Time-dependent damage in predictions of fatigue behaviour of normal and healing ligaments

Ligaments are dense fibrous tissues that connect bones across a joint and are exposed daily to creep and fatigue loading. Ligaments are tensile load-bearing tissues; therefore, fatigue loading will have a component of time-dependent damage from the non-zero mean stress and cycle-dependent damage from the oscillating stress. If time-dependent damage is not sufficient to completely predict the fatigue response, then cycle-dependent damage could be an important contributor. Using data from normal ligaments (current study and Thornton et al., Clin. Biomech. 22:932–940, 2007a) and healing ligaments (Thornton and Bailey, J. Biomech. Eng. 135:091004-1–091004-6, 2013), creep data was used to predict the fatigue response considering time-dependent damage. Relationships between creep lifetime and test stress or initial strain were modelled using exponential or power-law regression. In order to predict fatigue lifetimes, constant rates of damage were assumed and time-varying stresses were introduced into the expressions for time-dependent damage from creep. Then, the predictions of fatigue lifetime were compared with curvefits to the fatigue data where exponential or power-law regressions were used to determine the relationship between fatigue lifetime and test stress or initial strain. The fatigue prediction based on time-dependent damage alone greatly overestimated fatigue lifetime suggesting that time-dependent damage alone cannot account for all of the damage accumulated during fatigue and that cycle-dependent damage has an important role. At lower stress and strain, time-dependent damage was a greater relative contributor for normal ligaments than healing ligaments; however, cycle-dependent damage was a greater relative contributor with incremental increases in stress or strain for normal ligaments than healing ligaments.