Effect of viscoelasticity on inversion in axial deformation and on the volume of pressurized thin-walled tubes

Abstract

Axial prestretching can significantly affect the mechanical response of an inflated tube. This phenomenon is known, for example in the biomechanics of the cardiovascular system, where arteries, if excised from a body, manifest non-negligible shortening. Previous studies have shown that axially prestretched tubes are more easily distensible by internal pressure than their non-prestretched counterparts. It has even been found that, in the case of the material described by the Gent strain energy density function, the volume attained by a tube at a given internal pressure can be maximized by the initial elongation of the tube to the prestretch point referred to as inversion axial prestretching. However, to the best of our knowledge, all studies dealing so far with the effect of axial prestretching on the mechanical response of a pressurized tube have assumed elastic behavior. Nevertheless, soft tissues as well as elastomer materials are always more or less viscoelastic. The present study shifts our attention from purely theoretical elastic models to a more realistic assumption of viscoelastic behavior, which is modeled by means of the Quasilinear Theory of Viscoelasticity (QLV). The adopted model assumes the elastic part of the material response to be given by the Gent model. Results suggest that the viscoelastic tube loses the property of inversion in axial deformation but can still preserve the potential to optimize the inflation volume by means of axial prestretching. This result can be helpful in designing elastomer pipelines and pumps, as well as contributing to the understanding of the principals of blood circulation physiology.