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The development of a multi-axial failure criterion for trabecular skull bone has many clinical and biological implications. This failure criterion would allow for modeling of bone under daily loading scenarios that typically are multi-axial in nature. Some yield criteria have been developed to evaluate the failure of trabecular bone, but there is a little consensus among them. To help gain deeper understanding of multi-axial failure response of trabecular skull bone, we developed 30 microstructural finite element models of porous porcine skull bone and subjected them to multi-axial displacement loading simulations that spanned three-dimensional (3D) stress and strain space. High-resolution microcomputed tomography (microCT) scans of porcine trabecular bone were obtained and used to develop the meshes used for finite element simulations. In total, 376 unique multi-axial loading cases were simulated for each of the 30 microstructure models. Then, results from the total of 11,280 simulations (approximately 135,360 central processing unit-hours) were used to develop a mathematical expression, which describes the average three-dimensional yield surface in strain space. Our results indicate that the yield strain of porcine trabecular bone under multi-axial loading is nearly isotropic and despite a spread of yielding points between the 30 different microstructures, no significant relationship between the yield strain and bone volume fraction is observed. The proposed yield equation has simple format and it can be implemented into a macroscopic model for the prediction of failure of whole bones.

The Multi-Axial Failure Response of Porcine Trabecular Skull Bone Estimated Using Microstructural Simulations