Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A μCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure (N) and effective strain (Δσ/E₀): N=1.394×10^-25(Δσ/E₀)^-12.17, r²=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.