H.H. Bayraktar, A. Gupta, R.Y. Kwok, P. Papadopoulos and T.M. Keaveny
J. Biomech. Engrg., 126, pp. 677-684, (2004)


Despite the importance of multiaxial failure of trabecular bone in many biomechanics applications, to date no complete multiaxial failure criterion has been developed. By using experimentally validated nonlinear high-resolution, micro-mechanical finite element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelop. High-resolution finite element models of three human femoral neck trabecular bone specimens obtained through micro-computer tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the three-dimensional normal strain space indicated uncoupled yield behavior, whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error +/- SD less than -0.04+/-5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error +/- SD < 2.5+/6.5%). We conclude that the four-parameter "Modified Super-Ellipsoid" yield surface presented here describes the multiaxial failure behavior of trabecular bone very well.

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