A constitutive model for transversely isotropic dispersive materials

Due to their intrinsic complexity, it is not easy to model the mechanical behaviour of biomaterials. Despite the challenges they faced, some researchers have presented mathematical models to describe some aspects of the mechanical response of soft tissues. Since most of the materials of biological interest are composites made of different constituents reinforced by collagen and/or elastin fibres, material dispersion and anisotropy are non-negligible. Within the theory of elasticity, several models for anisotropic materials have been developed. The same cannot be said for anisotropic dispersive materials. The models available in the literature that account for material dispersion are valid only for isotropic materials. This paper aims at introducing a very general model for anisotropic dispersion in transversely isotropic bodies within the theory of simple materials of differential type. Our model has the potential to represent a first step towards a better understanding of the mechanical response of fibre-reinforced soft materials.