Convergence Behavior of High-Resolution Finite Element Models of Trabecular BoneSource: Journal of Biomechanical Engineering:;1999:;volume( 121 ):;issue: 006::page 629DOI: 10.1115/1.2800865Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 μm and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 μm resolution, the differences in apparent Young’s modulus at 40 μm resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 μm resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.
keyword(s): Resolution (Optics) , Bone , Finite element model , Shear (Mechanics) , Biological tissues , Thickness , Density , Elasticity , Stress , Polynomials , Shear modulus AND Modeling ,
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contributor author | G. L. Niebur | |
contributor author | A. C. Hsia | |
contributor author | T. M. Keaveny | |
contributor author | J. C. Yuen | |
date accessioned | 2017-05-08T23:58:57Z | |
date available | 2017-05-08T23:58:57Z | |
date copyright | December, 1999 | |
date issued | 1999 | |
identifier issn | 0148-0731 | |
identifier other | JBENDY-25898#629_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/121761 | |
description abstract | The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 μm and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 μm resolution, the differences in apparent Young’s modulus at 40 μm resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 μm resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Convergence Behavior of High-Resolution Finite Element Models of Trabecular Bone | |
type | Journal Paper | |
journal volume | 121 | |
journal issue | 6 | |
journal title | Journal of Biomechanical Engineering | |
identifier doi | 10.1115/1.2800865 | |
journal fristpage | 629 | |
journal lastpage | 635 | |
identifier eissn | 1528-8951 | |
keywords | Resolution (Optics) | |
keywords | Bone | |
keywords | Finite element model | |
keywords | Shear (Mechanics) | |
keywords | Biological tissues | |
keywords | Thickness | |
keywords | Density | |
keywords | Elasticity | |
keywords | Stress | |
keywords | Polynomials | |
keywords | Shear modulus AND Modeling | |
tree | Journal of Biomechanical Engineering:;1999:;volume( 121 ):;issue: 006 | |
contenttype | Fulltext |