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

Abstract

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.