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Abstract

We present a model of multilayer folding in which layers with bending stiffness EI are separated by a very stiff elastic medium of elasticity k2 and subject to a horizontal load P. By using a dynamical system analysis of the resulting fourth order equation, we show that as the end shortening per unit length E is increased, then if k2 is large there is a smooth transition from small amplitude sinusoidal solutions at moderate values of P to larger amplitude chevron folds, with straight limbs separated by regions of high curvature when P is large. The chevron solutions take the form of near heteroclinic connections in the phase-plane. By means of this analysis, values for P and the slope of the limbs are calculated in terms of E and k2.

Original languageEnglish
Pages (from-to)32-46
JournalPhysica D: Nonlinear Phenomena
Early online date11 May 2016
DOIs
Publication statusPublished - 1 Sep 2016

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limbs
folding
orbits
elastic media
systems analysis
dynamical systems
stiffness
elastic properties
curvature
slopes

Keywords

  • Bifurcation
  • Chevron folding
  • Fourth order equation
  • Heteroclinic connection

Cite this

Chevron folding patterns and heteroclinic orbits. / Budd, Christopher J.; Chakhchoukh, Amine N.; Dodwell, Timothy J.; Kuske, Rachel.

In: Physica D: Nonlinear Phenomena, 01.09.2016, p. 32-46.

Research output: Contribution to journalArticle

Budd, Christopher J. ; Chakhchoukh, Amine N. ; Dodwell, Timothy J. ; Kuske, Rachel. / Chevron folding patterns and heteroclinic orbits. In: Physica D: Nonlinear Phenomena. 2016 ; pp. 32-46.
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