A dynamic viscoelastic analogy for fluid-filled elastic tubes

TL;DR

This paper develops a viscoelastic analogy for fluid-filled elastic tubes, incorporating fluid viscosity effects using a fractional Maxwell model, with potential applications in biophysics and arterial pressure wave analysis.

Contribution

It introduces a novel viscoelastic analogy for fluid-filled elastic tubes that accounts for fluid viscosity effects via a fractional Maxwell model, extending previous models.

Findings

The derived evolution equations are integro-differential equations similar to those in viscoelastic solids.

The model exhibits creep behavior akin to fractional Maxwell models at short times.

Applications suggested in biophysics, especially in arterial pressure wave propagation.

Abstract

In this paper we evaluate the dynamic effects of the fluid viscosity for fluid filled elastic tubes in the framework of a linear uni-axial theory. Because of the linear approximation, the effects on the fluid inside the elastic tube are taken into account according to the Womersley theory for a pulsatile flow in a rigid tube. The evolution equations for the response variables are derived by means of the Laplace transform technique and they all turn out to be very same integro-differential equation of the convolution type. This equation has the same structure as the one describing uni-axial waves in linear viscoelastic solids characterized by a relaxation modulus or by a creep compliance. In our case, the analogy is connected with a peculiar viscoelastic solid which exhibits creep properties similar to those of a fractional Maxwell model (of order 1/2) for short times, and of a standard Maxwell model for long times. The present analysis could find applications in biophysics concerning the propagation of pressure waves within large arteries.