Unravelling the viscoelastic, buffer-like mechanical behavior of tendons: A numerical quantitative study at the fibril-fiber scale

Abstract

We investigate the capacity of tendons to bear substantial loads by exploiting their hierarchical structure and the viscous nature of their subunits. We model and analyze two successive tendon scales: the fibril and fiber subunits. We present a novel method for bridging intra-scale experimental observations by combining a homogenization analysis technique with a Bayesian inference method. This allows us to infer elastic and viscoelastic moduli at the embedded fibril scale that are mechanically compatible with the experimental data observed at the fiber scale. We identify the rather narrow range of moduli values at the fibrillar scale that can reproduce the mechanical behavior of the fiber, while we quantify the viscoelastic contribution of the embedding, non-collagenous matrix substance. The computed viscoelastic moduli suggest that a great part of the stress relaxation capacity of tendons needs to be attributed to the embedding matrix substance of its inner components, classifying it as a primal load relaxation constituent.