Finite element modeling of damage accumulation in trabecular bone under cyclic loading.

A two-dimensional finite element model of an idealized trabecular bone specimen was developed to study trabecular bone damage accumulation during cyclic compressive loading. The specimen was modeled as a two-dimensional honeycomb-like structure made up of an array of hexagonal cells. Each trabecula was modeled as a linearly elastic beam element with the same material properties as cortical bone. Initial microcracks were assumed to exist within the oblique trabeculae and to grow according to the Paris law. Forces and moments were computed in each trabecula and the microcracks were allowed to propagate until fracture occurred. Between cycles, fractured trabeculae were removed from the finite element mesh, and force and moment distributions were calculated for the next cycle. This iterative process was continued until the simulated trabecular bone specimen showed a 10% reduction in modulus. Creep failure was also studied using a single cell analysis, in which a closed-form solution was obtained after prescribing the creep properties of the trabeculae. The results of the crack propagation analysis showed that fractures of only a small number of individual trabeculae can cause a substantial reduction in the modulus of the trabecular bone specimen model. Statistical tests were performed to compare the slopes and intercepts of the S-N curves of our model predictions to those of experimentally derived S-N curves for bovine trabecular bone. There was no significant difference (p > 0.2 for both slope and intercept) between our model predictions and the experimentally derived S-N curves for the low-stress, high-cycle range. For the high-stress, low-cycle range, the crack propagation model overestimated the fatigue life for a given stress level (for slope, p < 0.001), while the creep analysis agreed well with the experimental data (for slope, p > 0.2). These findings suggest that the primary failure mechanism for low-stress, high-cycle fatigue of trabecular bone is crack growth and propagation, while the primary failure mechanism for high-stress, low-cycle fatigue is creep deformation and fracture. Furthermore, our results suggest that the modulus of trabecular bone at the specimen level may be highly sensitive to fractures of individual trabeculae.