Numerical Homogenization of Trabecular Bone Specimens using Composite Finite Elements
نویسندگان
چکیده
The approach on the left does not work for merely statistically periodic microstructures because periodic boundary conditions cannot be prescribed. Instead, macroscopic strains (ū) are imposed on the boundary ∂Ω of the bounding box and the stress response σ̄ is computed on a proper interior subset Ω#β := {x ∈ Ω | dist(x, ∂Ω) > β} shown in red on the far left. This avoids boundary artifacts (stiffening due to the Dirichlet boundary conditions (right) compared to periodic boundary conditions (far right)) as illustrated for uniaxial tension in the following figure.
منابع مشابه
Numerical Homogenization of Trabecular Bone Specimens using Composite Finite Elements pdfsubject
Numerical homogenization is a tool to determine effective macroscopic material properties for microstructured materials. This tool is tailored and applied to ensembles of young and elder human and of porcine and bovine vertebral bone specimens. On the microscale of the spongiosa a linearized Lamé–Navier type elasticity model is assumed and the computed macroscopic material properties are repres...
متن کاملA homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress.
A homogenization sampling procedure is introduced which allows computation of effective trabecular bone stiffness and individual trabecula level stress based on precise models of trabecular bone architecture. Three-dimensional digitized images of 53 trabecular bone specimens with a resolution of 50 microns per voxel were directly converted into three-dimensional finite element meshes by making ...
متن کاملApplication of homogenization theory to the study of trabecular bone mechanics.
It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hypothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and/or strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstruct...
متن کاملEstimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations
In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability an...
متن کاملHomogenization for composite material properties using smoothed finite element method
Numerical homogenization is an efficient way to determine effective material properties of composite materials. Conventionally, the finite element technique has been widely used in implementing the homogenization. However, the standard finite element method (FEM) leads to an overly-stiff model which gives poor accuracy especially using triangular elements in 2D or tetrahedral elements in 3D wit...
متن کامل