Trabecular bone is a major load-bearing tissue in the musculoskeletal system and is subjected to various multi-axial loads in vivo. For example, in the vertebral body, the trabecular bone is primarily subjected to uniaxial loads, in the proximal femur, trabecular bone is subjected to biaxial loads i.e. loads oriented at two mutually perpendicular directions, in distal radius, the trabecular bone can subjected to shear loads due to off-axis loading during a traumatic event. Understanding the multi-axial strength and underlying tissue-level failure mechanisms of human trabecular bone is of great clinical and scientific importance since age-related osteoporotic fractures primarily occur at trabecular bone sites, such as the hip, spine and wrist. With the onset of osteoporosis, there is an increase in porosity and deterioration of the microarchitecture of trabecular bone, which results in increased fragility and fracture susceptibility of trabecular bone.

Using high-resolution, micro-CT based nonlinear finite element models, we investigated the strength of trabecular bone under compression, shear, biaxial and multiaxial loading conditions. Under uniaxial loading, it was shown that the variation in both compressive and shear strength was primarily attributed to the volume fraction of the trabecular bone, but the observed scatter in the ratio of the shear and compressive strength was attributed to heterogeneity and anisotropy of the trabecular microarchitecture. At the tissue-level, it was shown that shear loading leads to predominantly tensile tissue failure unlike compression loading that makes trabecular bone much weaker under shear loading. Under biaxial loading, it was shown that the yield strength varied with both volume fraction and anisotropy, and most of the variation in biaxial strength could be primarily attributed to similar variation of the uniaxial strengths with minor variations due to trabecular microarchitecture. Based on these results, the complete multi-axial yield strength behavior of trabecular bone was investigated for over 200 multi-axial load cases. A new yield strength criterion was then formulated in the six-dimensional strain space to mathematically characterize the multiaxial failure criterion of human trabecular bone.

The research presented in this dissertation has provided considerable insight into the variation of both apparent-level strength and the tissue-level failure mechanisms of trabecular bone under various loading conditions. The role of bone volume fraction, anisotropy and microarchitecture on the uniaxial and multi-axial strength has been outlined. A multi-axial failure criterion has been formulated which can be used to noninvasively predict the strength of whole bones of osteoporotic patients using clinical CT scans.