Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear
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).
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.
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
|Date Deposited:||03 Jun 2010 11:16|
|Last Modified:||08 Jun 2012 12:51|
|Contributors:||Preston, S.P. (Author)
Jensen, O.E. (Author)
Richardson, Giles (Author)
|Date:||1 December 2007|
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