Stability and buckling of a flat circular, intrinsically curved filament spanned by a fluid film

Abstract eng:
We study stability and buckling behavior of generic flat circular configurations of flexible but inextensible loops made from filaments with intrinsic curvature and spanned by liquid films. Three dimensionless parameters govern stability and buckling. Of these, the dimensionless surface tension of the liquid film and the ratio of torsional rigidity to flexural rigidity of the filament are familiar from previous works. The remaining parameter, namely the dimensionless intrinsic curvature of the filament, captures the influence of the curvilinear rest configuration. In-plane and out-of-plane buckling modes corresponding to stable solution branches that bifurcate from the branch of flat circular solutions are found to exist. The critical value of the dimensionless surface tension needed to induce out-of-plane buckling is found to be less than that needed to induce in-plane buckling. The destabilizing influence of the intrinsic curvature can nevertheless be countered by increasing the torsional rigidity relative to the flexural rigidity.

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