A finite dissipative theory of temporary interfibrillar bridges in the extracellular matrix of ligaments and tendons

Abstract

The structural integrity and the biomechanical characteristics of ligaments and tendons result from the interactions between collagenous and non-collagenous proteins (e.g. proteoglycans, PGs) in the extracellular matrix. In this paper, a dissipative theory of temporary interfibrillar bridges in the anisotropic network of collagen type I, embedded in a ground substance, is derived. The glycosaminoglycan chains of decorin are assumed to mediate interactions between fibrils, behaving as viscous structures that transmit deformations outside the collagen molecules. This approach takes into account the dissipative effects of the unfolding preceding fibrillar elongation, together with the slippage of entire fibrils and the strain-rate-dependent damage evolution of the interfibrillar bridges. Thermodynamic consistency is used to derive the constitutive equations, and the transition state theory is applied to model the rearranging properties of the interfibrillar bridges. The constitutive theory is applied to reproduce the hysteretic spectrum of the tissues, demonstrating how PGs determine damage evolution, softening and non-recoverable strains in their cyclic mechanical response. The theoretical predictions are compared with the experimental response of ligaments and tendons from referenced studies. The relevance of the proposed model in mechanobiology research is discussed, together with several applications from medical practice to bioengineering science.