On arterial fiber dispersion and auxetic effect

There are two polar contemporary approaches to the constitutive modeling of arterial wall with anisotropy induced by collagen fibers. The first one is based on the angular integration (AI) of the strain energy on a unit sphere for the analytically defined fiber dispersion. The second one is based on the introduction of the generalized structure tensors (GST). AI approach is very involved computationally while GST approach requires somewhat complicated procedure for the exclusion of compressed fibers. We present some middle ground models, which are based on the use of 16 and 8 structure tensors. These models are moderately involved computationally and they allow excluding compressed fibers easily. We use the proposed models to study the role of the fiber dispersion in the constitutive modeling of the arterial wall. Particularly, we study the auxetic effect which can appear in anisotropic materials. The effect means thickening of the tissue in the direction perpendicular to its stretching. Such an effect was not observed in experiments while some simple anisotropic models do predict it. We show that more accurate account of the fiber dispersion suppresses the auxetic effect in a qualitative agreement with experimental observations.