Microstructure Modeling And Multi-scale Numerical Simulation Of Mechanical Properties Of Bone Materials

Bone is an important organ of the human body and an important part of the human motion system.Important physiological functions of the bone,such as exercise,weight bearing and protection of internal organs,are closely related to the mechanical properties of the bone.The morphology of the bone is determined by gene,but to the large extent its structure depends on mechanical environment.The process of bone regulates its own structure and form under situation of change of mechanical environment is called bone remodeling.For any biological individual,bone remodeling runs through their entire life.The research on bone remodeling has become an important research direction and a hotspot in the field of bone biomechanics.Researchers from all over the world positively explore the mechanism of bone remodeling,hoping to provide some guides for the prevention and therapy of bone diseases,the design and optimization of bone implant structures.With the development of scientific computing technology,numerical methods represented by finite element have become a major tool for studying bone remodeling.Combining bone adaptability theory and analysis of finite element can reproduce the entire process of bone remodeling,predict and analyze the mechanical properties of different stages of the bone much more accurately.In this thesis,by using cancellous bone unit cell microstructure modeling techniques,multi-scale methods based on the homogenization theory,a series of numerical simulation studies are carried out around structural and mechanical properties of bone materials and bone remodeling.The main research results are as follows:The theories of bone remodeling are systematically introduced,and the microscopic mechanism of bone remodeling and the mechanical excitation of bone remodeling are clarified.On this basis,a new smooth bone remodeling adaptive control equation is proposed,which introduces minor changes,that is the dead zone effect be more in line with the mechanical characteristics of bone as a living composite.In addition to describing the stable bone growth,under-load absorption and over-load absorption,this equation also adds the dead zone effect of two bone remodelings.This equation inherits the mathematical characteristics of various traditional equations,adds the effect of loading rate on the evolution of bone density,and qualitatively reproduces irreversible damage to bones due to high loading rates.There are many parameters that influence the results in the governing equation,such as initial density,excitation reference value,time-dependent constant,etc.In order to study the influence of these parameters on the convergence results and convergence speed,the sensitivity analysis of the parameters is performed in this thesis.The results show that the initial density has little influence on the convergence result and the convergence speed,while the excitation reference value has obvious influence on the convergence value and the convergence speed,and the time-dependent constant mainly influence the convergence speed.Bone remodeling cause structural changes and bone mass redistribution,which further leads to changes in bone material properties.Therefore,it is necessary to determine the constitutive relationship of bone materials,especially cancellous bone,with the distribution of bone mass.Therefore,it is necessary to determine the change rule of the constitutive relationship of bone materials,especially cancellous bone,with the distribution of bone mass.Because the constitutive relationship of cancellous bone is determined by its microstructure,accurate geometric modeling is very important for predicting material properties.In this thesis,a new microstructure unit cell model is established by introducing Schwarz surface,which has only one parameter,achieves porosity in the range of 15%-80%,and rapid generation of cancellous bone in different parts and different age groups.By comparing with CT scan images,it was found that this single cell is very close to the real bone microstructure,which well satisfies the main biological characteristics of cancellous bone.Then,using the unit cell model,the mechanical parameters such as equivalent elastic modulus,equivalent shear modulus and Poisson’s ratio of cancellous bone under different bone densities were predicted by the second-order multi-scale analysis method,and the influences of porosity of cancellous bone on these parameters were studied.The whole bone remodeling process simulation is a complex iterative process.In this thesis,the unit strain energy is used as the control variable,the equivalent parameters obtained from the multi-scale method and the newly proposed governing equation is used to program the two-dimensional plate cancellous bone and femur stress remodeling.For the two-dimensional plate structure,the changes in the absorption and osteogenesis of the trabeculae with changes in load are consistent with the results of existing experimental studies.For the femur,the bone density distribution obtained from the remodeling simulation is very close to that obtained from CT.The results of these examples show the validity and feasibility of the proposed governing equations and unit cell model in the finite element simulation of bone remodeling.Considering that the multi-scale method can not only effectively predict the equivalent parameters of the material,but also accurately reproduce the local features in the cancellous bone unit cell.Therefore,the proposed method in this thesis provides new ways for studying the bone remodeling from the microscopic structure.