Multilevel Finite Element Analysis For Femur

As a kind of natural biological composite material consisting of collagen fibers and hydroxyapatite, bone possesses high fracture strength and fracture toughness. The excellent mechanical behaviors are closely related to the macro and micro-structures of bone. The detailed study on the macro and micro-structures could reveal the mechanism of the strength and toughness of bone and provide a useful guidance to the study of artificial bone materials.This thesis investigates the relationship between the macro and micro-structures and the mechanical behaviors of bone by the experiments and computations combining macro and micro-structure analyses. Following works are accomplished and some instructive conclusions are obtained.①The mechanical properties along two different directions of a cattle's fan bone were tested with MTS testing system. It shows that the bone is a kind of elastic and anisotropic biomaterial. The strength of the bone along the two different directions is different.②The microstructures of the bone is observed with scanning electron microscope. It is found that the collagen fibers in the bone are arranged with helicoidal structure. It is also observed that there are Havers' canals in the bone and these canals connect with each other. These experimental results provide information for model analysis.③By combining CT scanning technology, Mimics Medical Imaging software, Imageware Rapid Prototyping software and ABAQUS software, the three-dimensional finite element model of human left femur is established. It is indicated that the CT scanning technology, Mimics Medical Imaging software and Imageware Rapid Prototyping software can be applied to the research of structural analysis of bone biomaterial. These analytical softwares can greatly improve computational and simulative precision of biological materials.④Multi-scale finite element method is applied to the investigation of the distributions of stresses and strains of femur under different scales. It shows that the maximum strain obtained by the microscopic model is 4 times higher than that obtained by the macroscopic model. It is cause that the microscopic model can provide more structural detail of the bone. It also shows that the maximum strain and strain rate in the microscopic model appear in the neighborhood of the lacunae and canaliculi of the bone, which is consistent to the experimental results in the biology.⑤The relationship between the mises stresses in the fiber and adhesive layers in the osteon of the bone and the helicoidal angle of the fibers are investigated with the UMAT subprogram of ABAQUS software. It shows that in the range of 0°to 90°of the helicoidal angle, the mises stress in the fiber layer will decrease with the increase of the angle. In the range of 90°to 180°, the mises stress will increase with the increase of the angle. It also shows that in the range of 0°to 45°of the angle, the mises stress in the adhesive layer will decrease with the increase of the angle. In the range of 45°to 90°, the mises stress in the adhesive layer will increase with the increase of the angle.⑥The XFEM of ABAQUS software is also applied to simulate the growth of the microscopic cracks in bone. It reveals that the growing direction of the macroscopic crack is closely related to the direction of the microscopic crack in the bone.