Skip Navigation



The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on December 1, 2007
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbm021
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
61/1/1    most recent
hbm021v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Preston, S. P.
Right arrow Articles by Richardson, G.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

BUCKLING OF AN AXISYMMETRIC VESICLE UNDER COMPRESSION: THE EFFECTS OF RESISTANCE TO SHEAR

S. P. Preston, O. E. Jensen and G. Richardson{dagger}

( School of Mathematical Sciences, University Park, University of Nottingham, Nottingham NG7 2RD )

{dagger} < giles.richardson{at}nottingham.ac.uk>

Received 29 May 2007. Revise 23 August 2007. Accepted 24 August 2007.


  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.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.