Costa Marques Marco, Belinha Jorge, Fonseca Oliveira António, Manzanares Céspedes Maria Cristina, Natal Jorge Renato
INEGI - Institute of Science and Innovation in Mechanical and Industrial Engineering, Porto, Portugal.
ISEP - Department of Mechanical Engineering, School of Engineering, Polytechnic of Porto, Porto, Portugal.
Acta Bioeng Biomech. 2019;21(2):101-113.
Bone tissue is a dynamic tissue, possessing different functional requirements at different scales. This layered organization indicates the existence of a hierarchical structure, which can be characterized to distinguish macro-scale from micro-scale levels. Structurally, both scales can be linked by the use of classic multiscale homogenization techniques. Since in bone tissue each micro-scale domain is distinct form its neighbour, applying a classic multiscale homogenization technique to a complete bone structure could represent an inadmissible computational cost. Thus, this work proposes a homogenization methodology that is computationally efficient, presenting a reduced computational cost, and is capable to define the homogenized microscale mechanical properties of the trabecular bone highly heterogeneous medium.
The methodology uses the fabric tensor concept in order to define the material principal directions. Then, using an anisotropic phenomenological law for bone tissue correlating the local apparent density with directional elasticity moduli, the anisotropic homogenized material properties of the micro-scale patch are fully defined. To validate the developed methodology, several numerical tests were performed, measuring the sensitivity of the technique to changes in the micro-patch size and preferential orientation.
The results show that the developed technique is robust and capable to provide a consistent material homogenization. Additionally, the technique was combined with two discrete numerical techniques: the finite element method and radial point interpolation meshless method.
Structural analyses were performed using real trabecular patches, showing that the proposed methodology is capable to accurately predict the micro-scale patch mechanical behavior in a fraction of the time required by classic homogenization techniques.
骨组织是一种动态组织，在不同尺度上具有不同的功能需求。这种分层结构表明存在一种层次结构，可通过其特征来区分宏观尺度和微观尺度。在结构上，这两个尺度可以通过经典的多尺度均匀化技术联系起来。由于在骨组织中，每个微观尺度区域与其相邻区域不同，将经典的多尺度均匀化技术应用于完整的骨结构可能会带来难以承受的计算成本。因此，这项工作提出了一种计算效率高、计算成本降低的均匀化方法，该方法能够定义高度异质的小梁骨微观尺度力学性能。
该方法使用织物张量概念来定义材料的主方向。然后，利用骨组织的各向异性唯象定律，将局部表观密度与方向弹性模量相关联，从而完全定义微观尺度小块的各向异性均匀化材料性能。为了验证所开发的方法，进行了若干数值测试，测量了该技术对微观小块尺寸和优先取向变化的敏感性。
结果表明，所开发的技术是稳健的，能够提供一致的材料均匀化。此外，该技术还与两种离散数值技术相结合：有限元法和径向点插值无网格法。
使用真实的小梁小块进行了结构分析，结果表明所提出的方法能够在经典均匀化技术所需时间的一小部分内准确预测微观尺度小块的力学行为。
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