A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement

In this paper the mechanical response of soft collagenous tissues with regular fiber arrangement (RSCTs) is described by means of a nanoscale model and a two-step micro-macro homogenization technique. The non-linear collagen constitutive behaviour is modelled at the nanoscale by a novel approach accounting for entropic mechanisms as well as stretching effects occurring in collagen molecules. Crimped fibers are reduced to equivalent straight ones at the microscale and the constitutive response of $RSCTs$ at the macroscale is formulated by homogenizing a fiber reinforced material. This approach has been applied to different $RSCTs$ (tendon, periodontal ligament and aortic media), resulting effective and accurate as proved by the excellent agreement with available experimental data. The model is based on few parameters, directly related to histological and morphological evidences and whose sensitivity has been widely investigated. Applications to simulation of some physiopathological mechanisms are also proposed, providing confirmation of clinical evidences and quantitative indications helpful for clinical practice