The filament-bundle elastica

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JournalIMA Journal of Applied Mathematics
DateAccepted/In press - 30 Mar 2018
DateE-pub ahead of print - 25 Jul 2018
DatePublished (current) - 25 Jul 2018
Issue number4
Volume83
Pages (from-to)634-654
Early online date25/07/18
Original languageEnglish

Abstract

Filament-bundles are ubiquitous in nature. They are composed by an assembly of flexible rods held together by elastic springs, such as found in ciliary systems and flagella. We study the static, post-transient, post-buckled configurations of a generalised filament-bundle elastica or flagella. We recur to linear and weakly non-linear analysis, as well as geometrically exact numerical solutions. The bundle cross-linking mechanics is characterised by non-local moments affecting distant parts of the bundle. This induces a bimodal post-buckling response sensitive to the interfilament sliding at the base. We report the occurrence of a novel reversed cusp catastrophe, reminiscent of the counterbend phenomenon, that folds and suppresses the saddle-node bifurcation back a pitchfork bistability landscape, found in classical elastica systems. The filament-bundle elastica can thus prevent violent jumps, non-uniqueness and hysteresis. This non-trivial folding of the imperfection-sensitivity diagram may impact bundle systems with naturally occurring buckling phenomena.

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