# Instability Investigation On Fluid-loaded Pre-stretched Cylindrical Membranes

Amit Patil, Arne B. Nordmark, Anders Eriksson

Published 2015 · Mathematics

This paper discusses the evaluation of instabilities on the quasi-static equilibrium path of fluid-loaded pre-stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point. The membrane is represented by only the in-plane stress components, for which an incompressible, isotropic hyperelastic material model is assumed. The free inflation problem yields governing equations and boundary conditions, which are discretized by finite differences and solved by a Newton–Raphson method. An incremental arclength-cubic extrapolation method is used to find generalized equilibrium paths, with different parametrizations. Limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter. An eigen-mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point. A limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio (length/radius) is high, whereas for smaller aspect ratios, the limit point with respect to fluid level is observed at over-filling. Pre-stretch is observed to have a stiffening effect in the pre-limit zone and a softening effect in the post-limit zone.

This paper references

10.1007/S11012-015-0102-7

Constrained inflation of a stretched hyperelastic membrane inside an elastic cone

Amit Patil (2015)

10.1016/0022-5096(78)90017-0

On the incremental equations in non-linear elasticity — II. Bifurcation of pressurized spherical shells

David M. Haughton (1978)

10.1016/J.IJSOLSTR.2012.10.004

Axisymmetric bifurcations of thick spherical shells under inflation and compression

Gal deBotton (2013)

10.1016/0020-7462(70)90027-2

Liquid filled membranes

Don L. Boyer (1970)

10.1098/rspa.1990.0055

Tension-field theory

David J. Steigmann (1990)

10.1016/0022-460X(90)90528-8

Application of the incremental harmonic balance method to cubic non-linearity systems

Yau K. Cheung (1990)

10.1016/0020-7683(92)90096-C

Inflation of an elastic cylindrical membrane: Non-linear deformation and instability

Roger E. Khayat (1992)

10.1243/03093247V222115

Free and constrained inflation of elastic membranes in relation to thermoforming — axisymmetric problems

J. M. Charrier (1987)

10.1016/S0020-7683(00)00151-7

Finite axisymmetric deformations of an initially stressed fluid-filled cylindrical membrane

Djenane Cordeiro Pamplona (2001)

10.1098/rsta.2009.0118

Axial-symmetry breaking in constrained membranes

Paolo Biscari (2009)

10.1002/nme.1620372203

Inflation of hyperelastic cylindrical membranes as applied to blow moulding. Part I. Axisymmetric case

Roger E. Khayat (1994)

10.1016/0020-7403(71)90013-0

The tensile instability of an inflated cylindrical membrane as affected by an axial load

Helen M Alexander (1971)

10.1016/S0020-7683(96)00119-9

Stability and bifurcation of finite deformations of elastic cylindrical membranes—Part I. Stability analysis

Yi-chao Chen (1997)

10.1016/S0889-9746(89)90038-8

Vibrations of an inextensible cylindrical membrane inflated with liquid

J.-C. Hsieh (1989)

10.1016/J.JMPS.2013.11.013

On the static and dynamic analysis of inflated hyperelastic circular membranes

Abhijit Chaudhuri (2014)

10.1016/0020-7462(95)00019-K

Point loads on a hemispherical elastic membrane

Xiaoguang Li (1995)

10.1002/cnm.2557

Finite element analysis of balloon-expandable coronary stent deployment: influence of angioplasty balloon configuration.

David Moral Martín (2013)

10.1002/1097-0207(20010220)50:5<1233::AID-NME77>3.0.CO;2-W

Dynamic inflation of non‐linear elastic and viscoelastic rubber‐like membranes

Erwan Verron (2001)

10.1016/0022-5096(79)90027-9

Bifurcation of inflated circular cylinders of elastic material under axial loading—II. Exact theory for thick-walled tubes

David R. Haughton (1979)

10.1093/imamat/56.3.303

Axisymmetric elastic membranes subjected to fluid loading

David M. Haughton (1996)

10.1016/J.EUROMECHSOL.2013.02.007

Finite inflation of an initially stretched hyperelastic circular membrane

Amit Patil (2013)

10.1115/1.3169168

Load-Supporting Fluid-Filled Cylindrical Membranes

Victor Namias (1985)

10.1016/J.CMA.2012.05.012

Instability of hyper-elastic balloon-shaped space membranes under pressure loads

Anders Eriksson (2012)

10.1016/0045-7949(95)00114-V

Computing critical points and secondary paths in nonlinear structural stability analysis by the finite element method

Jicong Shi (1996)

10.1016/J.IJNONLINMEC.2012.09.008

Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section

Ganesh Tamadapu (2013)

10.1007/S00707-010-0418-2

On the contact of an inflated spherical membrane-fluid structure with a rigid conical indenter

Touqeer Sohail (2011)

10.1122/1.551017

Dynamic inflation of hyperelastic spherical membranes

Erwan Verron (1999)

