7 - Size-dependent Dynamic Behavior of Trabecular Bone

Abstract

In order to investigate microstructure-related scale effects on macroscopic bone properties, Cosserat models of vertebral trabecular bone are constructed, based on micromechanical approaches. A micropolar equivalent continuum model is firstly constructed, the effective mechanical properties of which are expressed versus the geometrical and mechanical microparameters, accounting for bending, axial, transverse shear deformations, and torsion. The static and dynamic effective behaviors of vertebral trabecular bone in the form of beam structures are next analyzed, in terms of the deflection, torsion and eigenfrequencies of deformations. The governing differential equations of static and dynamic bending and torsion of trabecular bone are derived using variational principles based on non-classical theory, and explicit solutions are derived, accounting for length scale effects. The static bending and torsion behaviors developed by the non-classical theory show significant differences with those obtained by the classical theory when the ratio of the characteristic beam size to the internal material length scale parameter is small, or for small specimen sizes. The identified static and dynamical effective properties of bone are correlated to physiological factors, such as the age of patient, the effective bone density, and pathologies leading to a modification of the internal architecture.