The piezoelectric response of bone at the submicron scale is analyzed under mechanical loadings using the finite element (FE) method. A new algorithm is presented to virtually reconstruct realistic bone nanostructures, consisting of collagen fibrils embedded in a hydroxyapatite mineral network. This algorithm takes into account potential misalignments between fibrils, as well the porous structure of the mineral phase. A parallel non-iterative mesh generation algorithm is utilized to create high-fidelity FE models for several representative volume elements (RVEs) of the bone with various fibrils volume fractions and misalignments. The piezoelectric response of each RVE is simulated under three types of loading: the longitudinal compression, lateral compression, and shear. The resulting homogenized stress and electric field in RVEs with aligned fibrils showed a linear variation with the fibrils volume fraction under all loading conditions. For RVEs with misaligned fibrils, although more oscillations were observed in homogenized results, their difference with the results of RVEs with aligned fibrils subject to lateral compression and shear loadings were negligible. However, under longitudinal compression, the electric field associated with RVEs with misaligned fibrils was notably higher than that of RVEs with aligned fibrils for the same volume fraction.

使用有限元 (FE) 方法在机械载荷下分析亚微米级骨骼的压电响应。提出了一种新算法来虚拟重建逼真的骨纳米结构，该结构由嵌入羟基磷灰石矿物网络中的胶原原纤维组成。该算法考虑了原纤维之间的潜在错位，以及矿物相的多孔结构。并行非迭代网格生成算法用于为具有各种原纤维体积分数和错位的骨骼的几个代表性体积元素 (RVE) 创建高保真有限元模型。每个 RVE 的压电响应在三种类型的载荷下进行模拟：纵向压缩、横向压缩和剪切。在所有负载条件下，具有对齐原纤维的 RVE 中产生的均匀应力和电场显示出随原纤维体积分数的线性变化。对于具有未对齐原纤维的 RVE，尽管在均质化结果中观察到更多的振荡，但它们与具有对齐原纤维的 RVE 结果的差异可以忽略不计。然而，在纵向压缩下，对于相同体积分数，与具有未对齐原纤维的 RVE 相关的电场明显高于具有对齐原纤维的 RVE。它们与经受横向压缩和剪切载荷的对齐原纤维的 RVE 结果的差异可以忽略不计。然而，在纵向压缩下，对于相同体积分数，与具有未对齐原纤维的 RVE 相关的电场明显高于具有对齐原纤维的 RVE。它们与经受横向压缩和剪切载荷的对齐原纤维的 RVE 结果的差异可以忽略不计。然而，在纵向压缩下，对于相同体积分数，与具有未对齐原纤维的 RVE 相关的电场明显高于具有对齐原纤维的 RVE。