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Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear

Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear
Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear
We consider the axisymmetric deformation of an initially spherical, porous vesicle with incompressible membrane having finite resistance to in-plane shearing, as the vesicle is compressed between parallel plates. We adopt a thin-shell balance-of-forces formulation in which the mechanical properties of the membrane are described by a single dimensionless parameter, C, which is the ratio of the membrane's resistance to shearing to its resistance to bending. This results in a novel free-boundary problem which we solve numerically to obtain vesicle shapes as a function of plate separation, h. For small deformations, the vesicle contacts each plate over a small circular area. At a critical value of plate separation, hTC, there is a transcritical bifurcation from which a new branch of solutions emerges, representing buckled vesicles which contact each plate along a circular curve. For the values of C investigated, we find that the transcritical bifurcation is subcritical and that there is a further saddle-node bifurcation (fold) along the branch of buckled solutions at h = hSN (where hSN > hTC). The resulting bifurcation structure is commensurate with a hysteresis loop in which a sudden transition from an unbuckled solution to a buckled one occurs as h is decreased through hTC and a further sudden transition, this time from a buckled solution to an unbuckled one, occurs as h is increased through hSN. We find that hSN and hTC increase with C, that is, vesicles that resist shear are more prone to buckling.

0033-5614
1-24
Preston, S.P.
8fcc34d1-acbf-4f9c-9ab4-22a9282959f4
Jensen, O.E.
b72436bc-7fa6-4a5d-9373-b5bb648a762f
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Preston, S.P.
8fcc34d1-acbf-4f9c-9ab4-22a9282959f4
Jensen, O.E.
b72436bc-7fa6-4a5d-9373-b5bb648a762f
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91

Preston, S.P., Jensen, O.E. and Richardson, Giles (2007) Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear. Quarterly Journal of Mechanics and Applied Mathematics, 61 (1), 1-24. (doi:10.1093/qjmam/hbm021).

Record type: Article

Abstract

We consider the axisymmetric deformation of an initially spherical, porous vesicle with incompressible membrane having finite resistance to in-plane shearing, as the vesicle is compressed between parallel plates. We adopt a thin-shell balance-of-forces formulation in which the mechanical properties of the membrane are described by a single dimensionless parameter, C, which is the ratio of the membrane's resistance to shearing to its resistance to bending. This results in a novel free-boundary problem which we solve numerically to obtain vesicle shapes as a function of plate separation, h. For small deformations, the vesicle contacts each plate over a small circular area. At a critical value of plate separation, hTC, there is a transcritical bifurcation from which a new branch of solutions emerges, representing buckled vesicles which contact each plate along a circular curve. For the values of C investigated, we find that the transcritical bifurcation is subcritical and that there is a further saddle-node bifurcation (fold) along the branch of buckled solutions at h = hSN (where hSN > hTC). The resulting bifurcation structure is commensurate with a hysteresis loop in which a sudden transition from an unbuckled solution to a buckled one occurs as h is decreased through hTC and a further sudden transition, this time from a buckled solution to an unbuckled one, occurs as h is increased through hSN. We find that hSN and hTC increase with C, that is, vesicles that resist shear are more prone to buckling.

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Published date: 1 December 2007
Organisations: Applied Mathematics

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Local EPrints ID: 156323
URI: http://eprints.soton.ac.uk/id/eprint/156323
ISSN: 0033-5614
PURE UUID: 8cb75b56-f9e3-4d4c-90b4-1b8829a7380e

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Date deposited: 03 Jun 2010 11:16
Last modified: 08 Jan 2022 05:33

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Contributors

Author: S.P. Preston
Author: O.E. Jensen

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