Size dependent static and dynamic behavior of trabecular bone based on micromechanical models of the trabecular architecture

In order to investigate microstructure-related scale effects on bone macroscopic properties, Cosserat models of vertebral trabecular bone are constructed, based on micromechanical approaches. The effective static mechanical properties of cancellous bones considered as cellular solids are obtained thanks to the discrete homogenization technique, versus the geometrical and mechanical micro-parameters of the underlying topology within an identified representative unit cell. The cell walls of the bone microstructure are modeled as Timoshenko thick beams. An anisotropic micropolar equivalent continuum model is 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 behavior of vertebral trabecular bone is 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 beam characteristic 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. (C) 2013 Elsevier Ltd. All rights reserved.