An arterial constitutive model accounting for collagen content and cross-linking

It is apparent from the literature that the density of cross-links in collagenous tissue has a stiffening effect on the mechanical response of the tissue. This paper represents an initial attempt to characterize this effect on the elastic response, specifically in respect of arterial tissue. Two approaches are presented. First, a simple phenomenological continuum model with a cross-link-dependent stiffness is considered, and the influence of the cross-link density on the response in uniaxial tension is illustrated. In the second approach, a 3D model is developed that accounts for the relative orientation and stiffness of (two families of) collagen fibers and cross-links and their coupling using an invariant-based strain-energy function. This is also illustrated for uniaxial tension, and the influence of different cross-link arrangements and material parameters is detailed. Specialization of the model for plane strain is then used to show the effect of the cross-link orientation (relative to the fibers) and cross-link density on the shear stress versus the amount of shear deformation response. The elasticity tensor for the general (3D) case is provided with a view to subsequent finite element implementation.