On propagation of waves in pressurized fiber-reinforced hyperelastic tubes based on a reduced model

TL;DR

This paper develops a refined shell theory for hyperelastic tubes to analyze wave propagation, demonstrating improved accuracy over membrane theory and highlighting the influence of pressure, pre-stretch, and fiber angle on wave behavior.

Contribution

The authors derive a linearized incremental theory for hyperelastic shells and validate its effectiveness in modeling wave propagation in fiber-reinforced tubes.

Findings

The refined theory provides more accurate dispersion relations than membrane theory.

Bending effects significantly influence wave modes at large wavenumbers.

Pressure, pre-stretch, and fiber angle substantially affect wave dispersion.

Abstract

A refined dynamic finite-strain shell theory for incompressible hyperelastic materials was developed by the authors recently. In this paper, we first derive the associated linearized incremental theory, and then use it to investigate wave propagation in a fiber-reinforced hyperelastic tube that is subjected to an axial pre-stretch and internal pressure. We obtain the dispersion relations for both axisymmetric and non-axisymmetric waves and discuss their accuracy by comparing them with the exact dispersion relations. The bending effect is also examined by comparing the dispersion curves based on the present theory and membrane theory. It is shown that the present theory is more accurate than the membrane theory in studying wave propagation and the bending effect plays an important role in some wave modes for relatively large wavenumbers. The effects of the pressure, axial pre-stretch and fiber angle on the dispersion relations are displayed. These results provide the necessary validation for using the refined dynamic finite-strain shell theory and wave propagation to determine arterial properties.