Two-dimensional micromechanical analysis of fracture in human cortical bone tissue using the phase-field method

Document Type : Original Article

Authors

Department of Mechanical Engineering, Isfahan University of Technology

Abstract

Bone has a hierarchical structure which features a complex arrangement at different length scales, endowing it with unique mechanical, chemical, and biological capabilities. To understand the mechanical properties of bone, one must consider its hierarchical structure as well as its composition. In the current research, two-dimensional numerical models of the cortical tissue microstructure of bone were created as three-phase and four-phase composites by scripting in Python, and were imported into the Abaqus software. Subsequently, fracture analysis in the transverse section of dense tissue under tensile loading was conducted using the phase-field method formulation. Initially, as a benchmark problem, data related to bovine pelvic bone was attributed to a three-phase composite, and after validating the implemented phase-field method, the primary simulation was performed for three-phase and four-phase models, with data related to human cortical bone tissue. Then, for each of the simulated three-phase and four phase models with human data, a stress-strain diagram in the tensile loading state was extracted. The outputs, obtained from the simulation performed on the two numerical models, differed from each other. The difference indicates the significant role of the bone tissue microstructure in fracture. The results showed that the ultimate strength of the three-phase model is greater than that of the four-phase model. The presence of cement lines as a weaker material phase compared to other material phases caused this difference. Conversely, the flexibility of the four-phase model was greater than that of the three-phase model. This study demonstrated the role of cement lines in increasing flexibility and reducing ultimate strength. This feature could be a mechanism for deviation or even stopping a crack in the structural model. Additionally, at the end of the work, the effect of increased porosity on the reduction of the final strength of the bone was examined, and it was shown that with increased porosity, the final strength will significantly decrease.

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References

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