Modeling orthotropic elasticity, localized plasticity and fracture in trabecular bone

This work develops a model for the mechanical response of trabecular bone including plasticity, damage and fracture. It features a resultant lamellar orientation that captures trabecular strut anisotropic elasticity, and introduces asymmetric J2 plasticity with isotropic hardening to capture evolving strut tensile and compressive dissipative properties. A continuum compatibility based damage and fracture criterion is also proposed to model fracture surface generation. We investigated fracture of a trabecular bone network under a compressive load, for which failure modes of both tension and compression were identified at the strut level. The predicted trabecular network response was found to fall within the range of experimental results reported in literature. We also investigated the response of idealized struts under compression, tension and bending using our model. Individual struts were found to exhibit micro-buckling under compression and micro-necking under tension. These instabilities are however masked by the multiplicity and complexity of strut orientations at the trabecular network level.