Coiling of an elastic beam inside a disk: A model for spider-capture silk

Hervé Elettro (1) , Fritz Vollrath (2) , Arnaud Antkowiak (1) , Sébastien Neukirch (1)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 Department of Zoology, University of Oxford

Motivated by recent experimental observations of capillary-induced spooling of fibers inside droplets both in spider capture silk and in synthetic systems, we investigate the behavior of a fiber packed in a drop. Using a simplified 2D model, we provide analytical predictions for the buckling threshold and the deep post-buckling asymptotic behavior. The threshold for spooling is found to be in particularly good agreement with experimental results. We further solve the Elastica equations for a fiber confined in a soft potential, and track the equilibrium paths using numerical continuation techniques. A wealth of different paths corresponding to different symmetries is uncovered, and their stability is finally discussed.

Mots clés: Bioinspiration; Post-buckling; Bifurcations; Stability; Elastica; Equilibria paths; Continuation; Coiling; Packing; Elastocapillarity

Domaines: Mécanique [physics]

Hervé Elettro, Fritz Vollrath, Arnaud Antkowiak, Sébastien Neukirch. Coiling of an elastic beam inside a disk: A model for spider-capture silk. International Journal of Non-Linear Mechanics, 2015, 75, pp.59-66. ⟨10.1016/j.ijnonlinmec.2015.03.008⟩. ⟨hal-01141994⟩