Particularly optimized enriched element-free Galerkin method (POE-EFGM) for orthotropic fracture analysis of cortical bone

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.