Fig. 1

A Macroscopic FE model. a Macroscopic FE model of segment bone under axial compressive cyclic loading. B Macro–mesoscopic model. b Macro–mesoscopic model including endosteum, periosteum, interstitial bone, and hollow osteon. c The hollow osteon in macro–mesoscopic model. d One-eight symmetry model. Regional M and line L are selected to analyze the biomechanical responses along the radius of bone tissue. e Region M is divided to 8 small regions (Regions 1–8), and each small region contains one osteon (Osteon 1–8). f Some points are selected at the internal wall, the middle and the external wall, and the interstitial bone. C Mesoscopic model. g FE mesoscopic model including macro–meso interface (including osteon lamellae structure). The critical part near the periosteum in macro–mesoscopic model is refinement. h A cube (340 µm) that cut from the macro–mesoscopic model near the periosteum as mesoscale model. Line H is a part of L along radius direction of done tissue. i Transversal cross-section of the mesoscale model with 10 osteon lamellae. j The cement line