Effect of double-fibre reinforcement on localized bulging of an inflated cylindrical tube of arbitrary thickness

Juan Wang,Yibin Fu

doi:10.1007/s10665-017-9899-5

Abstract

We consider localized bulging of an inflated cylindrical hyperelastic tube of arbitrary thickness that is helically reinforced by two families of fibres. It is shown that localized bulging may become impossible, irrespective of the end conditions, when the tube wall becomes thick enough. This is in sharp contrast with an isotropic hyperelastic tube without fibre reinforcement for which localized bulging has previously been shown to be possible no matter how thick the tube wall is and for which the membrane theory provides a very good approximation for the ratio of wall-thickness/radius as large as 0.67. Our findings provide a feasible explanation on why aneurysms cannot occur in healthy arteries but become possible following pathological changes. They can also be used to guide the design of tubular structures where localized bulging should be prevented.

Highlights

It is well known that a localized bulge may appear in an inflated tubular balloon when the internal pressure reaches a certain critical value
Localized bulging has been commonly believed to be associated with the fact that in uniform inflation, the pressure against volume has an N shape in which the pressure has values of both a maximum and a minimum
Recent studies have shown that the correspondence between the maximum pressure in uniform inflation and initiation pressure for localized bulging only exists when the resultant axial force is fixed during inflation, which is the case if the movement of one end

Summary

Introduction

It is well known that a localized bulge may appear in an inflated tubular balloon when the internal pressure reaches a certain critical value. If aneurysm initiation in pathological arteries is accepted as a mechanical bifurcation phenomenon, an explanation must be found for the fact that aneurysms should not occur in healthy arteries One such explanation is offered in this paper: it is shown that under double-fibre reinforcement, localized bulging may become impossible if the wall thickness is large enough, with the threshold wall thickness depending on the strength and orientation of fibre reinforcement. Our present study is part of a systematic research program devoted to an improved understanding of the localized bulging phenomenon in inflated cylindrical tubes, and is the second paper in the series that examines the effects of bending stiffness after Fu et al [5] It compliments previous studies on the so-called limiting point instability which refers to the existence of a pressure maximum in uniform inflation.

Governing equations

Effects of bending stiffness and fibre reinforcement

Conclusion