Nano-micro-macro constitutive modelling of collagenous fibers in periodontal ligament and muscle-tendon units

In this paper the mechanical response of some collagenous tissues is addressed. The influence of modelling refinements of collagenous fibers response on tissue mechanical behaviour is focused, and a special insight on the effects of fibers nonlinearities is given. Two study cases are addressed: the periodontal ligament and the muscle-tendon unit. The first one is modelled as a reinforced composite with crimped collagenous fibers, and the dynamics of the muscle-tendon unit is described by an Hill-type model coupled with a nonlinear elastic model of tendon. In both cases, a new multiscale modelling of collagenous fibers is employed. This latter is able to describe their J-shaped response curve and is based on few histological and measurable data. In both cases, the proposed model allows to recover experimental evidences.