| Homogenization theory is an effective method for analyzing the distortion, stress, properties, heat exchange etc. of the composite material which has the periodical structure.The poly-bore cancellous bone can be see as the periodical micro-structure, the cycling loads on the cancellous bone may cause the fatigued damage on cancellous bone as men do daily movement ,and these can cause the emergence of microcracks on trabecular. In order to recognize the damage degree on damaged cancellous bone, we may study the rule of elastic modulus with respond to damage degree by using homogenization theory,integrating with the finite element method ,this paper firstly systemic analyzed the effect on rigidity of cancellous bone caused by mirocracks on trabecular systemicly.Firstly ,we synthetized the current reports on the form and the distribution of the mirocracks on cancellous bone and the effect on the mechanic property caused by microcracks.The general idea is the following :the form of miro-cracks and the diffuse damage character of vivo cancellous bone is that the microcrack mainly has two form , linear form and cross—hatched form ,the most ones are linear form, while the one on surface often appears as a group of parallel cracks ,they locate at vertical trabecular and parallel to the surface of the trabecular .the cross—hatched form crack is fewer than the linear one, they mainly appear at vertical trabecular. the diffuse damage mostly be found in trabecular packet on surface of the trabecular, and they are rare in the center of cancellous bone. The ultrastructure formed by damaged cracks can alleviate the stress on cancellous bone so as to prevent the fracture of trabecular entirely, and the exterior damage on the boundary of trabecular can be easily restore by the remodeling of the bone surface.By doing ex vivo experiment on cancellous bone and analyze the effect on the bone mechanic property we can see that: before the elastic modulus of thighbone decreases by 15%,there is no obvious accumulative damage, the accumulative damage can affect the mechanic property by reducing the modulus of bone, when the new cracks become apparent ,the previous ones can easily expand .the form of mirocracks on vivo cancellous bone and on ex vivo cancellous bone is resemble .With the increasing area of damaged bone ,the modulus of bone inclines charply at first, gradually come to stability.Based on the data of the microcrack form and the distribution character, we calculate the elastic modulus of cancellous bone with linear form and cross—hatched form mirocracks on it, using the rod-rod model structure base cell to simulate the low density cancellous bone, using the model of plate with hole structure base cell to simulate the high density one, we suppose the solid part of the cancellous bone is isotropy, whose elastic modulus is 5.0Gpa,and the possion ratio is 0.3,based on homogenization theory, we workout a special finite element procedure to calculate the elastic modulus of cancellous bone after being damaged, the result show that: when the bone density is low, the elastic modulus of damaged trabecular in main stress direction declines when the crack thickness increases, and the incline rate less than linear rate, but it inclines more than linear rate when the crack width increases. this phenomenon indicates that the crack width has the worse effect than the crack thickness. when the crack is linear form, the degressive rate of elastic modulus according to bone mass decrease more than linear rate, while the crack is cross—hatched form, it decrease more than linear rate, the effect of the linear form crack have on the cancellous bone is larger than that the cross—hatched orm crack have on it. these conclusion is important to study the change of rigidity of cancellous bone after it been damaged, they also has significance for preventing bone disease and for rehabilitate the damage of the trabecular.In the third place, we study the rule of change rate of elastic modulus when the microcrack spreads, we usi... |
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