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We investigate the mechanics of elastic fibres carrying liquid droplets. Insuch systems, buckling may localize inside the drop cavity if the fibre is thinenough. This so-called drop-on-coilable-fibre system exhibits a surprisingliquid-like response under compression, and a solid-like response undertension. Here we analyze this unconventional behavior in further details andfind theoretical, numerical and experimental evidences of negative stiffnessevents. We find that the first and main negative stiffness regime owes itsexistence to the transfer of capillary-stored energy into mechanical curvatureenergy. The following negative stiffness events are associated with changes inthe coiling morphology of the fibre. Eventually coiling becomes tightly lockedinto an ordered phase where liquid and solid deformations coexist.

Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology