Application of the Tsai-Wu quadratic multiaxial failure criterion to bovine trabecular bone

As a first step toward development of a multiaxial failure criterion for hu man trabecular bone, the Tsai-Wu quadratic failure criterion was modified a s a function of apparent density and applied to bovine tibial trabecular bo ne. Previous data from uniaxial compressive, tensile, and torsion tests (n = 139 total) were combined with those from new triaxial tests (n = 17) to c alibrate and then verify the criterion. Combinations of axial compression a nd radial pressure were used to produce the triaxial compressive stress sta tes. All tests were performed with minimal end artifacts in the principal m aterial coordinate system of the trabecular network. Results indicated that the stress interaction term F-12 exhibited a strong nonlinear dependence o n apparent density (r(2) > 0.99), ranging from -0.126 MPa-2 at low densitie s (0.29 g/cm(3)) to 0.005 MPa-2 at high densities (0.63 g/cm3). After calib ration and when used to predict behavior of new specimens without any curve -fitting, the Tsai-Wu criterion had a mean (+/- SD) error of -32.6 +/- 10.6 percent Except for the highest density triaxial specimens, most (15/17 spe cimens) failed at axial stresses close to their predicted uniaxial values, and some reinforcement for transverse lending was observed We conclude that the Tsai-Wu quadratic criterion, as formulated here, is at best only a rea sonable predictor of the multiaxial failure behavior of trabecular bone, an d further work is required before it can be confidently applied to human bo ne.