Nonlinear Model for Viscoelastic Behavior of Achilles Tendon

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Abstract
Although the mechanical properties of ligament and tendon are well documented in research literature, very few unified mechanical formulations can describe a wide range of different loadings. The aim of this study was to propose a new model, which can describe tendon responses to various solicitations such as cycles of loading, unloading, and reloading or successive relaxations at different strain levels. In this work, experiments with cycles of loading and reloading at increasing strain level and sequences of relaxation were performed on white New Zealand rabbit Achilles tendons. We presented a local formulation of thermodynamic evolution outside equilibrium at a representative element volume scale to describe the tendon’s macroscopic behavior based on the notion of relaxed stress. It was shown that the model corresponds quite well to the experimental data. This work concludes with the complexity of tendons’ mechanical properties due to various microphysical mechanisms of deformation involved in loading such as the recruitment of collagen fibers, the rearrangement of the microstructure (i.e., collagens type I and III, proteoglycans, and water), and the evolution of relaxed stress linked to these mechanisms.

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