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

Sylvain Reboux, Giles Richardson, Oliver E. Jensen

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    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 forcedisplacement 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. pdfS0956792509990015a.pdfdispartPapers © 2009 Copyright Cambridge University Press 2009.
    Original languageEnglish
    Pages (from-to)479-518
    Number of pages39
    JournalEuropean Journal of Applied Mathematics
    Issue number6
    Publication statusPublished - Dec 2009


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