Localized bulging in an inflated bilayer tube of arbitrary thickness: Effects of the stiffness ratio and constitutive model

Yang, Ye; Yang, Lo; Althobaiti, Ali; Xie, Yuxin

doi:10.1016/j.ijsolstr.2019.06.009

Cited by 17 publications

(13 citation statements)

References 62 publications

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“…Accordingly, theoretical or numerical analysis was performed to supply mechanical insight into possible pathogenesis behind aneurysms, see Alhayani et al (2014); Fu and II'ichev (2015); DasGupta (2017, 2018) and the references therein. In particular, our previous analysis reveals a fact that an aneurysm is more prone to appear as the innermost layer of an artery stiffens (Ye et al, 2019). This qualitatively interprets why the risk of aneurysm formation for a person becomes higher with aging (Kohn et al, 2015).…”

Section: Introductionsupporting

confidence: 57%

“…Within the framework of nonlinear elasticity, an explicit bifurcation condition for thick tubes was derived by Fu et al (2016), and the accuracy of membrane assumption was examined. This bifurcation condition paves a convenient way to study localized bugling in rotating cylinders (Wang et al, 2017), fiber-reinforced tubes (Wang and Fu, 2018), and layered tubes (Liu et al, 2019;Ye et al, 2019). Furthermore, a comprehensive understanding of localized bulging can provide useful insight into localized necking (Fu et al, 2018).…”

Section: Introductionmentioning

confidence: 90%

“…This concise bifurcation condition was first proposed by Fu et al (2016) in the framework of finite elasticity. Later, its applicability to localized bulging in bilayer tubes was verified numerically using FE analysis in commercial software Abaqus (Liu et al, 2019;Ye et al, 2019). Recently, Yu and Fu (2021) offered analytical proof of this bifurcation condition with two relatively weak assumptions.…”

Section: Primary Deformation and Bifurcation Conditionmentioning

confidence: 98%

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

Liu¹,

Yang²,

Xie³

2022

Preprint

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We study the initiation and evolution of aneurysmal morphology in a pressurized soft tube where the elastic modulus is non-uniform in the radial direction. The primary deformation prior to instability is characterized within the framework of nonlinear elasticity for a general material constitution and a generic modulus gradient. To unravel the influence of modulus gradient on aneurysm formation, we employ the incompressible Gent model and select three representative modulus gradients, including a linear, an exponential, and a sinusoidal function. In particular, the sinusoidal distribution can be used to model actual artery structure. In addition, two prototypical loading conditions are considered, namely, either the resultant axial force or the axial length can be fixed. Based on an explicit bifurcation condition in terms of the internal pressure and the resultant axial force for aneurysm formation or localized bulging, an exhaustive theoretical analysis on bulge initiation is carried out and the effect of geometric and material parameters and modulus gradient on the critical stretch generating localized bulging is revealed. It turns out that the modulus mismatch, as well as the position of maximum modulus, can dramatically affect the onset of localized bulging. Then we analytically elucidate the influence of modulus gradient on bulge propagation according to Maxwell's equal-area rule and conduct a finite element analysis of bulge evolution. To perform post-bifurcation analysis, a robust finite element model for graded Gent material is established in Abaqus by UHYPER subroutine coding. Interestingly, it is found that a sinusoidally distributed modulus has negligible influence on the critical stretch of bulge initiation, the deformation process of bugle growth, and the maximum size of a bulge. The current analysis not only can be used to qualitatively explain why a healthy human artery evolves into a sandwich structure where the intermediate layer is stiffest but also can provide useful insight into localized instabilities such as necking and beading in graded structures.

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Section: Introductionsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 90%

Section: Primary Deformation and Bifurcation Conditionmentioning

confidence: 98%

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

Liu¹,

Yang²,

Xie³

2022

Preprint

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“…It was shown in Fu et al (2016) that the bifurcation condition for localized bulging of inflated tubes of arbitrary wall thickness takes a very simple form, namely that the Jacobian determinant of the internal pressure and resultant axial force as functions of two principal stretches is zero. This result makes it possible to examine the effect of rotation (Wang et al, 2017b), fibre-reinforcement (Wang & Fu, 2018), and multi-layering (Liu et al, 2019;Ye et al, 2019) in a systematic manner. An experimental study guided by these newly emerged theoretical results has also been conducted (Wang et al, 2019).…”

Section: Introductionmentioning

confidence: 97%

Weakly nonlinear analysis of localized bulging of an inflated hyperelastic tube of arbitrary wall thickness

Yang

2020

Journal of the Mechanics and Physics of Solids

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A weakly nonlinear analysis is conducted for localized bulging of an inflated hyperelastic cylindrical tube of arbitrary wall thickness. Analytical expressions are obtained for the coefficients in the amplitude equation despite the fact that the primary deformation is inhomogeneous and the incremental governing equations have variable coefficients. It is shown that for each value of wall thickness a localized bulging solution does indeed bifurcate subcritically from the primary solution for almost all values of fixed axial force or fixed axial stretch for which the bifurcation condition is satisfied, as reported in all previous experimental studies, but there also exist extreme cases of fixed axial stretch for which localized bulging gives way to localized necking. Validation is carried out by comparing with results obtained under the membrane assumption and with fully numerical simulations based on Abaqus. It is shown that even for thin-walled tubes the membrane approximation becomes poorer and poorer as the tube is subjected to increasingly larger and larger axial stretch or force prior to inflation.

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“…Following these works, a form of bifurcation condition based on the Jacobian function of the internal pressure and axial force, which in turn are expressed in terms of the axial and circumferential stretches, is obtained [27]. Using this method, the effects of multi-layering [28,29] and fibre reinforcement [30] have been examined. In all of these studies, the footprint of BCs is evident.…”

Section: Introductionmentioning

confidence: 99%

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

2021

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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.

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Localized bulging in an inflated bilayer tube of arbitrary thickness: Effects of the stiffness ratio and constitutive model

Cited by 17 publications

References 62 publications

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

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

Weakly nonlinear analysis of localized bulging of an inflated hyperelastic tube of arbitrary wall thickness

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

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