General theory for plane extensible elastica with arbitrary undeformed shape Articles uri icon

authors

  • Taloni, Alessandro
  • VILONE, DANIELE
  • Ruta, Giuseppe

publication date

  • September 2023

start page

  • 1

end page

  • 11

volume

  • 193

International Standard Serial Number (ISSN)

  • 0020-7225

Electronic International Standard Serial Number (EISSN)

  • 1879-2197

abstract

  • A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This expression appears to be suitable for one-dimensional models of polymers or vesicles, the natural configuration of which is characterized by locally changing curvature. In a linear setting, we derive the macroscopic stress-strain relations, providing an universal criterion for the neutral curve location. In this respect, we further demonstrate that the neutral curve existence constitutes the fundamental requirement for the conformational dynamics of any inextensbile biological filament.

subjects

  • Mathematics

keywords

  • elasticity; linear deformations; neutral curve