Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), 1040 Vienna, Austria.
J Theor Biol. 2009 Sep 21;260(2):230-52. doi: 10.1016/j.jtbi.2009.05.021. Epub 2009 Jun 2.
There is an ongoing discussion on how bone strength could be explained from its internal structure and composition. Reviewing recent experimental and molecular dynamics studies, we here propose a new vision on bone material failure: mutual ductile sliding of hydroxyapatite mineral crystals along layered water films is followed by rupture of collagen crosslinks. In order to cast this vision into a mathematical form, a multiscale continuum micromechanics theory for upscaling of elastoplastic properties is developed, based on the concept of concentration and influence tensors for eigenstressed microheterogeneous materials. The model reflects bone's hierarchical organization, in terms of representative volume elements for cortical bone, for extravascular and extracellular bone material, for mineralized fibrils and the extrafibrillar space, and for wet collagen. In order to get access to the stress states at the interfaces between crystals, the extrafibrillar mineral is resolved into an infinite amount of cylindrical material phases oriented in all directions in space. The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their intercrystalline, intermolecular, lacunar, and vascular porosities, and the elastic and strength properties of hydroxyapatite and (molecular) collagen.
关于如何从骨的内部结构和组成来解释骨强度，目前正在进行讨论。通过回顾最近的实验和分子动力学研究，我们在此提出了一种关于骨材料失效的新观点：羟基磷灰石矿物质晶体沿着层状水膜的相互韧性滑动，随后是胶原蛋白交联的断裂。为了将这一观点转化为数学形式，我们基于特征应力微不均匀材料的集中和影响张量的概念，开发了一种用于弹塑性特性上转换的多尺度连续体细观力学理论。该模型反映了骨的层次组织结构，包括皮质骨的代表性体积元、血管外和细胞外骨材料、矿化原纤维和原纤维外空间以及湿胶原蛋白。为了了解晶体之间界面的应力状态，将原纤维外的矿物质分解为无限数量的、在空间各个方向取向的圆柱形材料相。该多尺度细观力学模型能够根据不同物种的骨的矿物质/胶原蛋白含量、骨间、分子间、腔隙和血管孔隙以及羟基磷灰石和（分子）胶原蛋白的弹性和强度特性，令人满意地预测不同骨的强度特性。
