, but the computational cost of this method is greater than the other methods [13, 14].  
In summary, each numerical method has its own mechanical characteristics for predicting cortical bone fracture, so the simulation application field under various loading conditions may be different [15]. However, few studies have investigated the differences in prediction accuracy under the three numerical methods. This study aimed to evaluate the accuracy and applicability of the three numerical methods in simulating cortical bone fracture under three-point bending load. The rat femur samples were first obtained and used in the three-point bending experiment. Then, the rat femur FE models were established on the basis of the femoral micro images, and the three fracture simulations under three-point bending were performed. The predicted results in each simulation were compared with the experimental data to determine the prediction accuracy. Meanwhile, the fracture parameters and fracture patterns among the three simulations were compared and analyzed to reveal the reason for the differences in the predicted results. Finally, the numerical method that was suitable for simulating cortical bone fracture under three-point bending load was determined.