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An asymptotic analysis of the buckling of a highly shear resistant vesicle

An asymptotic analysis of the buckling of a highly shear resistant vesicle
An asymptotic analysis of the buckling of a highly shear resistant vesicle
The static compression between two smooth plates of an axisymmetric capsule or vesicle is investigated by means of asymptotic analysis. The governing equations of the vesicle are derived from thin-shell theory and involve a bending stiffness B, a shear modulus H, the unstressed vesicle radius a and a constant surface-area constraint. The sixth-order free-boundary problem obtained by a balance-of-forces approach is addressed in the limit when the dimensionless parameter C = Ha2/B is large and the plate displacements are small. When the plate displacement is of order aC?1/2, the vesicle undergoes a sub-critical buckling instability which is captured by leading-order asymptotics. Asymptotic linear and quadratic force–displacement relations for the pre- and post-buckled solutions are determined. The leading-order post-buckled solution is described by a simple fourth-order problem, exhibiting stress-focusing with stretching and bending confined to a narrow boundary layer. In contrast, in the pre-buckled state, stretching occurs over a larger length scale than bending. The results are in good qualitative agreement with numerical simulations for finite values of C
0956-7925
479-518
Reboux, Sylvain
11e4dfba-7947-49b8-8686-df86931a56d0
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Jensen, Oliver E.
efc79b33-9dce-4600-8a10-33692c1fbbda
Reboux, Sylvain
11e4dfba-7947-49b8-8686-df86931a56d0
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Jensen, Oliver E.
efc79b33-9dce-4600-8a10-33692c1fbbda

Reboux, Sylvain, Richardson, Giles and Jensen, Oliver E. (2009) An asymptotic analysis of the buckling of a highly shear resistant vesicle. European Journal of Applied Mathematics, 20 (6), 479-518. (doi:10.1017/S0956792509990015).

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Abstract

The static compression between two smooth plates of an axisymmetric capsule or vesicle is investigated by means of asymptotic analysis. The governing equations of the vesicle are derived from thin-shell theory and involve a bending stiffness B, a shear modulus H, the unstressed vesicle radius a and a constant surface-area constraint. The sixth-order free-boundary problem obtained by a balance-of-forces approach is addressed in the limit when the dimensionless parameter C = Ha2/B is large and the plate displacements are small. When the plate displacement is of order aC?1/2, the vesicle undergoes a sub-critical buckling instability which is captured by leading-order asymptotics. Asymptotic linear and quadratic force–displacement relations for the pre- and post-buckled solutions are determined. The leading-order post-buckled solution is described by a simple fourth-order problem, exhibiting stress-focusing with stretching and bending confined to a narrow boundary layer. In contrast, in the pre-buckled state, stretching occurs over a larger length scale than bending. The results are in good qualitative agreement with numerical simulations for finite values of C

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Published date: December 2009

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Local EPrints ID: 69571
URI: http://eprints.soton.ac.uk/id/eprint/69571
ISSN: 0956-7925
PURE UUID: d48719e7-d525-429d-9885-6350923a123c

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Date deposited: 19 Nov 2009
Last modified: 08 Jan 2022 05:24

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Author: Sylvain Reboux
Author: Oliver E. Jensen

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