A Cellular Solid Criterion for Predicting the Axial-Shear Failure Properties of Bovine Trabecular Bone

[+] Author and Article Information
C. M. Fenech

Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720

T. M. Keaveny

Orthopædic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720; Department of Orthopædic Surgery, University of California, San Francisco, CA 94143

J Biomech Eng 121(4), 414-422 (Aug 01, 1999) (9 pages) doi:10.1115/1.2798339 History: Received March 17, 1998; Revised February 11, 1999; Online October 30, 2007


In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai–Wu, Principal Strain, and von Mises phenomenological criteria—all normalized to minimize effects of interspecimen heterogeneity of strength—to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (± S.D.) percentage errors between measured values and criterion predictions were 7.7 ± 12.6 percent, 19.7 ± 23.2 percent, 22.8 ± 18.9 percent, and 82.4 ± 64.5 percent for the Cellular Solid, Tsai–Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were –5.2 ± 11.8 percent, 14.3 ± 12.5 percent, 6.9 ± 7.6 percent, and 57.7 ± 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.

Copyright © 1999 by The American Society of Mechanical Engineers
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