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.

在本文中，应用多尺度原理来开发一种自下而上的建模策略，用于分析骨的弹性损伤反应，从而迈出了在宏观尺度上对皮质骨组织进行精细机械描述的第一步。涵盖多个长度尺度的主要结构特征。通过考虑圆柱形薄片的多层排列并考虑腔隙微空隙和薄层间区域来描述单个骨，后者被建模为软界面。已经构想了多步均质化程序并在数值上应用来描述骨成分的等效机械响应，升级主要的子尺度机制。通过有限元技术实施了一种渐进的基于应力的损伤方法，允许描述层间和/或层内脆性破坏模式。所提出的方法已通过数值再现不同负载条件下孤立骨的可用实验测试成功验证。目前以组织学为导向的多尺度模型显示为合理且一致的，为进一步了解可能与衰老或疾病有关的全面生物物理/生化变化对骨骼生物力学的影响开辟了道路。