Vascular disorders, mostly involving arteries, are responsible for more morbidity and mortality than any other human disease. In the last decade it became evident that the reason for these diseases is related to the mechanics of the arteries. The vast majority of constitutive models used in the literature to describe the passive behavior of arterial wall are phenomenological, meaning they are based on curve fitting of experimental measurements. This research adopts a micro-mechanical based model accounting for the contributions of the mechanically significant constituents of the arterial wall in a rigorous way. Here we apply this method to characterize the macroscopic responses of the media and the adventitia. This approach will allow to construct patient specific constitutive models for the media and the adventitia from non-invasive monitoring of the tissues histologies. In this work, a 3D finite element model imitating a unit-cell of the media and the adventitia is constructed presenting the role of a lab for the application of a new variational estimate accounting for the histology and the material properties of these tissues. The micro-mechanical models predictions are compared and calibrated with an existing phenomenological model of a healthy human coronary artery in a specific loading experiment to retrieve the material properties of the tissue constituents. Once all the histological properties and the behaviors of the individual constituents are accounted for, the overall responses of the media and the adventitia are examined under three types of loadings corresponding to inflation of the artery, inflation and axial elongation, and a combination of inflation, elongation and a twist of the artery. Predictions of the two micro-mechanical models and phenomenological model are compared and analyzed. Throughout, the analytical predictions of the overall stresses and structure are in agreement with the numerical simulations.
