Instability analysis in pressurized three-layered fiber-reinforced anisotropic rubber tubes in torsion

Ren, Jiusheng; Zhou, Jin-wen; Yuan, Xiying

doi:10.1016/j.ijengsci.2010.12.013

Cited by 13 publications

(6 citation statements)

References 20 publications

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“…An inflated rubber tube is also susceptible, at least theoretically, to buckling into an axially symmetric periodic mode [27][28][29][30] and the limit point instability [31][32][33][34]. These two types of buckling/instability were not thought to be relevant to localized bulging for a long time, and only recently have their connections become clear [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Localized bulging of an inflated rubber tube with fixed ends

Wang

2022

Phil. Trans. R. Soc. A.

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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 localized bulge and is predicted by a bifurcation condition, whereas the asymptote is the Maxwell pressure corresponding to a ‘two-phase’ propagation state. By contrast, when the tube is first pre-stretched and then has its ends fixed during subsequent inflation, the pressure as a function of the 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 the pre-stretch and tube length, the ascending branches all converge to a single curve that is dependent only on the ratio of the 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 to 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. This article is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.

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Section: Introductionmentioning

confidence: 99%

Localized bulging of an inflated rubber tube with fixed ends

Wang

2022

Phil. Trans. R. Soc. A.

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“…The first strand consists of bifurcation and stability studies in which the bifurcation or instability modes are periodic in the axial and/or azimuthal direction; see, for instance, Shield (1972), Haughton & Ogden (1979a,b), Chen (1997), Chen & Haughton (2003), Merodio & Haughton (2010), and Rodriguez & Merodio (2011). The second strand is concerned with the socalled "limiting-point" instability, which refers to the fact that under uniform inflation the pressure as a function of internal volume may reach a maximum; see Alexander (1971), Benedict et al (1979), Kanner & Horgan (2007), Ren et al (2011), Horny et al (2015), and the references therein. The third strand comprises analytical, experimental and numerical studies of localized bulging; see, for instance, Yin (1977), Chater & Hutchinson (1991), Kyriakides & Chang (1990, Shi & Moita (1996), Pamplona et al (2006), Goncalves et al (2008).…”

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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“…An inflated rubber tube is also susceptible, at least theoretically, to buckling into an axially symmetric periodic mode (Shield, 1972;Haughton & Ogden, 1979a,b;Chen, 1997) and the limiting point instability (Alexander, 1971;Kanner & Horgan, 2007;Ren et al, 2011;Horny et al, 2015). These two types of buckling/instability were not thought to be relevant to localised bulging for a long time and it was only recently that their connections had become clear (Fu et al, 2008(Fu et al, , 2016Yu & Fu, 2021).…”

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.

show abstract

Instability analysis in pressurized three-layered fiber-reinforced anisotropic rubber tubes in torsion

Cited by 13 publications

References 20 publications

Localized bulging of an inflated rubber tube with fixed ends

Localized bulging of an inflated rubber tube with fixed ends

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

Localised bulging of an inflated rubber tube with fixed ends

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