A recruitment model of tendon viscoelasticity that incorporates fibril creep and explains strain-dependent relaxation

Soft tissues exhibit complex viscoelastic behaviour, including strain-rate dependence, hysteresis and straindependent relaxation. In this paper, a model for soft tissue viscoelasticity is developed that captures all of these features and is based upon collagen recruitment, whereby fibrils contribute to tissue stiffness only when taut. We build upon existing recruitment models by additionally accounting for fibril creep and by explicitly modelling the contribution of the matrix to the overall tissue viscoelasticity. The fibrils and matrix are modelled as linear viscoelastic and each fibril has an associated critical strain (corresponding to its length) at which it becomes taut. The model is used to fit relaxation tests on three rat-tail tendon fascicles and predict their response to cyclic loading. It is shown that all of these mechanical tests can be reproduced accurately with a single set of constitutive parameters, the only difference between each fascicle being the distribution of their fibril crimp lengths. By accounting for fibril creep we are able to predict how the fibril length distribution of a fascicle changes over time under a given deformation. Furthermore, the phenomenon of strain-dependent relaxation is explained as arising from the competition between the fibril and matrix relaxation functions.