On prediction of the compressive strength and failure patterns of human vertebrae using a quasi-brittle continuum damage finite element model.

Damage of bone structures is mainly conditioned by bone quality related to the bone strength. The purpose of this work was to present a simple and reliable numerical treatment of a quasi-brittle damage constitutive model coupled with two different elastic modulus and to compare the numerical results with the experimental ones. To achieve this goal, a QCT based finite element model was developed within the framework of CDM (Continuum Damage Mechanics) and implemented in the FE code (ABAQUS). It described the propagation of brittle cracks which will help to predict the ultimate load fracture of a human vertebra by reproducing the experimental failure under quasi-static compressive loading paths of nineteen cadaveric lumbar vertebral bodies. The numerical computations delivered by the proposed method showed a better agreement with the available experimental results when bone volume fraction related Young's modulus (E(BV/TV)) is used instead of density related Young's modulus (E(ρ)). Also, the study showed that the maximum relative error (%) in failure was 8.47% when E(BV/TV) is used, whereas the highest relative error (%) was 68.56% when E(ρ) is adopted. Finally, a mesh sensitivity analysis revealed that the element size has a weak incidence on the computed load magnitude. The numerical results provided by the proposed quasi-brittle damage model combined with E(BV/TV) are a reliable tool for the vertebrae fracture prediction.