Application of the Tsai–Wu Quadratic Multiaxial Failure Criterion to Bovine Trabecular Bone

[+] Author and Article Information
T. M. Keaveny

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

E. F. Wachtel, S. P. Zadesky, Y. P. Arramon

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

J Biomech Eng 121(1), 99-107 (Feb 01, 1999) (9 pages) doi:10.1115/1.2798051 History: Received December 10, 1997; Revised August 20, 1998; Online October 30, 2007


As a first step toward development of a multiaxial failure criterion for human trabecular bone, the Tsai–Wu quadratic failure criterion was modified as a function of apparent density and applied to bovine tibial trabecular bone. Previous data from uniaxial compressive, tensile, and torsion tests (n = 139 total) were combined with those from new triaxial tests (n = 17) to calibrate and then verify the criterion. Combinations of axial compression and radial pressure were used to produce the triaxial compressive stress states. All tests were performed with minimal end artifacts in the principal material coordinate system of the trabecular network. Results indicated that the stress interaction term F12 exhibited a strong nonlinear dependence on apparent density (r2 > 0.99), ranging from −0.126 MPa−2 at low densities (0.29 g/cm3 ) to 0.005 MPa−2 at high densities (0.63 g/cm3 ). After calibration 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 specimens) failed at axial stresses close to their predicted uniaxial values, and some reinforcement for transverse loading was observed. We conclude that the Tsai–Wu quadratic criterion, as formulated here, is at best only a reasonable predictor of the multiaxial failure behavior of trabecular bone, and further work is required before it can be confidently applied to human bone.

Copyright © 1999 by The American Society of Mechanical Engineers
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