Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Sorbonne Université, Campus Pierre et Marie Curie
Paris, Francetel: +33 1 44 27 72 61 (secr. 37 90)
e-mail: sebastien.neukirch (-atat-) sorbonne-universite.fr
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Geometry and mechanics of uniform n-plies: from engineering ropes to biological filaments
Sébastien Neukirch & G. van der Heijden
Journal of Elasticity, 69 (2002) 41-72
Abstract : We study the mechanics of uniform n-plies, that is, structures formed by n helical strands plied together. We first show that the well-known lock-up phenomenon for n = 2, described by a pitchfork bifurcation, gets unfolded for higher n. Geometrically, n-plies with n > 2 are all found to behave qualitatively the same. Next we consider the mechanics of n-plies, allowing for axial end forces and end moments. An expression for the interstrand pressure force is derived and used to investigate the birdcage failure mode of plied structures.
Mathematics Subject Classifications (2000): 34B08, 37J35, 74B20, 74G05, 74G60, 74K10
Key words : multi-strand plies, rod mechanics, end loads, constitutive relations, twist-stretch coupling, strand separation, birdcaging, helix, link, writhe, wire rope, DNA, proteins.
download the-print version : PDF (1.6 Mo) or gzipped PS (1.4 Mo)
DOI: 10.1023/A:1027390700610download the journal version PDF (412 ko) - Note that formula (17) is incorrect and has to be replaced by formula (17) of the pre-print version.