ABSTRACT
And fourth, since trabecular bone is anisotropic at the apparent level, it is important to distinguish between its behavior in its principal material coordinate system compared with an arbitrary coordinate system. The former is characterized mathematically as when the elastic stiffness matrix is sparse, i.e., that coordinate system for which there is no coupling between the shear and normal elastic behaviors. It has been shown analytically
and using high-resolution finite-element models
that if the anisotropy of the trabecular hard tissue is ignored-a reasonable assumption since the individual trabeculae are loaded mostly uniaxially-the principal material coordinate system of elastic anisotropy at the apparent level coincides with the principal microstructural coordinate system of the trabecular network as derived from the fabric tensor. For simplicity of nomenclature, the term
on-axis
is used here to describe the situation when loading is along the main trabecular orientation, and
off-axis
refers to when loading is oblique to this. On-axis elastic and strength properties for orthotropic or higher symmetry materials are considered as the inherent material properties since the off-axis properties (except for those at 90
off-axis) depend on both the on-axis properties and the angles of misalignment between the on-and off-axis coordinate systems. Thus, the strength properties of primary interest from a constitutive modeling perspective are those measured in the on-axis coordinate system.
