Objective To predict the tissue-level failure strain of the cortical bone and discuss the effects of different running speeds on the mechanical properties of rat femoral cortical bone.Methods The threshold for cortical bone tissue-level failure strain was assigned,and fracture simulation under three-point bending was performed on a rat femoral finite element model.The predicted load-displacement curves in each simulation were compared and fitted with the experimental data to back-calculate the tissue-level failure strain.Results The cortical bone tissue-level failure strains at different running speeds were statistically different,which indicated that different running speeds had certain impacts on the micromechanical properties of the cortical bone structures.At a running speed of 12 m/min,the cortical bone structure expressed the greatest tissue-level failure strain,and at a running speed of 20 m/min,the cortical bone structure expressed the lowest tissue-level failure strain.Conclusions Based on the changing trends of tissue-level failure strain and in combination with the changes in macro-level failure load and tissue-level elastic modulus of cortical bone structures,the effects of different running speeds on the mechanical properties of cortical bone structures were discussed in this study.The appropriate running speed for improving the mechanical properties of the cortical bone was explored,thereby providing a theoretical basis for improving bone strength through running exercises.

BACKGROUND:Current fracture simulation for cortical bone structure is mainly based on three numerical methods:the element instantaneous failure,continuum damage mechanics,and extended finite element methods.Although many studies focus on cortical bone fracture simulation,few have compared the differences in prediction accuracy using the three numerical methods. OBJECTIVE:To probe the accuracy and applicability of the three numerical methods in simulating cortical bone fracture under bending load. METHODS:The rat femur samples were primarily used to perform the three-point bending experiment.The rat femoral finite element models were established based on the micro-CT images of the femur samples and the three numerical methods were used to conduct the fracture simulations under three-point bending loads.The predicted fracture loads and fracture patterns were compared with the experimental data to determine the accuracy of various numerical methods in simulating cortical bone fracture. RESULTS AND CONCLUSION:(1)The discernible differences in the failure processes could be observed in the same finite element model under the three numerical simulations due to different element failure strategies.(2)The simulation results showed that the fracture simulation using the continuum damage mechanics method was in better agreement with the experimental results.(3)The numerical method that was suitable for simulating cortical bone fracture under bending load could be determined by comparing it with experimental results.The variations in the fracture parameters were observed,and the reason for the differences in the predicted results using different numerical methods was also discussed,which aided in determining the range of applicability of structural fracture simulation for each numerical method and then improving the simulation accuracy.

BACKGROUND: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 modes even in the same structure. OBJECTIVE:To propose an approach to predict the critical energy release rate in the femoral cortical bone structure under different failure modes. METHODS:Three-point bending and axial compression experiments and the corresponding fracture simulations were performed on the rat femoral cortical bone structures.Different critical energy release rates were repeatedly assigned to the models to perform fracture simulation,and the predicted load-displacement curves in each simulation were compared with the experimental data to back-calculate the critical energy release rate.The successful fit was that the differences in the fracture parameters between the predicted and experimental results were less than 5%. RESULTS AND CONCLUSION:(1)The results showed that the cortical bone structure occurred tensile open failure under three-point bending load,and the predicted critical energy release rate was 0.16 N/mm.(2)The same cortical bone structure occurred shear open failure under axial compression load,and the predicted critical energy release rate was 0.12 N/mm,which indicates that the critical energy release rate of the same cortical bone structure under different failure modes was different.(3)A comprehensive analysis from the perspectives of material mechanical properties and damage mechanism was conducted to reveal the reasons for the differences in the critical energy release rate in the cortical bone structure under different failure modes,which provided a theoretical basis for the measurement of the energy release rate and the accurate fracture simulation.

Objective To predict the micro-level energy release rate in the rat femoral cortical bone and investigate the variation in the micro-level energy release rate with age.Methods Based on previous experimental data and numerical simulation of fracture modes for cortical bone,load-displacement curves and fracture modes measured by simulation and experiment were compared,and the micro-level energy release rates of rat femoral cortical bone at different months were predicted by back-calculation.Results It was predicted that the micro-level energy release rate of rat femoral cortical bone at 1-,3-,5-,7-,9-,11-,and 15-month age was 0.08-0.12,0.12-0.14,0.15-0.19,0.25-0.28,0.23-0.25,0.19-0.22,and 0.13-0.16 N/mm,respectively.Conclusions The decrease in the microlevel energy release rate with increasing age led to a decreasing failure load,indicating that the microlevel energy release rate is one of the main factors determining fracture occurrence;however,no significant decrease was observed at the time of fracture,indicating that the microlevel energy release rate was not linearly proportional to the fracture time.These results can help explain the mechanism of cortical bone fractures at the clinical level.