Fate of a bulge in an inflated hyperelastic tube: theory and experiment

Abstract

Mechanical instability in a pre-tensioned finite hyperelastic tube subjected to a slowly increasing internal pressure produces a spatially localized bulge at a critical pressure. This instability is studied in controlled experiments on inflated latex rubber tubes, from the perspective of buckling observed in aneurysms and their rupture risk. The fate of the bulge under continued inflation is governed by the end-conditions and the initial tension in the tube. In a tube with one end fixed and a weight attached to the other freely moving end, the bulge propagates axially at low initial tension, growing in length, and the tube relaxes by extension without buckling. Rupture occurs when the tension is high. By contrast, the bulge formed in an initially stretched tube held fixed at both its ends can buckle or rupture, depending on the amount of initial tension. Experiments are reported for different initial tensions and boundary conditions (BCs). Failure maps in the stretch parameter space and in stretch–tension space are constructed by extending existing theories for bulge formation and buckling analyses to the experimentally relevant BCs. Failure maps deduced from the theory are compared against experiments, and the underlying assumptions are critically assessed. Experiments reveal that buckling provides an alternative route to relieve the stress built up during inflation. Hence, buckling, when it occurs, can be a protective fail-safe mechanism against the rupture of a bulge in an inflated elastic tube.

Inflation-induced aneurysm formation and evolution in graded cylindrical tubes of arbitrary thickness

“…Correspondingly, (2.14) and (2.15) provide two algebraic equations for the two unknowns λ a and λ z and solving them for a given pressure and a given axial force yields the solution that characterizes the primary deformation. This kind of loading type has been used in the experimental investigations carried out by Kyriakides andChang (1990, 1991); Guo et al (2016); Wang et al (2019); Hejazi et al (2021). In the other loading condition, the tube is first uniformly stretched and then the two ends are fastened.…”

“…We emphasize that this scenario corresponds to the in vivo situation for human arteries (Horný et al, 2014). Also, such an experimental setup was employed by Pamplona et al (2006); Goncalves et al (2008); Wang et al (2019); Hejazi et al (2021). Since λ z is prescribed, the internal pressure P is only a function of λ a , and the primary deformation is fully determined by equation (2.14).…”

“…On the one hand, if either the resultant axial force N or the prescribed axial stretch λ z is greater enough, localized bulging can disappear (Liu et al, 2019). On the other hand, if the axial stretch λ z is less than a threshold value, global buckling can replace localized bulging (Lin et al, 2020;Hejazi et al, 2021). In this paper, we intend to investigate localized bulging (aneurysm formation) in graded tubes and further to elucidate the influence of modulus gradient on bulge formation, growth, and propagation.…”

“…Inflation of a cylindrical rubber tube usually generates a prototypical localization instability, known as localized bulging, and such an interesting phenomenon was first recorded in detail and primarily analyzed by Mallock (1891). With applications to bulge initiation and propagation in pressure vessels (Chater and Hutchinson, 1984;Kamalarasa and Calladine, 1988;Kyriakides, 2007) and aneurysm formation in human arteries (Rodríguez and Merodio, 2011;Sakalihasan et al, 2018), inflation of a cylindrical hyperelastic tube offers a pertinent paradigm to study the mechanism of localized instabilities (Kyriakides andChang, 1990, 1991;Hejazi et al, 2021). In addition, recent advances on inflated tubes and localized bulging can shed light on bifurcation in arteries affected by Marfan's syndrome (Haughton and Merodio, 2009;Merodio and Haughton, 2010), bulge prevention in energy harvesting devices (Bucchi and Hearn, 2013), inflation-driven soft robots (Jin et al, 2021), inflation of nematic elastomers (He et al, 2020), and bulge formation subject to additional effects of electric actuation (Lu et al, 2015), swelling (Demirkoparan and Merodio, 2017), magnetic field (Reddy and Saxena, 2018), and plasticity (Takla, 2018).…”

“…either the resultant axial force or the axial length is specified, are adopted in experiments. The former was adopted in Kyriakides andChang (1990, 1991); Wang et al (2019); Hejazi et al (2021) while the latter was used in Pamplona et al (2006); Goncalves et al (2008); Guo et al (2016); Wang et al (2019); Hejazi et al (2021). On the one hand, the resultant axial force can be fixed by suspending a dead weight at one end while air comes into the tube from the other end.…”