Radial waves in fiber-reinforced axially symmetric hyperelastic media

TL;DR

This paper derives and analyzes wave equations for shear displacements in fiber-reinforced hyperelastic media, including Mooney-Rivlin, radial fiber, and viscoelastic models, relevant for biological tissues like blood vessels.

Contribution

It presents a unified derivation of nonlinear wave equations in fiber-reinforced hyperelastic media, extending to radial fiber orientations and viscoelastic effects.

Findings

Displacements in Mooney-Rivlin materials follow a linear cylindrical wave equation.

Extended models incorporate radial fiber projections and dissipative effects.

Wave equations are derived and analyzed for various fiber configurations and viscoelasticity.

Abstract

Complex elastic media such as biological membranes, in particular, blood vessels, may be described as fiber-reinforced solids in the framework of nonlinear hyperelasticity. Finite axially symmetric anti-plane shear displacements in such solids are considered. A general nonlinear wave equation governing such motions is derived. It is shown that in the case of Mooney-Rivlin materials with standard quadratic fiber energy term, the displacements are governed by a linear cylindrical wave equation. Extensions of the model onto the case when fibers have a radial projection, as well as onto a viscoelastic case taking into account dissipative effects, are considered; wave equations governing shear displacements in those cases are derived and analyzed.