Department of Mechanical Engineering, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA.
Biomech Model Mechanobiol. 2019 Apr;18(2):463-478. doi: 10.1007/s10237-018-1096-6. Epub 2018 Nov 23.
Bone ultrastructure at sub-lamellar length scale is a key structural unit in bone that bridges nano- and microscale hierarchies of the tissue. Despite its influence on bulk response of bone, the mechanical behavior of bone at ultrastructural level remains poorly understood. To fill this gap, in this study, a two-dimensional cohesive finite element model of bone at sub-lamellar level was proposed and analyzed under tensile and compressive loading conditions. In the model, ultrastructural bone was considered as a composite of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM) that is comprised of hydroxyapatite (HA) polycrystals bounded via thin organic interfaces of non-collagenous proteins (NCPs). The simulation results indicated that in compression, EFM dictated the pre-yield deformation of the model, then damage was initiated via relative sliding of HA polycrystals along the organic interfaces, and finally shear bands were formed followed by delamination between MCF and EFM and local buckling of MCF. In tension, EFM carried the most of load in pre-yield deformation, and then an array of opening-mode nano-cracks began to form within EFM after yielding, thus gradually transferring the load to MCF until failure, which acted as crack bridging filament. The failure modes, stress-strain curves, and in situ mineral strain of ultrastructural bone predicted by the model were in good agreement with the experimental observations reported in the literature, thus suggesting that this model can provide new insights into sub-microscale mechanical behavior of bone.
在亚层状长度尺度上，骨的超微结构是连接骨组织纳米和微尺度层次的关键结构单元。尽管它对骨的整体响应有影响，但骨在超微结构水平上的力学行为仍未得到很好的理解。为了填补这一空白，本研究提出并分析了亚层状骨的二维内聚有限元模型在拉伸和压缩载荷条件下的力学行为。在该模型中，超微结构骨被视为矿化胶原纤维（MCFs）嵌入在由羟磷灰石（HA）多晶体组成的细胞外基质（EFM）中的复合材料，HA 多晶体通过薄的非胶原蛋白（NCP）有机界面结合在一起。模拟结果表明，在压缩条件下，EFM 控制模型的预屈服变形，然后通过 HA 多晶体沿有机界面的相对滑动引发损伤，最后形成剪切带，随后 MCF 与 EFM 分层和 MCF 局部屈曲。在拉伸条件下，EFM 在预屈服变形中承载了大部分载荷，然后在屈服后，EFM 内开始形成一系列张开型纳米裂纹，从而逐渐将载荷传递到 MCF 直至失效，失效后 MCF 充当裂纹桥接纤维。该模型预测的超微结构骨的失效模式、应力-应变曲线和原位矿物应变与文献中报道的实验观察结果吻合良好，这表明该模型可以为骨的亚微观力学行为提供新的见解。
