Due to their intrinsic complexity, it is not easy to model the mechanical behaviour of biomaterials. Despite the difficulties encountered, some scholars have successfully introduced mathematical models to describe some aspects of the mechanical response of soft tissues. However, none of these models accounts for material dispersion. Since most of materials of biological interest are composite made of different constituents reinforced by collagen and/or elastin fibres, material dispersion and anisotropy are nonnegligible. Within the theory of elasticity, several models for anisotropic materials have been developed. The same cannot be said for anisotropic dispersive materials. The existing models accounting for material dispersion have been introduced only for isotropic materials. The aim of this manuscript is to introduce the most general model for anisotropic dispersion in transversely isotropic materials. Our model has the potentiality to represent a first step toward a better understanding of the mechanical response of fibre-reinforced soft materials.
This video was produced by the Isaac Newton Institute, as part of the workshop Mathematical mechanical biology: old school and new school, methods and applications, forming part of the programme Uncertainty quantification and stochastic modelling of materials.
