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A multiscale homogenization procedure combining the fabric tensor with a natural neighbour meshless method

机译：结合织物张量和自然邻域无网格方法的多尺度均质化程序

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摘要

Bone is a material that can be classified as a hierarchical structure, where the different structural levels can be identified from the microscale to macroscale. Multiscale models enable to model the material using homogenization techniques. In this work a innovative homogenization technique for trabecular bone tissue is proposed, which uses the fabric tensor concept and a bone phenomenological material law, linking the apparent density with the trabecular bone mechanical proprieties. The proposed methodology efficiently homogenize the trabecular bone highly heterogeneous medium, allowing to define its homogenized microscale mechanical properties and to reduce the analysis computational cost (when compared with classical homogenization techniques). The homogenization technique is combined with the natural neighbour radial point interpolation method (NNRPIM). The NNRPIM uses the natural neighbour mathematical concept to enforce the nodal connectivity and build the background integration mesh, required to numerically integrate the integro-differential elasticity equations. Furthermore, the NNRPIM uses the radial point interpolators technique to construct its interpolating shape functions. In order to verify the efficiency of the technique several examples are solved using a confined square patch of trabecular bone under compression. In the end, the results obtained with a classic homogenization technique and the proposed methodology are compared.
机译：骨是可以分类为分层结构的材料，可以从微观到宏观识别不同的结构层次。多尺度模型可以使用均质技术对材料进行建模。在这项工作中，提出了一种创新的用于小梁骨组织的均质化技术，该技术使用织物张量概念和骨现象学的材料定律，将表观密度与小梁骨的机械特性联系起来。所提出的方法可以有效地均化小梁骨高度异质的介质，从而可以定义其均质的微尺度力学性能并降低分析计算成本（与经典均质技术相比）。均质化技术与自然邻点径向点插值方法（NNRPIM）相结合。 NNRPIM使用自然邻域数学概念来增强节点连接性并构建背景积分网格，这是对积分微分弹性方程进行数值积分所需的。此外，NNRPIM使用径向点插值器技术构造其插值形状函数。为了验证该技术的效率，使用压缩的小梁骨的方形小块来解决几个示例。最后，比较了使用经典均质技术和拟议方法获得的结果。

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