The filament-bundle elastica

Hermes Augusto Buarque Gadelha

doi:10.1093/imamat/hxy011

The filament-bundle elastica

Hermes Augusto Buarque Gadelha

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	634-654
Journal	IMA Journal of Applied Mathematics
Volume	83
Issue number	4
Early online date	25 Jul 2018
DOIs	https://doi.org/10.1093/imamat/hxy011
Publication status	Published - 25 Jul 2018

Bibliographical note

© The Author(s) 2018. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Access to Document

10.1093/imamat/hxy011

IMA_bundle_elastica_final
© The Author(s) 2018. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details
Accepted author manuscript, 2.53 MBLicence: Unspecified

Cite this

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title = "The filament-bundle elastica",

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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N2 - 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.

AB - 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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