Prediction of the critical energy release rate for rat femoral cortical bone structure under different failure conditions

Critical energy release rate is a global fracture parameter that could be measured during the failing process, and its value may change under different failure conditions even in the same bone structure. The aim of this study was to propose an approach that combined the experimental test and finite element analysis to predict the critical energy release rates in the femoral cortical bone structures under compression and three-point bending loads.Three-point bending and compression experiments and the corresponding fracture simulations were performed on the rat femoral cortical bone structures. Different values of energy release rate were repeatedly assigned to the finite element models to perform fracture simulations, and then the load-displacement curves predicted in each simulation were compared with the experimental data to back-calculate the critical energy release rate.The predicted data were similar to the experimental results when the calibrated energy release rate was suitable. The results showed that the cortical bone structure occurred shear open failure under compression load, and the predicted critical energy release rate was 0.12 N/mm. The same cortical bone structure occurred tensile open failure under three-point bending load, and the predicted critical energy release rate was 0.16 N/mm.The critical energy release rates were different under various failure conditions in one cortical bone structure. A comprehensive analysis from the perspectives of material mechanical properties, failure mode, and damage fracture mechanism was conducted to reveal the reasons for the differences in the critical energy release rate in the cortical bone structure, which provided a theoretical basis for the measurement of the critical energy release rate and the accurate fracture simulation.