The micropolar behaviour of cortical bone: size and surface effects in 3 point bending

The heterogeneous microstructure of cortical bone may be important in the determination of stress concentrations and shielding in the vicinity of orthopaedic implants. We hypothesise that micropolar elasticity can parameterise the microstructure of cortical bone to better predict local stresses. Threepoint bending tests on bovine mid-diaphyseal bone demonstrated a size effect in which sample stiffness decreased as size reduced. However, computational predictions indicate that the size effect depends entirely on the surface condition: smooth surfaces result in increased stiffness as size decreases, whilst surfaces corrugated by the microstructure demonstrated an identically strong, yet opposite, effect. We have thus established the connection between anti-micropolar behaviour and surface heterogeneity, of significant relevance to all heterogeneous solids. For bone in particular, we have shown that the micropolar characteristic length is consistent with the Haversian canal diameter. Haversian canals are therefore of fundamental importance in understanding local stress and strain fields in cortical bone.