Damage modeling of vertebral trabecular bone.

摘要

With the underlying goal of understanding the fracture process and risk of fracture with decreased bone mass, there has been a great deal of experimental work directed towards predicting the stiffness and strength of bones, such as vertebrae. There is strong evidence that the mechanical behavior of trabecular bone can be treated at the apparent or continuum-level, and key assumptions of this work are that the accumulation of damage is of primary importance when considering fracture risk and that this behavior can be described using continuum damage mechanics (CDM) models. Experimental study of human vertebral trabecular bone specimens under uniaxial strain-controlled loading demonstrated a high degree of nonlinearity well below the apparent yield point, and at low strains (less than 0.1%) this behavior could be successfully described with multiaxial 3-parameter generalized Maxwell models. Orthotropic damage was determined assuming a strain-energy equivalence approach, and transverse damage values were on the order of 2–3% of the axial damage values. Residual stress response and stiffness degradation observed in experimental work were described using plasticity and damage mechanics models, with parameters determined from experimental data and the literature. These models were combined, along with the viscoelastic model, in a unified constitutive model to describe the damaging viscoelastic-viscoplastic behavior of human vertebral trabecular bone. This unified model was implemented in finite element analyses and applied to the experimental stress response, demonstrating reasonable predictions of the experimental behavior. Finally, the unified constitutive model was used in finite element analyses to investigate the behavior of idealized vertebrae with uniform or focal reductions in bone mass subjected to strain-controlled loading. When differences in apparent compliance were considered, bone mass loss led to increased effect of accumulated damage, especially for focal loss and, at the element level, damage had the greatest effect in elements with lower trabecular volume fraction. Although this work represents an initial effort in the study of trabecular bone mechanics and applied investigation of vertebral behavior, a CDM-based constitutive model was successfully developed and implemented in finite element investigations at the specimen and vertebral body level.