Osteon orientations play a critical role in defining the orthotropic properties of cortical bone. Cortical bone has different mechanical and materials properties in longitudinal and transverse directions, which are mainly due to the different osteon orientations. This study aims to consider a pre-existing technique with modifications in enrichment techniques for modeling and orthotropic fracture analysis of cortical bone. It is hypothesized that the incorporation of orthotropic enrichment functions in the fracture analysis increased the complexity and computational time of the solution. Therefore, two methods for the solution were considered, one with the orthotropic enrichment functions “element-free Galerkin method” (EFGM) and another one is with the isotropic enrichment functions “particularly optimized enriched element-free Galerkin method” (POE-EFGM) to determine the solution accuracy and computational time. Additionally, the effects of different crack orientations, osteon orientations, and boundary loading conditions (Mode-I, mode-II, and mixed-mode (I+II)) on stress intensity factor (SIF) of cortical bone were investigated. Results of this present study were compared with available results and methods (numerical or semi-analytical) from the previously published studies to understand the effectiveness of the POE-EFGM. POE-EFGM was found to be effective than EFGM in optimizing the solution and minimizing the computational cost up to 40%. POE-EFGM could be helpful in complex and extensive computational analyses. Results of the present study also suggested that the SIF of the cortical bone was significantly affected by the osteon orientations, crack orientations, and boundary loading conditions.

Osteon 方向在定义皮质骨的正交各向异性特性方面起着关键作用。皮质骨在纵向和横向上具有不同的力学和材料特性，这主要是由于骨单元的取向不同。本研究旨在考虑一种预先存在的技术，并对用于皮质骨建模和正交各向异性骨折分析的富集技术进行修改。假设在裂缝分析中加入正交各向异性富集函数会增加解决方案的复杂性和计算时间。因此，考虑了两种求解方法，一种具有正交各向异性富集函数“无元素伽辽金法”（EFGM），另一种是具有各向同性富集函数“特别优化的富集无元素伽辽金法”（POE-EFGM）确定求解精度和计算时间。此外，研究了不同裂纹方向、骨子方向和边界载荷条件（模式-I、模式-II 和混合模式 (I+II)）对皮质骨应力强度因子 (SIF) 的影响。发现 POE-EFGM 在优化解决方案和将计算成本最小化方面比 EFGM 更有效，高达 40%。POE-EFGM 可能有助于复杂和广泛的计算分析。本研究的结果还表明，皮质骨的 SIF 受骨子方向、裂纹方向和边界载荷条件的显着影响。