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 d uring cyclic compressive loading. The specimen was modeled as a two-di mensional honeycomb-like structure made up of an array of hexagonal ce lls. Each trabecula was modeled as a linearly elastic beam element wit h the same material properties as cortical bone. Initial microcracks w ere assumed to exist within the oblique trabeculae and to grow accordi ng to the Paris law. Forces and moments were computed in each trabecul a and the microcracks were allowed to propagate until fracture occurre d. Between cycles, fractured trabeculae were removed from the finite e lement mesh, and force and moment distributions were calculated for th e next cycle. This iterative process was continued until the simulated trabecular bone specimen showed a 10% reduction in modulus. Creep fai lure was also studied using a single cell analysis, in which a closed- form solution was obtained after prescribing the creep properties of t he trabeculae. The results of the crack propagation analysis showed th at fractures of only a small number of individual trabeculae can cause a substantial reduction in the modulus of the trabecular bone specime n model. Statistical tests were performed to compare the slopes and in tercepts of the S-N curves of our model predictions to those of experi mentally derived S-N curves for bovine trabecular bone. There was no s ignificant difference (p > 0.2 for both slope and intercept) between o ur model predictions and the experimentally derived S-N curves for the low-stress, high-cycle range. For the high-stress, low-cycle range, t he crack propagation model overestimated the fatigue life for a given stress level (for slope, p < 0.001), while the creep analysis agreed w ell with the experimental data (for slope, p < 0.2). These findings su ggest that the primary failure mechanism for low-stress, high-cycle fa tigue of trabecular bone is crack growth and propagation, while the pr imary failure mechanism for high-stress, low-cycle fatigue is creep de formation and fracture. Furthermore, our results suggest that the modu lus of trabecular bone at the specimen level may be highly sensitive t o fractures of individual trabeculae.