Asymptotic Expansion Homogenization And Its Applications In Elastic Modulus Of Cancellous Bone

Based on asymptotic expansion homogenization,the numerical relationship between apparent density and equivalent elastic modulus of cancellous bone are studied using finite element program.Based on asymptotic expansion homogenization,the finite element scheme are derived and the finite element program are get. Because research object is micro model of cancellous bone that is a 3D structure, we choose hexahedron non-conforming element. Implementation procedure of finite element program has been studied elaborated, including how to handle inside DOF; how to store global stiffness matrix; how to solve linear equations; how to handle boundary conditions and preprocessing.The numerical relationship between apparent density and equivalent elastic modulus of cancellous bone are fitted using linear regression, quadratic polynomial, cubic polynomial and the exponential, and we get the equations. Besides, exponential equation was get by piecewise fitting. Finally, the numerical relationship between proportion elastic modulus and equivalent elastic modulus of cancellous bone are studied.