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

By S.P. Preston, O.E. Jensen and Giles Richardson


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 &gt; 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. <br/><br/

Year: 2007
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Provided by: e-Prints Soton

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