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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December 1999
Technical Papers
Convergence Behavior of High-Resolution Finite Element Models of Trabecular Bone
G. L. Niebur,
G. L. Niebur
Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740
e-mail: gln@biomech2.me.berkeley.edu
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J. C. Yuen,
J. C. Yuen
Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740
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A. C. Hsia,
A. C. Hsia
Ford Motor Company, Dearborn, MI 48073
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T. M. Keaveny
T. M. Keaveny
Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740; and Department of Orthopædic Surgery, University of California, San Francisco, CA
e-mail: tmk@me.berkeley.edu
Search for other works by this author on:
G. L. Niebur
Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740
e-mail: gln@biomech2.me.berkeley.edu
J. C. Yuen
Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740
A. C. Hsia
Ford Motor Company, Dearborn, MI 48073
T. M. Keaveny
Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740; and Department of Orthopædic Surgery, University of California, San Francisco, CA
e-mail: tmk@me.berkeley.edu
J Biomech Eng. Dec 1999, 121(6): 629-635 (7 pages)
Published Online: December 1, 1999
Article history
Received:
October 28, 1998
Revised:
July 21, 1999
Online:
October 30, 2007
Citation
Niebur, G. L., Yuen, J. C., Hsia, A. C., and Keaveny, T. M. (December 1, 1999). "Convergence Behavior of High-Resolution Finite Element Models of Trabecular Bone." ASME. J Biomech Eng. December 1999; 121(6): 629–635. https://doi.org/10.1115/1.2800865
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