| Accurately characterizing the mechanical properties of bones is of great significance to the fields of engineering technology and medicine.In the field of engineering,automobile accidents cause a large number of casualties every year,and the design of safety protection equipment in the process of automobile collision needs to know the mechanical properties of human bones accurately.In the field of medicine,knowing the mechanical properties of human bones is helpful to evaluate the effect of treatment measures for bone diseases in clinical trials,which plays an important role in studying fractures and other bone diseases caused by osteoporosis.Nanoindentation can measure the micro-mechanical properties of bone,which breaks through the limitation of traditional biomechanical test on samples.However,the obtained mechanical properties of bone are limited,and the commonly used Oliver-Pharr(OP)analysis method also has limitations on heterogeneous materials such as cortical bone.Therefore,it is very important to use finite element method to solve the mechanical parameters of bone reversely.The load-depth curve of nanoindentation is not a one-toone mapping relationship with elastic-plastic parameters.Introducing other additional test parameters(height of pile up or double indenters)to solve the multi-solution problem is not suitable for bones,and reverse analysis using representative strain may be controversial.Therefore,it is very important to propose a method to accurately obtain the elastic-plastic parameters of bones from the load-depth curve of nanoindentation.The main contents of this study are as follows:1、Combing with the finite element method,a reverse identification algorithm is proposed to obtain the elastic-plastic parameters of the bone from the cyclic loading and unloading load-depth curve of the spherical indenter.A global optimization strategy for updating approximate model based on region of interest reduction was constructed using LS-OPT and Abaqus.The influence of model size,mesh type,mesh accuracy,friction and other factors on the load-depth curve were explored.The results showed that the length and width of the model should be more than 10 times and 5times of the spherical indenter radius to avoid the size effect on the calculation.The influence of mesh accuracy and friction factor on load-depth curve should be carefully considered.2、Using finite element simulation analysis,the identification results of material parameters under four different maximum indentation depths(0.06 R,0.1R,0.2R,0.3R)were explored.The research shows that the proposed identification algorithm can obtain unique solution with high accuracy at different indentation depths(including the shallow indentations).At the same time,the results of reverse identification of material parameters under load control cyclic loading and different cyclic loading and unloading times(1,5,10)under displacement control were explored.Research showed that there may be multiple solutions under load control,and the number of cyclic loading determined the uniqueness of the solution.Using 10 or more loading times can enhance the work hardening characteristics to obtain the hardening index accurately,however,1 and 5 loading times were not enough to characterize the hardening characteristics,there was a multi-solution problem in the solution process.3、The DOE(Design of Experiment)analysis of three material parameters was carried out by Isight,and the influence of three parameter factors on the response of objective function at different levels was studied.The main effects analysis showed that the yield stress and hardening exponent had a linear negative effect on the objective function,and there was a second-order main effect between the young’ modulus and the objective function.The interaction effect analysis and Pareto analysis further showed that the three parameters had obvious interaction with each other,and the interaction effect of young’ modulus and yield stress,young’ modulus and hardening exponent has a negative effect on the objective function.The interaction effect of yield stress and hardening exponent has a positive effect on the objective function.Among the three groups of interaction effects,the interaction effect of young’ modulus and yield stress has the greatest influence on the objective function,and the interaction effect of yield stress and hardening exponent has the least influence.4、Nanoindentation test and tensile test were carried out on Q355,the elasticplastic parameters of Q355 were obtained by identification algorithm.The results were compared with the stress-strain curve obtained by tensile test.The optimized loaddepth curve was in good agreement with the experimental curve,and there was a big error in the identification effect of young’ modulus,which might be related to the minimum influence of young’ modulus and the test method.The yield stress and hardening exponent obtained were consistent with the existing research data.Nanoindentation samples were prepared in four quadrants of bovine femoral cortical bone anterior,posterior,medial,and lateral,and the mechanical parameters of different areas of cortical bone were identified by load-depth curve.The results showed that the loading section of the load-depth curve was in good agreement with the experimental curve,there was a certain deviation in the unloading section,and there was a big error in the young’ modulus.The hardening exponent of the posterior quadrant was large,converging to the upper boundary,and the solution results of other quadrants were basically within the reference range of the literature.In conclusion,this study puts forward a new method for obtaining the mechanical properties of bones from the load-depth curve of nanoindentation test.Although it still has certain limitations in identifying material parameters,it is of great significance in characterizing the mechanical properties of bones,establishing a high fidelity bio-finite element model,developing automobile safety protection devices and evaluating the therapeutic effects of related measures for bone diseases. |
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