Convergence Behavior of High-Resolution Finite Element Models of Trabecular Bone

Journal of Biomechanical Engineering - Tập 121 Số 6 - Trang 629-635 - 1999
Glen L. Niebur1, Jonathan C. Yuen1, Andy C. Hsia2, Tony M. Keaveny3
1Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740
2Ford Motor Company, Dearborn, MI 48073
3Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740; and Department of Orthopædic Surgery, University of California, San Francisco, CA

Tóm tắt

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.

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Thông tin xuất bản

Journal of Biomechanical Engineering

Tập 121 Số 6

629-635

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