A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone

In a long-term effort to develop a complete multi-axial failure criterion f or human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai-W u, 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 C ellular Solid criterion that was developed here assumed that vertical trabe culae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, r espectively. Twenty-seven bovine tibial trabecular bone specimens were dest ructively tested on-axis without end artifacts, loaded either in combined t ension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6 ). For compression-shear, the mean (+/- S.D.) percentage errors between mea sured 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 Cell ular Solid. Tsai-Wu, Principal Strain, and von Mises criteria, respectively ; corresponding mean errors for tension-shear were -5.2 +/- 11.8 percent, 1 4.3 +/- 12.5 percent, 6.9 +/- 7.6 percent, and 57.7 +/- 46.3 percent. Stati stical analysis indicated that the Cellular Solid criterion was the best pe rformer for compression-shear, and performed as well as the Principal Strai n criterion for tension-sheer. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More impor tantly the results firmly establish the importance of cellular solid analys is for understanding and predicting the multiaxial failure behavior of trab ecular bone.