Viscoelastic shear lag model to predict the micromechanical behavior of tendon under dynamic tensile loading

Abstract

Owing to its viscoelastic nature, tendon exhibits stress rate-dependent breaking and stiffness function. A Kelvin-Voigt viscoelastic shear lag model is proposed to illustrate the micromechanical behavior of the tendon under dynamic tensile conditions. Theoretical closed-form expressions are derived to predict the deformation and stress transfer between fibrils and interfibrillar matrix while tendon is dynamically stretched. The results from the analytical solutions demonstrate that how the fibril overlap length and fibril volume fraction affect the stress transfer and mechanical properties of tendon. We find that the viscoelastic property of interfibrillar matrix mainly results in collagen fibril failure under fast loading rate or creep rupture of tendon. However, discontinuous fibril model and hierarchical structure of tendon ensure relative sliding under slow loading rate, helping dissipate energy and protecting fibril from damage, which may be a key reason why regularly staggering alignment microstructure is widely selected in nature. According to the growth, injury, healing and healed process of tendon observed by many researchers, the conclusions presented in this paper agrees well with the experimental findings. Additionally, the emphasis of this paper is on micromechanical behavior of tendon, whereas this analytical viscoelastic shear lag model can be equally applicable to other soft or hard tissues, owning the similar microstructure.