Study of bifurcation in a pressurized hyperelastic membrane tube enclosed by a soft substrate

Varatharajan, N.; DasGupta, Anirvan

doi:10.1016/j.ijnonlinmec.2017.05.004

Cited by 16 publications

(7 citation statements)

References 49 publications

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“…It is also probably the simplest prototypical example to demonstrate the coexistence of two uniform deformations and how a high-gradient theory in lower dimension can be derived from the exact nonlinear elasticity theory (Lestringant & Audoly, 2018). Recent interest in the localized bulging problem has also been spurred by its relevance to modelling aneurysm initiation and rupture (Ren, 2007;Varatharajan & DasGupta, 2017;Alhayani et al, 2013Alhayani et al, , 2014Demirkoparan & Merodio, 2017b), suppression of localized bulging in energy harvesting devices (Bucchi & Hearn, 2013a,b), and potential use of electroelastic tubes in actuators (Lu et al, 2015;An et al, 2015;Wang et al, 2017a). Other recent studies have addressed the effects of swelling (Demirkoparan & Merodio, 2017a), viscoelasticity/chemorheology (Wineman, 2015(Wineman, , 2017, and plasticity (Takla, 2018).…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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“…Some authors [23][24][25] , have modeled wall's channels by means of hyperelastic models and have performed numerical studies to investigate the formation and growth of aneurysms in cylindrical channels and the elasticity of arterial tissue affected by Marfan's syndrome was analyzed by Merodio and Haughton [26,27] . However, most of the research works found in the literature have used only one constitutive hyperelastic model.…”

Section: Introductionmentioning

confidence: 99%

Biomechanical analysis of PDMS channels using different hyperelastic numerical constitutive models

Cardoso¹,

Fernandes²,

Lima³

et al. 2018

Mechanics Research Communications

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a b s t r a c tBrain aneurysms are pathological dilatations of cerebral arteries and are known as one of the most common and serious cerebrovascular events. However, patients with cerebral aneurysms do not exhibit evident symptoms until they rupture. The main objective of the present study is to perform numerical characterizations of the biomechanical behavior of aneurysms in order to analyze the blood vessel wall behavior during the formation of an aneurysm. By taking into account different geometric and physiological parameters, flow simulations of a well-known Newtonian fluid (glycerin) was performed using the commercial finite volume method package Ansys® -Fluent, and pressure along the channel was determined. These pressures were imported into the channel, in the Ansys®-Static Structural, in order to evaluate and analyze the displacement and strain fields in the channel wall, caused by the internal pressure induced by the fluid flow. All calculations were performed by using the most widely accepted hyperelastic constitutive models and it was found that any constitutive model can be applied to this kind of studies, allowing to visualize where pressure achieves its maximum value and consequently, the most favorable region where the rupture is more likely to occur.

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“…In particular, it is now known that the bifurcation condition for localized bulging coincides with the condition for the limiting point instability in the case of free ends although this connection is lost in the case of fixed ends. Recognising that localised bulging is a "zero wavenumber" bifurcation phenomenon, recent studies have examined the weakly nonlinear near-critical behaviour (Ye et al, 2020), and the effects of rotation, fibre-reinforcement, tethering and multi-layering on bulge initiation (Wang et al, 2017;Varatharajan & DasGupta, 2017;Liu et al, 2019;Ye et al, 2019). The methodology developed has also been extended to study surface tension induced necking (Fu et al, 2021;Emery & Fu, 2021b,a,c).…”

Section: Introductionmentioning

confidence: 99%

Localised bulging of an inflated rubber tube with fixed ends

Guo¹,

Wang²,

Fu³

2022

Preprint

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When a rubber tube with free ends is inflated under volume control, the pressure will first reach a maximum and then decrease monotonically to approach a constant asymptote. The pressure maximum corresponds to the initiation of a localised bulge and is predicted by a bifurcation condition, whereas the asymptote is the Maxwell pressure corresponding to a "two-phase" propagation state. In contrast, when the tube is first pre-stretched and then has its ends fixed during subsequent inflation, the pressure versus bulge amplitude has both a maximum and a minimum, and the behaviour on the right ascending branch has previously not been fully understood. We show that for all values of pre-stretch and tube length, the ascending branches all converge to a single curve that is only dependent on the ratio of tube thickness to the outer radius. This curve represents the Maxwell state to be approached in each case (if Euler buckling or axisymmetric wrinkling does not occur first), but this state is pressure-dependent in contrast with the free-ends case. We also demonstrate experimentally that localized bulging cannot occur when the pre-stretch is sufficiently large and investigate what strain-energy functions can predict this observed phenomenon.

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Study of bifurcation in a pressurized hyperelastic membrane tube enclosed by a soft substrate

Cited by 16 publications

References 49 publications

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

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

Biomechanical analysis of PDMS channels using different hyperelastic numerical constitutive models

Localised bulging of an inflated rubber tube with fixed ends

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