A microstructure-based study on compact human bones: hierarchical length scale parameter

This paper presents a microstructure-based study on compact human bone using the modified couple stress theory and investigates some of its mechanical behaviors at the micro-scale. First of all, length scale parameters in torsion and bending are assessed for bone micro-samples on the basis of experimental data proposed by Yang and Lakes. Then, the effect of micro-rotations on the torsion and bending of single osteons is studied and compared with experimental results obtained by Ascenzi et al., and the length scale parameter of osteons is consequently obtained. According to the present study on osteons and using an approximate formulation of multi-layered tubes under torsion, a material length scale parameter of lamellae is acquired to capture the size effect. These achievements lead to introducing a hierarchical structure for the material length scale parameter of the modified couple stress theory. In addition, the buckling, static nonlinear response, torsional vibration, and flexural dispersion analyses of osteons are presented.