Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes

Alain Goriely, Michael Tabor

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells reinforced by one or two families of fibres. We consider both small and large deformations and the reduction from thick cylindrical shells (tubes) to thin shells (cylindrical membranes). In particular, a number of universal parameter regimes can be identified where the response behaviour of the cylinder is qualitatively different. This include the possibility of inversion of twist or axial strain when the cylinder is subject to internal pressure.

Original languageEnglish (US)
Article number20130011
JournalProceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences
Volume469
Issue number2153
DOIs
StatePublished - May 8 2013

Fingerprint

cylindrical shells
Cylindrical Shell
Tube
Inversion
Membrane
inversions
tubes
membranes
Membranes
Nonlinear Elasticity
Thin Shells
Large Deformation
Twist
Biology
elastic shells
Elasticity
internal pressure
axial strain
Fiber
Engineering

Keywords

  • Anisotropy
  • Fibre-reinforced
  • Inversion
  • Nonlinear elasticity
  • Perversion

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

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AB - Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells reinforced by one or two families of fibres. We consider both small and large deformations and the reduction from thick cylindrical shells (tubes) to thin shells (cylindrical membranes). In particular, a number of universal parameter regimes can be identified where the response behaviour of the cylinder is qualitatively different. This include the possibility of inversion of twist or axial strain when the cylinder is subject to internal pressure.

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