Non-linear tendon fatigue life under uncertainties

Tendons play a pivotal role in facilitating joint movement by transmitting muscular forces to bones. The intricate hierarchical structure and diverse material composition of tendons contribute to their non-linear mechanical response. However, comprehensively grasping their mechanical properties poses a challenge due to inherent variability in biological tissues. This necessitates a thorough examination of uncertainties associated with properties measurements, particularly under diverse loading conditions. Given the cyclic loading experienced by tendons throughout an individual's lifespan, understanding their mechanical behaviour under such circumstances becomes crucial. This study addresses this need by introducing a generalised Paris Erdogan Law tailored for non-linear materials. To examine uncertainties within this proposed framework, Monte Carlo Analysis is employed. This approach allows for a thorough exploration of the uncertainties associated with tendon mechanics, contributing to a more robust comprehension of their behaviour under cyclic loading conditions. Finally, self-healing has been integrated into the fatigue law of tendons through the proposal of a healing function, formulated as a polynomial function of the maximum stress. This approach allows to account for an increase in the number of cycles for each stress value due to self-repair after the damage event generated by longterm cycling load over the individual's life span.