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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
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume330
Early online date11 May 2016
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

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

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