Elasto-damage mechanics of osteons: A bottom-up multiscale approach

In this paper, a multiscale rationale is applied to develop a bottom-up modelling strategy for analysing the elasto-damage response of osteons, resulting in a first step towards a refined mechanical description of cortical bone tissue at the macroscale. Main structural features over multiple length scales are encompassed. A single osteon is described by considering a multi-layered arrangement of cylindrical lamellae and accounting for both lacunar micro-voids and thin interlamellar regions, these latter modelled as soft interfaces. A multi-step homogenization procedure has been conceived and numerically applied to describe the equivalent mechanical response of osteon constituents, upscaling dominant subscale mechanisms. A progressive stress-based damage approach has been implemented via a finite-element technique, allowing to describe interlaminar and/or intralaminar brittle failure modes. Proposed approach has been successfully validated by numerically reproducing available experimental tests of isolated osteons under different loading conditions. Present histologically-oriented multiscale model revealed to be sound and consistent, opening towards further insights about the influence on bone biomechanics of through-the-scales biophysical/biochemical alterations, possibly related to ageing or diseases.