10.1016/0045-7825(94)90163-5

Fold lines for sensitivity analyses in structural instability

Anders S. Eriksson (1994)

10.1016/J.IJSOLSTR.2015.04.025

Contact mechanics of a circular membrane inflated against a deformable substrate

Amit Patil (2015)

10.1016/J.IJNONLINMEC.2011.05.011

Fluid pressure loading of a hyperelastic membrane

A. P. S. Selvadurai (2012)

10.1016/0045-7825(96)01047-X

The post-critical analysis of axisymmetric hyper-elastic membranes by the finite element method

Jing Li Shi (1996)

10.1108/eb023727

A simple method for the calculation of postcritical branches

Werner Wagner (1988)

10.1006/jfls.1995.1053

A Complete Linear Theory for a Two-Dimensional Floating and Liquid-Filled Membrane Structure in Waves

Rui Zhao (1995)

10.1122/1.549185

The Inflation of Axially Symmetric Membranes by Linearly Varying Hydrostatic Pressure

Lee-po Yu (1970)

10.1016/j.euromechsol.2008.11.006

A semi-analytical approach for the nonlinear two-dimensional analysis of fluid-filled thin-walled pliable membrane tubes

Esmaeal Ghavanloo (2009)

10.1103/PHYSREVE.88.053201

Geometrical feature of the scaling behavior of the limit-point pressure of inflated hyperelastic membranes.

Ganesh Tamadapu (2013)

10.1016/0020-7683(79)90081-7

An incremental approach to the solution of snapping and buckling problems

E. Riks (1979)

10.1098/rspa.2004.1419

A nonlinear, anisotropic and axisymmetric model for balloon angioplasty

D. A. Eftaxiopoulos (2005)

10.1093/imamat/36.1.85

The Relaxed Energy Density for Isotropic Elastic Membranes

Allen C. Pipkin (1986)

10.1016/J.COMPSTRUC.2014.07.021

Non-unique response of Mooney-Rivlin model in bi-axial membrane stress

Anders Eriksson (2014)

10.1016/0020-7225(71)90017-6

Tensile instability of initially spherical balloons

Harold Alexander (1971)

10.1016/S0263-8231(03)00023-5

Numerical analysis of rubber balloons

Erwan Verron (2003)

10.1063/1.3054128

Flow of artificial microcapsules in microfluidic channels: A method for determining the elastic properties of the membrane

Yannick Lefebvre (2008)

10.1098/rspa.2014.0282

Free and constrained inflation of a pre-stretched cylindrical membrane

Amit Patil (2014)

10.1115/1.2894115

The mechanics of axially symmetric liposomes.

Djenane Cordeiro Pamplona (1993)

10.1016/0020-7462(95)00004-8

Finite deformation of a pressurized toroidal membrane

Xiaoguang Li (1995)

Inflatable dams

HO Anwar (1967)

10.1115/1.3138234

Mechanics and Thermodynamics of Biomembranes

Evan Evans (2017)

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10.1007/s11071-020-05661-z

Intra-well and cross-well chaos in membranes and shells liable to buckling

Frederico M. A. Silva (2020)

10.1016/J.IJNONLINMEC.2016.08.002

Cylindrical membrane partially stretched on a rigid cylinder

Alexey M. Kolesnikov (2016)

10.1016/J.IJMECSCI.2018.06.034

Mechanical behaviour of short membranous liquid-filled cylinders under axial loadings

Majid Soleimani (2018)

10.1016/J.IJSOLSTR.2017.12.015

Instabilities in the axisymmetric magnetoelastic deformation of a cylindrical membrane

Narravula Harshavardhan Reddy (2017)

10.1016/J.IJNONLINMEC.2017.09.004

Instability investigation for rotating thin spherical membrane

Yang Zhou (2017)

10.1016/J.IJNONLINMEC.2017.06.017

Limit points in the free inflation of a magnetoelastic toroidal membrane

Narravula Harshavardhan Reddy (2017)

10.1016/J.EUROMECHSOL.2015.05.015

Wrinkling of cylindrical membranes with non-uniform thickness

Amit Patil (2015)

10.1016/J.IJNONLINMEC.2017.08.008

Tension of a cylindrical membrane partially stretched over a rigid cylinder

Alexey M. Kolesnikov (2017)

10.1016/J.IJMECSCI.2017.07.011

Multi-parametric stability investigation for thin spherical membranes with contacts

Yang Zhou (2017)

10.1016/J.IJSOLSTR.2015.04.025

Contact mechanics of a circular membrane inflated against a deformable substrate

Amit Patil (2015)

10.1016/J.JMPS.2016.05.014

Instabilities of wrinkled membranes with pressure loadings

Amit Patil (2016)

Inflation and Instabilities of Hyperelastic Membranes

Amit Patil (2016)

10.1007/s00466-019-01755-7

A wrinkling model for pneumatic membranes and the complementarity computational framework

Liang Zhang (2020)