A probabilistic damage model based on direct 3-D correlation of strain to damage formation following fatigue loading of rat femora

Abstract

Microdamage accumulates in bone due to repetitive or excessive mechanical loading, and accumulation of damage can lead to an increase in fracture susceptibility. Understanding the stress or strain criterion for damage formation would allow improved predictive modeling to better assess experimental results or evaluate training regimens. Finite element models coupled with three-dimensional measurements of damage were used to directly correlate damage formation to the local strain state in whole rat femora subjected to three-point bending fatigue. Images of accumulated damage from contrast-enhanced micro-CT were overlaid onto the calculated strain result to determine the strain associated with damage. Most microdamage accumulated in areas where the first principal strain exceeded 0.5%, but damage also occurred at lower strains when applied over sufficiently large volumes. As such, a single threshold strain was not a good predictor of damage. In order to capture the apparently stochastic nature of damage formation, a Weibull statistical model was applied. The model provided a good fit to the data, and a fit based on a subset of the data was able to predict the results in the remaining samples with an RMS error of 17%. These results demonstrate that damage formation is dependent on principal strain, but has a random component that is likely due to the presence of pores or flaws smaller than the resolution of the model that act as stress concentrations in bone.